Approximate Quantum Error Correction Revisited: Introducing the Alpha-Bit
Abstract We establish that, in an appropriate limit, qubits of communication should be regarded as composite resources, decomposing cleanly into independent correlation and transmission components. Because qubits of communication can establish ebits of entanglement, qubits are more powerful resource...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Hayden, Patrick [verfasserIn] |
|---|
| Format: |
Artikel |
|---|---|
| Sprache: |
Englisch |
| Erschienen: |
2020 |
|---|
| Anmerkung: |
© Springer-Verlag GmbH Germany, part of Springer Nature 2020 |
|---|
| Übergeordnetes Werk: |
Enthalten in: Communications in mathematical physics - Springer Berlin Heidelberg, 1965, 374(2020), 2 vom: 10. Feb., Seite 369-432 |
|---|---|
| Übergeordnetes Werk: |
volume:374 ; year:2020 ; number:2 ; day:10 ; month:02 ; pages:369-432 |
| Links: |
|---|
| DOI / URN: |
10.1007/s00220-020-03689-1 |
|---|
| Katalog-ID: |
OLC2038922454 |
|---|
| LEADER | 01000caa a22002652 4500 | ||
|---|---|---|---|
| 001 | OLC2038922454 | ||
| 003 | DE-627 | ||
| 005 | 20230504121143.0 | ||
| 007 | tu | ||
| 008 | 200819s2020 xx ||||| 00| ||eng c | ||
| 024 | 7 | |a 10.1007/s00220-020-03689-1 |2 doi | |
| 035 | |a (DE-627)OLC2038922454 | ||
| 035 | |a (DE-He213)s00220-020-03689-1-p | ||
| 040 | |a DE-627 |b ger |c DE-627 |e rakwb | ||
| 041 | |a eng | ||
| 082 | 0 | 4 | |a 530 |a 510 |q VZ |
| 100 | 1 | |a Hayden, Patrick |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Approximate Quantum Error Correction Revisited: Introducing the Alpha-Bit |
| 264 | 1 | |c 2020 | |
| 336 | |a Text |b txt |2 rdacontent | ||
| 337 | |a ohne Hilfsmittel zu benutzen |b n |2 rdamedia | ||
| 338 | |a Band |b nc |2 rdacarrier | ||
| 500 | |a © Springer-Verlag GmbH Germany, part of Springer Nature 2020 | ||
| 520 | |a Abstract We establish that, in an appropriate limit, qubits of communication should be regarded as composite resources, decomposing cleanly into independent correlation and transmission components. Because qubits of communication can establish ebits of entanglement, qubits are more powerful resources than ebits. We identify a new communications resource, the zero-bit, which is precisely half the gap between them; replacing classical bits by zero-bits makes teleportation asymptotically reversible. This decomposition of a qubit into an ebit and two zero-bits has wide-ranging consequences including applications to state merging, the quantum channel capacity, entanglement distillation, quantum identification and remote state preparation. The source of these results is the theory of approximate quantum error correction. The action of a quantum channel is reversible if and only if no information is leaked to the environment, a characterization that is useful even in approximate form. However, different notions of approximation lead to qualitatively different forms of quantum error correction in the limit of large dimension. We study the effect of a constraint on the dimension of the reference system when considering information leakage. While the resulting condition fails to ensure that the entire input can be corrected, it does ensure that all subspaces of dimension matching that of the reference are correctable. The size of the reference can be characterized by a parameter $$\alpha $$; we call the associated resource an $$\alpha $$-bit. Changing $$\alpha $$ interpolates between standard quantum error correction and quantum identification, a form of equality testing for quantum states. We develop the theory of $$\alpha $$-bits, including the applications above, and determine the $$\alpha $$-bit capacity of general quantum channels, finding single-letter formulas for the entanglement-assisted and amortised variants. | ||
| 700 | 1 | |a Penington, Geoffrey |0 (orcid)0000-0002-8627-5237 |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Communications in mathematical physics |d Springer Berlin Heidelberg, 1965 |g 374(2020), 2 vom: 10. Feb., Seite 369-432 |w (DE-627)129555002 |w (DE-600)220443-5 |w (DE-576)015011755 |x 0010-3616 |7 nnns |
| 773 | 1 | 8 | |g volume:374 |g year:2020 |g number:2 |g day:10 |g month:02 |g pages:369-432 |
| 856 | 4 | 1 | |u https://doi.org/10.1007/s00220-020-03689-1 |z lizenzpflichtig |3 Volltext |
| 912 | |a GBV_USEFLAG_A | ||
| 912 | |a SYSFLAG_A | ||
| 912 | |a GBV_OLC | ||
| 912 | |a SSG-OLC-PHY | ||
| 912 | |a SSG-OLC-MAT | ||
| 912 | |a SSG-OPC-MAT | ||
| 912 | |a GBV_ILN_22 | ||
| 912 | |a GBV_ILN_70 | ||
| 912 | |a GBV_ILN_2018 | ||
| 912 | |a GBV_ILN_2279 | ||
| 912 | |a GBV_ILN_2409 | ||
| 912 | |a GBV_ILN_4277 | ||
