Generalized bipartite quantum state discrimination problems with sequential measurements

TL;DR

This paper formulates and analyzes a convex optimization framework for bipartite quantum state discrimination using sequential measurements, providing conditions for optimality and symmetry considerations.

Contribution

It introduces a convex programming approach to optimize sequential quantum measurements, deriving dual problems and conditions for optimality and symmetry.

Findings

Existence of finite-outcome optimal measurements when solutions exist.

Optimal solutions can preserve problem symmetries.

Analytical solutions are obtainable in specific examples.

Abstract

We investigate an optimization problem of finding quantum sequential measurements, which forms a wide class of state discrimination problems with the restriction that only sequential measurements are allowed. Sequential measurements from Alice to Bob on a bipartite system are considered. Using the fact that the optimization problem can be formulated as a problem with only Alice's measurement and is convex programming, we derive its dual problem and necessary and sufficient conditions for an optimal solution. In the problem we address, the output of Alice's measurement can be infinite or continuous, while sequential measurements with a finite number of outcomes are considered. It is shown that there exists an optimal sequential measurement in which Alice's measurement with a finite number of outcomes as long as a solution exists. We also show that if the problem has a certain symmetry, then there exists an optimal solution with the same type of symmetry. A minimax version of the problem is considered, and necessary and sufficient conditions for a minimax solution are derived. An example in which our results can be used to obtain an analytical expression for an optimal sequential measurement is finally provided.