Adaptive Procedures for Discriminating Between Arbitrary Tensor-Product Quantum States
Discriminating between quantum states is a fundamental task in quantum information theory. Given two quantum states, ρ+ and ρ-, the Helstrom measurement distinguishes between them with minimal probability of error. However, finding and experimentally implementing the Helstrom measurement can be challenging for quantum states on many qubits. Due to this difficulty, there is a great interest in identifying local measurement schemes which are close to optimal. In the first part of this work, we generalize previous work by Acin et al. (Phys. Rev. A 71, 032338) and show that a locally greedy (LG) scheme using Bayesian updating can optimally distinguish between any two states that can be written as a tensor product of arbitrary pure states. We then show that the same algorithm cannot distinguish tensor products of mixed states with vanishing error probability (even in a large subsystem limit), and introduce a modified locally-greedy (MLG) scheme with strictly better performance. In the second part of this work, we compare these simple local schemes with a general dynamic programming (DP) approach. The DP approach finds the optimal series of local measurements and optimal order of subsystem measurement to distinguish between the two tensor-product states.1