| 951 | |a AR | ||
| 952 | |d 374 |j 2020 |e 2 |b 10 |c 02 |h 369-432 | ||
| author_variant |
p h ph g p gp |
|---|---|
| matchkey_str |
article:00103616:2020----::prxmtqatmrocretorvstdnrd |
| hierarchy_sort_str |
2020 |
| publishDate |
2020 |
| allfields |
10.1007/s00220-020-03689-1 doi (DE-627)OLC2038922454 (DE-He213)s00220-020-03689-1-p DE-627 ger DE-627 rakwb eng 530 510 VZ Hayden, Patrick verfasserin aut Approximate Quantum Error Correction Revisited: Introducing the Alpha-Bit 2020 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag GmbH Germany, part of Springer Nature 2020 Abstract We establish that, in an appropriate limit, qubits of communication should be regarded as composite resources, decomposing cleanly into independent correlation and transmission components. Because qubits of communication can establish ebits of entanglement, qubits are more powerful resources than ebits. We identify a new communications resource, the zero-bit, which is precisely half the gap between them; replacing classical bits by zero-bits makes teleportation asymptotically reversible. This decomposition of a qubit into an ebit and two zero-bits has wide-ranging consequences including applications to state merging, the quantum channel capacity, entanglement distillation, quantum identification and remote state preparation. The source of these results is the theory of approximate quantum error correction. The action of a quantum channel is reversible if and only if no information is leaked to the environment, a characterization that is useful even in approximate form. However, different notions of approximation lead to qualitatively different forms of quantum error correction in the limit of large dimension. We study the effect of a constraint on the dimension of the reference system when considering information leakage. While the resulting condition fails to ensure that the entire input can be corrected, it does ensure that all subspaces of dimension matching that of the reference are correctable. The size of the reference can be characterized by a parameter $$\alpha $$; we call the associated resource an $$\alpha $$-bit. Changing $$\alpha $$ interpolates between standard quantum error correction and quantum identification, a form of equality testing for quantum states. We develop the theory of $$\alpha $$-bits, including the applications above, and determine the $$\alpha $$-bit capacity of general quantum channels, finding single-letter formulas for the entanglement-assisted and amortised variants. Penington, Geoffrey (orcid)0000-0002-8627-5237 aut Enthalten in Communications in mathematical physics Springer Berlin Heidelberg, 1965 374(2020), 2 vom: 10. Feb., Seite 369-432 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:374 year:2020 number:2 day:10 month:02 pages:369-432 https://doi.org/10.1007/s00220-020-03689-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_70 GBV_ILN_2018 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4277 AR 374 2020 2 10 02 369-432 |
| spelling |
10.1007/s00220-020-03689-1 doi (DE-627)OLC2038922454 (DE-He213)s00220-020-03689-1-p DE-627 ger DE-627 rakwb eng 530 510 VZ Hayden, Patrick verfasserin aut Approximate Quantum Error Correction Revisited: Introducing the Alpha-Bit 2020 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag GmbH Germany, part of Springer Nature 2020 Abstract We establish that, in an appropriate limit, qubits of communication should be regarded as composite resources, decomposing cleanly into independent correlation and transmission components. Because qubits of communication can establish ebits of entanglement, qubits are more powerful resources than ebits. We identify a new communications resource, the zero-bit, which is precisely half the gap between them; replacing classical bits by zero-bits makes teleportation asymptotically reversible. This decomposition of a qubit into an ebit and two zero-bits has wide-ranging consequences including applications to state merging, the quantum channel capacity, entanglement distillation, quantum identification and remote state preparation. The source of these results is the theory of approximate quantum error correction. The action of a quantum channel is reversible if and only if no information is leaked to the environment, a characterization that is useful even in approximate form. However, different notions of approximation lead to qualitatively different forms of quantum error correction in the limit of large dimension. We study the effect of a constraint on the dimension of the reference system when considering information leakage. While the resulting condition fails