Quantum retrodiction made fully symmetric

TL;DR

This paper develops a fully symmetric formalism for quantum retrodiction applicable to arbitrary sources, expanding its theoretical framework and demonstrating its implications for quantum communication and the no-signaling principle.

Contribution

It introduces a general symmetric formalism for quantum retrodiction beyond unbiased sources, with a specific example and implications for quantum communication.

Findings

General symmetric formalism for arbitrary sources

Optimal solution to retrodiction dual to unambiguous state discrimination

Connection between retrodiction and no-signaling principle

Abstract

Quantum retrodiction is a time-symmetric approach to quantum mechanics with applications in a number of important problems. One of the major challenges to its more widespread applicability is the restriction of its symmetric formalism to unbiased sources. The main result of this paper is to develop a general theory yielding a symmetric formalism for arbitrary sources. We then highlight on a specific example, by presenting the optimal solution to the retrodiction problem that is dual to unambiguous state discrimination, how the generalized approach works. We also show how this formalism leads to a symmetric formulation of the communication channel between Alice and Bob and point to the intrinsic connection between retrodiction and the no-signaling principle.