Draft:Petz recovery map: Difference between revisions
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{{Short description|A kind of quantum channels that have many applications in quantum information theory.}} |
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{{Sources exist|date=January 2024}} |
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Submission declined on 16 February 2024 by The Herald ( reliable sources. Reliable sources are required so that information can be verified. If you need help with referencing, please see Referencing for beginners and Citing sources.
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- Comment: Need more inline citations to denote notability and verifiability, preferably online sources. The Herald (Benison) (talk) 09:57, 16 February 2024 (UTC)
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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