to ensure that the entire input can be corrected, it does ensure that all subspaces of dimension matching that of the reference are correctable. The size of the reference can be characterized by a parameter $$\alpha $$; we call the associated resource an $$\alpha $$-bit. Changing $$\alpha $$ interpolates between standard quantum error correction and quantum identification, a form of equality testing for quantum states. We develop the theory of $$\alpha $$-bits, including the applications above, and determine the $$\alpha $$-bit capacity of general quantum channels, finding single-letter formulas for the entanglement-assisted and amortised variants. Penington, Geoffrey (orcid)0000-0002-8627-5237 aut Enthalten in Communications in mathematical physics Springer Berlin Heidelberg, 1965 374(2020), 2 vom: 10. Feb., Seite 369-432 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:374 year:2020 number:2 day:10 month:02 pages:369-432 https://doi.org/10.1007/s00220-020-03689-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_70 GBV_ILN_2018 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4277 AR 374 2020 2 10 02 369-432 |
| allfields_unstemmed |
10.1007/s00220-020-03689-1 doi (DE-627)OLC2038922454 (DE-He213)s00220-020-03689-1-p DE-627 ger DE-627 rakwb eng 530 510 VZ Hayden, Patrick verfasserin aut Approximate Quantum Error Correction Revisited: Introducing the Alpha-Bit 2020 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag GmbH Germany, part of Springer Nature 2020 Abstract We establish that, in an appropriate limit, qubits of communication should be regarded as composite resources, decomposing cleanly into independent correlation and transmission components. Because qubits of communication can establish ebits of entanglement, qubits are more powerful resources than ebits. We identify a new communications resource, the zero-bit, which is precisely half the gap between them; replacing classical bits by zero-bits makes teleportation asymptotically reversible. This decomposition of a qubit into an ebit and two zero-bits has wide-ranging consequences including applications to state merging, the quantum channel capacity, entanglement distillation, quantum identification and remote state preparation. The source of these results is the theory of approximate quantum error correction. The action of a quantum channel is reversible if and only if no information is leaked to the environment, a characterization that is useful even in approximate form. However, different notions of approximation lead to qualitatively different forms of quantum error correction in the limit of large dimension. We study the effect of a constraint on the dimension of the reference system when considering information leakage. While the resulting condition fails to ensure that the entire input can be corrected, it does ensure that all subspaces of dimension matching that of the reference are correctable. The size of the reference can be characterized by a parameter $$\alpha $$; we call the associated resource an $$\alpha $$-bit. Changing $$\alpha $$ interpolates between standard quantum error correction and quantum identification, a form of equality testing for quantum states. We develop the theory of $$\alpha $$-bits, including the applications above, and determine the $$\alpha $$-bit capacity of general quantum channels, finding single-letter formulas for the entanglement-assisted and amortised variants. Penington, Geoffrey (orcid)0000-0002-8627-5237 aut Enthalten in Communications in mathematical physics Springer Berlin Heidelberg, 1965 374(2020), 2 vom: 10. Feb., Seite 369-432 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:374 year:2020 number:2 day:10 month:02 pages:369-432 https://doi.org/10.1007/s00220-020-03689-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_70 GBV_ILN_2018 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4277 AR 374 2020 2 10 02 369-432 |
| allfieldsGer |
10.1007/s00220-020-03689-1 doi (DE-627)OLC2038922454 (DE-He213)s00220-020-03689-1-p DE-627 ger DE-627 rakwb eng 530 510 VZ Hayden, Patrick verfasserin aut Approximate Quantum Error Correction Revisited: Introducing the Alpha-Bit 2020 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag GmbH Germany, part of Springer Nature 2020 Abstract We establish that, in an appropriate limit, qubits of communication should be regarded as composite resources, decomposing cleanly into independent correlation and transmission components. Because qubits of communication can establish ebits of entanglement, qubits are more powerful resources than ebits. We identify a new communications resource, the zero-bit, which is