Quantum Bayesian Inference in Quasiprobability Representations
- URL: http://arxiv.org/abs/2301.01952v2
- Date: Wed, 28 Jun 2023 05:13:40 GMT
- Title: Quantum Bayesian Inference in Quasiprobability Representations
- Authors: Clive Cenxin Aw, Kelvin Onggadinata, Dagomir Kaszlikowski, Valerio
Scarani
- Abstract summary: Bayes' rule plays a crucial piece of logical inference in information and physical sciences alike.
quantum versions of Bayes' rule have been expressed in the language of Hilbert spaces.
- Score: 0.0
- License: http://creativecommons.org/licenses/by-sa/4.0/
- Abstract: Bayes' rule plays a crucial piece of logical inference in information and
physical sciences alike. Its extension into the quantum regime has been the
object of several recent works. These quantum versions of Bayes' rule have been
expressed in the language of Hilbert spaces. In this paper, we derive the
expression of the Petz recovery map within any quasiprobability representation,
with explicit formulas for the two canonical choices of normal quasiprobability
representations (which include Discrete Wigner representations) and of
representations based on symmetric, informationally complete positive
operator-valued measures (SIC-POVMs). By using the same mathematical syntax of
(quasi-)stochastic matrices acting on (quasi-)stochastic vectors, the core
difference in logical inference between classical and quantum theory is found
in the manipulation of the reference prior rather than in the representation of
the channel.
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