Petz recovery map
This article, Petz recovery map, has recently been created via the Articles for creation process. Please check to see if the reviewer has accidentally left this template after accepting the draft and take appropriate action as necessary.
Reviewer tools: Inform author |
This article, Petz recovery map, has recently been created via the Articles for creation process. Please check to see if the reviewer has accidentally left this template after accepting the draft and take appropriate action as necessary.
Reviewer tools: Inform author |
- Comment: Need more inline citations to denote notability and verifiability, preferably online sources. The Herald (Benison) (talk) 09:57, 16 February 2024 (UTC)
- Comment: I think the declination by The Herald (Benison) was a bit harsh, but it illustrates what I mentioned when I draftified the article -- it's notability needs to be apparent to a non-specialist. I suggest you ask for help by posting to WT:PHYSICS where I know there are people who are somewhat experts in these areas. I have published in other areas of physics, but not this area so I am not the person to help.Ldm1954 (talk) 14:24, 16 February 2024 (UTC)
An editor has performed a search and found that sufficient sources exist to establish the subject's notability. (January 2024) |
In quantum information theory, the Petz recovery map is a quantum map that proposed by Dénes Petz[1]. The Petz recovery map is a quantum channel associated with a given quantum channel and quantum state. This recovery map is designed in a manner that, when applied to an output state resulting from the given quantum channel acting on an input state, it enables the inference of the original input state. In essence, the Petz recovery map serves as a tool for reconstructing information about the initial quantum state from its transformed counterpart under the influence of the specified quantum channel.
The Petz recovery map finds applications in various domains, including quantum retrodiction[2], quantum error correction[3], and entanglement wedge reconstruction for black hole physics[4][5].
Definition
Suppose we have a quantum state which is described by a density operator and a quantum channel , the Petz recovery map is defined as[1][6]
Notice that is the Hilbert-Schmidt adjoint of .
The Petz map has been generalized in various ways in the field of quantum information theory[7][8].
Properties of the Petz recovery map
- The Petz recovery map is a completely positive map, since (i) sandwiching by the positive semi-definite operator is completely positive; (ii) is also completely positive when is completely positive; and (iii) sandwiching by the positive semi-definite operator is completely positive.
- It's also clear that is is trace non-increasing
- From 1 and 2, when is invertable, the Petz recovery map is a quantum channel, viz., a completely positive trace-preserving (CPTP) map.
References
- ^ a b Petz, Dénes (1986-03-01). "Sufficient subalgebras and the relative entropy of states of a von Neumann algebra" (PDF). Communications in Mathematical Physics. 105 (1): 123–131. Bibcode:1986CMaPh.105..123P. doi:10.1007/BF01212345. ISSN 1432-0916. S2CID 18836173.
- ^ Leifer, M. S.; Spekkens, Robert W. (2013-11-27). "Towards a formulation of quantum theory as a causally neutral theory of Bayesian inference". Physical Review A. 88 (5): 052130. Bibcode:2013PhRvA..88e2130L. doi:10.1103/PhysRevA.88.052130. S2CID 43563970.
- ^ Furuya, Keiichiro; Lashkari, Nima; Ouseph, Shoy (2022-01-27). "Real-space RG, error correction and Petz map". Journal of High Energy Physics. 2022 (1): 170. Bibcode:2022JHEP...01..170F. doi:10.1007/JHEP01(2022)170. ISSN 1029-8479.
- ^ Chen, Chi-Fang; Penington, Geoffrey; Salton, Grant (2020-01-28). "Entanglement wedge reconstruction using the Petz map". Journal of High Energy Physics. 2020 (1): 168. arXiv:1902.02844. Bibcode:2020JHEP...01..168C. doi:10.1007/JHEP01(2020)168. ISSN 1029-8479.
- ^ Cotler, Jordan; Hayden, Patrick; Penington, Geoffrey; Salton, Grant; Swingle, Brian; Walter, Michael (2019-07-24). "Entanglement Wedge Reconstruction via Universal Recovery Channels". Physical Review X. 9 (3): 031011. Bibcode:2019PhRvX...9c1011C. doi:10.1103/PhysRevX.9.031011.
- ^ Khatri, Sumeet; Wilde, Mark M. (2024-02-11), Principles of Quantum Communication Theory: A Modern Approach, doi:10.48550/arXiv.2011.04672, retrieved 2024-03-21
- ^ Junge, Marius; Renner, Renato; Sutter, David; Wilde, Mark M.; Winter, Andreas (2016). Universal recoverability in quantum information. pp. 2494–2498. doi:10.1109/ISIT.2016.7541748. ISBN 978-1-5090-1806-2. S2CID 18189775. Retrieved 2024-01-03.
- ^ Cree, Sam; Sorce, Jonathan (2022-06-01). "Approximate Petz Recovery from the Geometry of Density Operators". Communications in Mathematical Physics. 392 (3): 907–919. arXiv:2108.10893. Bibcode:2022CMaPh.392..907C. doi:10.1007/s00220-022-04357-2. ISSN 1432-0916. S2CID 237292763.