precisely half the gap between them; replacing classical bits by zero-bits makes teleportation asymptotically reversible. This decomposition of a qubit into an ebit and two zero-bits has wide-ranging consequences including applications to state merging, the quantum channel capacity, entanglement distillation, quantum identification and remote state preparation. The source of these results is the theory of approximate quantum error correction. The action of a quantum channel is reversible if and only if no information is leaked to the environment, a characterization that is useful even in approximate form. However, different notions of approximation lead to qualitatively different forms of quantum error correction in the limit of large dimension. We study the effect of a constraint on the dimension of the reference system when considering information leakage. While the resulting condition fails to ensure that the entire input can be corrected, it does ensure that all subspaces of dimension matching that of the reference are correctable. The size of the reference can be characterized by a parameter $$\alpha $$; we call the associated resource an $$\alpha $$-bit. Changing $$\alpha $$ interpolates between standard quantum error correction and quantum identification, a form of equality testing for quantum states. We develop the theory of $$\alpha $$-bits, including the applications above, and determine the $$\alpha $$-bit capacity of general quantum channels, finding single-letter formulas for the entanglement-assisted and amortised variants. Penington, Geoffrey (orcid)0000-0002-8627-5237 aut Enthalten in Communications in mathematical physics Springer Berlin Heidelberg, 1965 374(2020), 2 vom: 10. Feb., Seite 369-432 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:374 year:2020 number:2 day:10 month:02 pages:369-432 https://doi.org/10.1007/s00220-020-03689-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_70 GBV_ILN_2018 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4277 AR 374 2020 2 10 02 369-432 |
| allfieldsSound |
10.1007/s00220-020-03689-1 doi (DE-627)OLC2038922454 (DE-He213)s00220-020-03689-1-p DE-627 ger DE-627 rakwb eng 530 510 VZ Hayden, Patrick verfasserin aut Approximate Quantum Error Correction Revisited: Introducing the Alpha-Bit 2020 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag GmbH Germany, part of Springer Nature 2020 Abstract We establish that, in an appropriate limit, qubits of communication should be regarded as composite resources, decomposing cleanly into independent correlation and transmission components. Because qubits of communication can establish ebits of entanglement, qubits are more powerful resources than ebits. We identify a new communications resource, the zero-bit, which is precisely half the gap between them; replacing classical bits by zero-bits makes teleportation asymptotically reversible. This decomposition of a qubit into an ebit and two zero-bits has wide-ranging consequences including applications to state merging, the quantum channel capacity, entanglement distillation, quantum identification and remote state preparation. The source of these results is the theory of approximate quantum error correction. The action of a quantum channel is reversible if and only if no information is leaked to the environment, a characterization that is useful even in approximate form. However, different notions of approximation lead to qualitatively different forms of quantum error correction in the limit of large dimension. We study the effect of a constraint on the dimension of the reference system when considering information leakage. While the resulting condition fails to ensure that the entire input can be corrected, it does ensure that all subspaces of dimension matching that of the reference are correctable. The size of the reference can be characterized by a parameter $$\alpha $$; we call the associated resource an $$\alpha $$-bit. Changing $$\alpha $$ interpolates between standard quantum error correction and quantum identification, a form of equality testing for quantum states. We develop the theory of $$\alpha $$-bits, including the applications above, and determine the $$\alpha $$-bit capacity of general quantum channels, finding single-letter formulas for the entanglement-assisted and amortised variants. Penington, Geoffrey (orcid)0000-0002-8627-5237 aut Enthalten in Communications in mathematical physics Springer Berlin Heidelberg, 1965 374(2020), 2 vom: 10. Feb., Seite 369-432 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:374 year:2020 number:2 day:10 month:02 pages:369-432 https://doi.org/10.1007/s00220-020-03689-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_70 GBV_ILN_2018 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4277 AR 374 2020 2 10 02 369-432 |
