Conditional uncertainty principle
We develop a general operational framework that formalizes the concept of conditional uncertainty in a measure-independent fashion. Our formalism is built upon a mathematical relation which we call conditional majorization. We define conditional majorization and, for the case of classical memory, we...
| Main Authors: | , , , , , |
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| Format: | Journal Article |
| Language: | English |
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2018
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| Online Access: | https://hdl.handle.net/10356/85195 http://hdl.handle.net/10220/45155 |
| _version_ | 1824454168080809984 |
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| author | Gour, Gilad Grudka, Andrzej Horodecki, Michał Kłobus, Waldemar Łodyga, Justyna Narasimhachar, Varun |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Gour, Gilad Grudka, Andrzej Horodecki, Michał Kłobus, Waldemar Łodyga, Justyna Narasimhachar, Varun |
| author_sort | Gour, Gilad |
| collection | NTU |
| description | We develop a general operational framework that formalizes the concept of conditional uncertainty in a measure-independent fashion. Our formalism is built upon a mathematical relation which we call conditional majorization. We define conditional majorization and, for the case of classical memory, we provide its thorough characterization in terms of monotones, i.e., functions that preserve the partial order under conditional majorization. We demonstrate the application of this framework by deriving two types of memory-assisted uncertainty relations, (1) a monotone-based conditional uncertainty relation and (2) a universal measure-independent conditional uncertainty relation, both of which set a lower bound on the minimal uncertainty that Bob has about Alice's pair of incompatible measurements, conditioned on arbitrary measurement that Bob makes on his own system. We next compare the obtained relations with their existing entropic counterparts and find that they are at least independent. |
| first_indexed | 2025-02-19T03:18:01Z |
| format | Journal Article |
| id | ntu-10356/85195 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2025-02-19T03:18:01Z |
| publishDate | 2018 |
| record_format | dspace |
| spelling | ntu-10356/851952023-02-28T20:11:59Z Conditional uncertainty principle Gour, Gilad Grudka, Andrzej Horodecki, Michał Kłobus, Waldemar Łodyga, Justyna Narasimhachar, Varun School of Physical and Mathematical Sciences Science::Physics Quantum Physics Conditional Majorization We develop a general operational framework that formalizes the concept of conditional uncertainty in a measure-independent fashion. Our formalism is built upon a mathematical relation which we call conditional majorization. We define conditional majorization and, for the case of classical memory, we provide its thorough characterization in terms of monotones, i.e., functions that preserve the partial order under conditional majorization. We demonstrate the application of this framework by deriving two types of memory-assisted uncertainty relations, (1) a monotone-based conditional uncertainty relation and (2) a universal measure-independent conditional uncertainty relation, both of which set a lower bound on the minimal uncertainty that Bob has about Alice's pair of incompatible measurements, conditioned on arbitrary measurement that Bob makes on his own system. We next compare the obtained relations with their existing entropic counterparts and find that they are at least independent. Ministry of Education (MOE) National Research Foundation (NRF) Published version This work is supported by ERC Advanced Grant QOLAPS and National Science Centre Grants Mae- stro No. DEC-2011/02/A/ST2/00305 and OPUS 9 No. 2015/17/B/ST2/01945. V.N. acknowledges financial support from the Ministry of Education of Singapore, the National Research Foundation (NRF Fellowship Reference No. NRF- NRFF2016-02), and the John Templeton Foundation (Grant No. 54914). 2018-07-20T04:02:52Z 2019-12-06T15:59:13Z 2018-07-20T04:02:52Z 2019-12-06T15:59:13Z 2018 Journal Article Gour, G., Grudka, A., Horodecki, M., Kłobus, W., Łodyga, J. & Narasimhachar, V. (2018). Conditional uncertainty principle. Physical Review A, 97(4). https://dx.doi.org/10.1103/PhysRevA.97.042130 2469-9926 https://hdl.handle.net/10356/85195 http://hdl.handle.net/10220/45155 10.1103/PhysRevA.97.042130 4 97 en DEC-2011/02/A/ST2/00305 2015/17/B/ST2/0194 NRF-NRFF2016-02 54914 Physical Review A © 2018 American Physical Society. This paper was published in Physical Review A and is made available as an electronic reprint (preprint) with permission of American Physical Society. The published version is available at: [http://dx.doi.org/10.1103/PhysRevA.97.042130]. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law. 14 p. application/pdf |
| spellingShingle | Science::Physics Quantum Physics Conditional Majorization Gour, Gilad Grudka, Andrzej Horodecki, Michał Kłobus, Waldemar Łodyga, Justyna Narasimhachar, Varun Conditional uncertainty principle |
| title | Conditional uncertainty principle |
| title_full | Conditional uncertainty principle |
| title_fullStr | Conditional uncertainty principle |
| title_full_unstemmed | Conditional uncertainty principle |
| title_short | Conditional uncertainty principle |
| title_sort | conditional uncertainty principle |
| topic | Science::Physics Quantum Physics Conditional Majorization |
| url | https://hdl.handle.net/10356/85195 http://hdl.handle.net/10220/45155 |
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