Violating the Modified Helstrom Bound with Nonprojective Measurements
arXiv:1410.0096 · doi:10.1103/PhysRevA.91.040301
Abstract
We consider the discrimination of two pure quantum states with three allowed outcomes: a correct guess, an incorrect guess, and a non-guess. To find an optimum measurement procedure, we define a tunable cost that penalizes the incorrect guess and non-guess outcomes. Minimizing this cost over all projective measurements produces a rigorous cost bound that includes the usual Helstrom discrimination bound as a special case. We then show that nonprojective measurements can outperform this modified Helstrom bound for certain choices of cost function. The Ivanovic-Dieks-Peres unambiguous state discrimination protocol is recovered as a special case of this improvement. Notably, while the cost advantage of the latter protocol is destroyed with the introduction of any amount of experimental noise, other choices of cost function have optima for which nonprojective measurements robustly show an appreciable, and thus experimentally measurable, cost advantage. Such an experiment would be an unambiguous demonstration of a benefit from nonprojective measurements.
5 pages, 2 figures
References in corpus (26)
- Logic gates at the surface code threshold: Superconducting qubits poised for fault-tolerant quantum computing
- Unambiguous Discrimination Between Linearly-Independent Quantum States
- Implementing a strand of a scalable fault-tolerant quantum computing fabric
- Quantum back-action of variable-strength measurement
- Optimum Unambiguous Discrimination Between Linearly Independent Symmetric States
- Mapping the optimal route between two quantum states
- Partial-measurement back-action and non-classical weak values in a superconducting circuit
- Designing Optimal Quantum Detectors Via Semidefinite Programming
- Maximum Confidence Quantum Measurements
- Experimental Demonstration of Optimal Unambiguous State Discrimination
- Unambiguous discrimination of mixed states
- Demonstration of near-Optimal Discrimination of Optical Coherent States
- Optical realization of optimal unambiguous discrimination for pure and mixed quantum states
- Optimal discrimination of mixed quantum states involving inconclusive results
- Unambiguous discrimination between quantum mixed states
- Reduction Theorems for Optimal Unambiguous State Discrimination of Density Matrices
- General Strategies for Discrimination of Quantum States
- Optimal quantum detectors for unambiguous detection of mixed states
- Optimal discrimination of quantum states with a fixed rate of inconclusive outcomes
- Experimental Realization of Maximum Confidence State Discrimination for the Extraction of Quantum Information
- Optimal Discrimination of Qubit States - Methods, Solutions, and Properties
- Optimal state discrimination with a fixed rate of inconclusive results: Analytical solutions and relation to state discrimination with a fixed error rate
- Optimal bounded-error strategies for projective measurements in non-orthogonal state discrimination
- Minimum-error discrimination of entangled quantum states
- Implementing generalized measurements with superconducting qubits
- Optimal minimum-cost quantum measurements for imperfect detection