| language |
English |
| source |
Enthalten in Communications in mathematical physics 374(2020), 2 vom: 10. Feb., Seite 369-432 volume:374 year:2020 number:2 day:10 month:02 pages:369-432 |
| sourceStr |
Enthalten in Communications in mathematical physics 374(2020), 2 vom: 10. Feb., Seite 369-432 volume:374 year:2020 number:2 day:10 month:02 pages:369-432 |
| format_phy_str_mv |
Article |
| institution |
findex.gbv.de |
| dewey-raw |
530 |
| isfreeaccess_bool |
false |
| container_title |
Communications in mathematical physics |
| authorswithroles_txt_mv |
Hayden, Patrick @@aut@@ Penington, Geoffrey @@aut@@ |
| publishDateDaySort_date |
2020-02-10T00:00:00Z |
| hierarchy_top_id |
129555002 |
| dewey-sort |
3530 |
| id |
OLC2038922454 |
| language_de |
englisch |
| fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2038922454</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230504121143.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200819s2020 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00220-020-03689-1</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2038922454</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s00220-020-03689-1-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">530</subfield><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Hayden, Patrick</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Approximate Quantum Error Correction Revisited: Introducing the Alpha-Bit</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2020</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer-Verlag GmbH Germany, part of Springer Nature 2020</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract We establish that, in an appropriate limit, qubits of communication should be regarded as composite resources, decomposing cleanly into independent correlation and transmission components. Because qubits of communication can establish ebits of entanglement, qubits are more powerful resources than ebits. We identify a new communications resource, the zero-bit, which is precisely half the gap between them; replacing classical bits by zero-bits makes teleportation asymptotically reversible. This decomposition of a qubit into an ebit and two zero-bits has wide-ranging consequences including applications to state merging, the quantum channel capacity, entanglement distillation, quantum identification and remote state preparation. The source of these results is the theory of approximate quantum error correction. The action of a quantum channel is reversible if and only if no information is leaked to the environment, a characterization that is useful even in approximate form. However, different notions of approximation lead to qualitatively different forms of quantum error correction in the limit of large dimension. We study the effect of a constraint on the dimension of the reference system when considering information leakage. While the resulting condition fails to ensure that the entire input can be corrected, it does ensure that all subspaces of dimension matching that of the reference are correctable. The size of the reference can be characterized by a parameter $$\alpha $$; we call the associated resource an $$\alpha $$-bit. Changing $$\alpha $$ interpolates between standard quantum error correction and quantum identification, a form of equality testing for quantum states. We develop the theory of $$\alpha $$-bits, including the applications above, and determine the $$\alpha $$-bit capacity of general quantum channels, finding single-letter formulas for the entanglement-assisted and amortised variants.</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Penington, Geoffrey</subfield><subfield code="0">(orcid)0000-0002-8627-5237</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Communications in mathematical physics</subfield><subfield code="d">Springer Berlin Heidelberg, 1965</subfield><subfield code="g">374(2020), 2 vom: 10. Feb., Seite 369-432</subfield><subfield code="w">(DE-627)129555002</subfield><subfield code="w">(DE-600)220443-5</subfield><subfield code="w">(DE-576)015011755</subfield><subfield code="x">0010-3616</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:374</subfield><subfield code="g">year:2020</subfield><subfield code="g">number:2</subfield><subfield code="g">day:10</subfield><subfield code="g">month:02</subfield><subfield code="g">pages:369-432</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1007/s00220-020-03689-1</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-PHY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OPC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_22</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2018</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2279</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2409</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4277</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">374</subfield><subfield code="j">2020</subfield><subfield code="e">2</subfield><subfield code="b">10</subfield><subfield code="c">02</subfield><subfield code="h">369-432</subfield></datafield></record></collection>
