Generalized bipartite quantum state discrimination problems with sequential measurements

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.

References in corpus (9)

• Minimum-error discrimination between mixed quantum states
• State discrimination with error margin and its locality
• Optimal conclusive discrimination of two states can be achieved locally
• Optimal bounded-error strategies for projective measurements in non-orthogonal state discrimination
• Generalized quantum state discrimination problems
• Qubit State Discrimination
• Optimal sequential measurements for bi-partite state discrimination
• The capacity of coherent-state adaptive decoders with interferometry and single-mode detectors
• Optimal discrimination of optical coherent states cannot always be realized by interfering with coherent light, photon counting, and feedback

Cited by in corpus (4)

• Local unambiguous discrimination of symmetric ternary states
• Demonstration of optimal non-projective measurement of binary coherent states with photon counting
• Discrimination of symmetric states in operational probabilistic theory
• Unbounded entanglement-sustaining sequential local quantum state discrimination