|
| author |
Hayden, Patrick |
| spellingShingle |
Hayden, Patrick ddc 530 Approximate Quantum Error Correction Revisited: Introducing the Alpha-Bit |
| authorStr |
Hayden, Patrick |
| ppnlink_with_tag_str_mv |
@@773@@(DE-627)129555002 |
| format |
Article |
| dewey-ones |
530 - Physics 510 - Mathematics |
| delete_txt_mv |
keep |
| author_role |
aut aut |
| collection |
OLC |
| remote_str |
false |
| illustrated |
Not Illustrated |
| issn |
0010-3616 |
| topic_title |
530 510 VZ Approximate Quantum Error Correction Revisited: Introducing the Alpha-Bit |
| topic |
ddc 530 |
| topic_unstemmed |
ddc 530 |
| topic_browse |
ddc 530 |
| format_facet |
Aufsätze Gedruckte Aufsätze |
| format_main_str_mv |
Text Zeitschrift/Artikel |
| carriertype_str_mv |
nc |
| hierarchy_parent_title |
Communications in mathematical physics |
| hierarchy_parent_id |
129555002 |
| dewey-tens |
530 - Physics 510 - Mathematics |
| hierarchy_top_title |
Communications in mathematical physics |
| isfreeaccess_txt |
false |
| familylinks_str_mv |
(DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 |
| title |
Approximate Quantum Error Correction Revisited: Introducing the Alpha-Bit |
| ctrlnum |
(DE-627)OLC2038922454 (DE-He213)s00220-020-03689-1-p |
| title_full |
Approximate Quantum Error Correction Revisited: Introducing the Alpha-Bit |
| author_sort |
Hayden, Patrick |
| journal |
Communications in mathematical physics |
| journalStr |
Communications in mathematical physics |
| lang_code |
eng |
| isOA_bool |
false |
| dewey-hundreds |
500 - Science |
| recordtype |
marc |
| publishDateSort |
2020 |
| contenttype_str_mv |
txt |
| container_start_page |
369 |
| author_browse |
Hayden, Patrick Penington, Geoffrey |
| container_volume |
374 |
| class |
530 510 VZ |
| format_se |
Aufsätze |
| author-letter |
Hayden, Patrick |
| doi_str_mv |
10.1007/s00220-020-03689-1 |
| normlink |
(ORCID)0000-0002-8627-5237 |
| normlink_prefix_str_mv |
(orcid)0000-0002-8627-5237 |
| dewey-full |
530 510 |
| title_sort |
approximate quantum error correction revisited: introducing the alpha-bit |
| title_auth |
Approximate Quantum Error Correction Revisited: Introducing the Alpha-Bit |
| abstract |
Abstract We establish that, in an appropriate limit, qubits of communication should be regarded as composite resources, decomposing cleanly into independent correlation and transmission components. Because qubits of communication can establish ebits of entanglement, qubits are more powerful resources than ebits. We identify a new communications resource, the zero-bit, which is precisely half the gap between them; replacing classical bits by zero-bits makes teleportation asymptotically reversible. This decomposition of a qubit into an ebit and two zero-bits has wide-ranging consequences including applications to state merging, the quantum channel capacity, entanglement distillation, quantum identification and remote state preparation. The source of these results is the theory of approximate quantum error correction. The action of a quantum channel is reversible if and only if no information is leaked to the environment, a characterization that is useful even in approximate form. However, different notions of approximation lead to qualitatively different forms of quantum error correction in the limit of large dimension. We study the effect of a constraint on the dimension of the reference system when considering information leakage. While the resulting condition fails to ensure that the entire input can be corrected, it does ensure that all subspaces of dimension matching that of the reference are correctable. The size of the reference can be characterized by a parameter $$\alpha $$; we call the associated resource an $$\alpha $$-bit. Changing $$\alpha $$ interpolates between standard quantum error correction and quantum identification, a form of equality testing for quantum states. We develop the theory of $$\alpha $$-bits, including the applications above, and determine the $$\alpha $$-bit capacity of general quantum channels, finding single-letter formulas for the entanglement-assisted and amortised variants. © Springer-Verlag GmbH Germany, part of Springer Nature 2020 |
| abstractGer |
Abstract We establish that, in an appropriate limit, qubits of communication should be regarded as composite resources, decomposing cleanly into independent correlation and transmission components. Because qubits of communication can establish ebits of entanglement, qubits are more powerful resources than ebits. We identify a new communications resource, the zero-bit, which is precisely half the gap between them; replacing classical bits by zero-bits makes teleportation asymptotically reversible. This decomposition of a qubit into an ebit and two zero-bits has wide-ranging consequences including applications to state merging, the quantum channel capacity, entanglement distillation, quantum identification and remote state preparation. The source of these results is the theory of approximate quantum error correction. The action of a quantum channel is reversible if and only if no information is leaked to the environment, a characterization that is useful even in approximate form. However, different notions of approximation lead to qualitatively different forms of quantum error correction in the limit of large dimension. We study the effect of a constraint on the dimension of the reference system when considering information leakage. While the resulting condition fails to ensure that the entire input can be corrected, it does ensure that all subspaces of dimension matching that of the reference are correctable. The size of the reference can be characterized by a parameter $$\alpha $$; we call the associated resource an $$\alpha $$-bit. Changing $$\alpha $$ interpolates between standard quantum error correction and quantum identification, a form of equality testing for quantum states. We develop the theory of $$\alpha $$-bits, including the applications above, and determine the $$\alpha $$-bit capacity of general quantum channels, finding single-letter formulas for the entanglement-assisted and amortised variants. © Springer-Verlag GmbH Germany, part of Springer Nature 2020 |
| abstract_unstemmed |
Abstract We establish that, in an appropriate limit, qubits of communication should be regarded as composite resources, decomposing cleanly into independent correlation and transmission components. Because qubits of communication can establish ebits of entanglement, qubits are more powerful resources than ebits. We identify a new communications resource, the zero-bit, which is precisely half the gap between them; replacing classical bits by zero-bits makes teleportation asymptotically reversible. This decomposition of a qubit into an ebit and two zero-bits has wide-ranging consequences including applications to state merging, the quantum channel capacity, entanglement distillation, quantum identification and remote state preparation. The source of these results is the theory of approximate quantum error correction. The action of a quantum channel is reversible if and only if no information is leaked to the environment, a characterization that is useful even in approximate form. However, different notions of approximation lead to qualitatively different forms of quantum error correction in the limit of large dimension. We study the effect of a constraint on the dimension of the reference system when considering information leakage. While the resulting condition fails to ensure that the entire input can be corrected, it does ensure that all subspaces of dimension matching that of the reference are correctable. The size of the reference can be characterized by a parameter $$\alpha $$; we call the associated resource an $$\alpha $$-bit. Changing $$\alpha $$ interpolates between standard quantum error correction and quantum identification, a form of equality testing for quantum states. We develop the theory of $$\alpha $$-bits, including the applications above, and determine the $$\alpha $$-bit capacity of general quantum channels, finding single-letter formulas for the entanglement-assisted and amortised variants. © Springer-Verlag GmbH Germany, part of Springer Nature 2020 |
| collection_details |
GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_70 GBV_ILN_2018 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4277 |
| container_issue |
2 |
| title_short |
Approximate Quantum Error Correction Revisited: Introducing the Alpha-Bit |
| url |
https://doi.org/10.1007/s00220-020-03689-1 |
| remote_bool |
false |
| author2 |
Penington, Geoffrey |
| author2Str |
Penington, Geoffrey |
| ppnlink |
129555002 |
| mediatype_str_mv |
n |
| isOA_txt |
false |
| hochschulschrift_bool |
false |
| doi_str |
10.1007/s00220-020-03689-1 |
| up_date |
2024-07-03T20:52:40.826Z |
| _version_ |
1803592621963083776 |
| fullrecord_marcxml |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2038922454</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230504121143.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200819s2020 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00220-020-03689-1</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2038922454</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s00220-020-03689-1-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">530</subfield><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Hayden, Patrick</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Approximate Quantum Error Correction Revisited: Introducing the Alpha-Bit</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2020</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer-Verlag GmbH Germany, part of Springer Nature 2020</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract We establish that, in an appropriate limit, qubits of communication should be regarded as composite resources, decomposing cleanly into independent correlation and transmission components. Because qubits of communication can establish ebits of entanglement, qubits are more powerful resources than ebits. We identify a new communications resource, the zero-bit, which is precisely half the gap between them; replacing classical bits by zero-bits makes teleportation asymptotically reversible. This decomposition of a qubit into an ebit and two zero-bits has wide-ranging consequences including applications to state merging, the quantum channel capacity, entanglement distillation, quantum identification and remote state preparation. The source of these results is the theory of approximate quantum error correction. The action of a quantum channel is reversible if and only if no information is leaked to the environment, a characterization that is useful even in approximate form. However, different notions of approximation lead to qualitatively different forms of quantum error correction in the limit of large dimension. We study the effect of a constraint on the dimension of the reference system when considering information leakage. While the resulting condition fails to ensure that the entire input can be corrected, it does ensure that all subspaces of dimension matching that of the reference are correctable. The size of the reference can be characterized by a parameter $$\alpha $$; we call the associated resource an $$\alpha $$-bit. Changing $$\alpha $$ interpolates between standard quantum error correction and quantum identification, a form of equality testing for quantum states. We develop the theory of $$\alpha $$-bits, including the applications above, and determine the $$\alpha $$-bit capacity of general quantum channels, finding single-letter formulas for the entanglement-assisted and amortised variants.</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Penington, Geoffrey</subfield><subfield code="0">(orcid)0000-0002-8627-5237</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Communications in mathematical physics</subfield><subfield code="d">Springer Berlin Heidelberg, 1965</subfield><subfield code="g">374(2020), 2 vom: 10. Feb., Seite 369-432</subfield><subfield code="w">(DE-627)129555002</subfield><subfield code="w">(DE-600)220443-5</subfield><subfield code="w">(DE-576)015011755</subfield><subfield code="x">0010-3616</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:374</subfield><subfield code="g">year:2020</subfield><subfield code="g">number:2</subfield><subfield code="g">day:10</subfield><subfield code="g">month:02</subfield><subfield code="g">pages:369-432</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1007/s00220-020-03689-1</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-PHY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OPC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_22</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2018</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2279</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2409</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4277</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">374</subfield><subfield code="j">2020</subfield><subfield code="e">2</subfield><subfield code="b">10</subfield><subfield code="c">02</subfield><subfield code="h">369-432</subfield></datafield></record></collection>
|
| score |
7.399641 |