Optimal quantum detectors for unambiguous detection of mixed states
arXiv:quant-ph/0312061 · doi:10.1103/PhysRevA.69.062318
Abstract
We consider the problem of designing an optimal quantum detector that distinguishes unambiguously between a collection of mixed quantum states. Using arguments of duality in vector space optimization, we derive necessary and sufficient conditions for an optimal measurement that maximizes the probability of correct detection. We show that the previous optimal measurements that were derived for certain special cases satisfy these optimality conditions. We then consider state sets with strong symmetry properties, and show that the optimal measurement operators for distinguishing between these states share the same symmetries, and can be computed very efficiently by solving a reduced size semidefinite program.
Submitted to Phys. Rev. A
References in corpus (10)
- Unambiguous Discrimination Between Linearly-Independent Quantum States
- Optimum Unambiguous Discrimination Between Linearly Independent Symmetric States
- Unambiguous discrimination of mixed states
- A Semidefinite Programming Approach to Optimal Unambiguous Discrimination of Quantum States
- Optimal discrimination of mixed quantum states involving inconclusive results
- Optimal distinction between non-orthogonal quantum states
- Reduction Theorems for Optimal Unambiguous State Discrimination of Density Matrices
- Mixed quantum state detection with inconclusive results
- General Strategies for Discrimination of Quantum States
- Von Neumann Measurement is Optimal for Detecting Linearly Independent Mixed Quantum States
Cited by in corpus (44)
- Duality of Quantum Coherence and Path Distinguishability
- Optimum unambiguous discrimination of two mixed quantum states
- Unambiguous discrimination among quantum operations
- Complete hierarchies of efficient approximations to problems in entanglement theory
- Optimum Unambiguous Discrimination of Linearly Independent Pure States
- Quantum state discrimination: a geometric approach
- Programmable quantum state discriminators with simple programs
- Optimal state discrimination with a fixed rate of inconclusive results: Analytical solutions and relation to state discrimination with a fixed error rate
- Optimal Unambiguous State Discrimination of two density matrices and its link with the Fidelity
- Optimum unambiguous discrimination of two mixed states and application to a class of similar states
- Complete solution for unambiguous discrimination of three pure states with real inner products
- Generalized quantum state discrimination problems
- Discrimination of two mixed quantum states with maximum confidence and minimum probability of inconclusive results
- Unambiguous state discrimination: optimal solution and case study
- Optimal probabilistic estimation of quantum states
- Optimal unambiguous state discrimination of two density matrices: A second class of exact solutions
- Experimental scheme for unambiguous discrimination of linearly independent symmetric states
- Unambiguous State Discrimination of two density matrices in Quantum Information Theory
- Optimum unambiguous identification of d unknown pure qudit states
- Unambiguous discrimination of mixed quantum states
- Channel-Adapted Quantum Error Correction
- Structural approach to unambiguous discrimination of two mixed quantum states
- Unambiguous discrimination of mixed states: A description based on system-ancilla coupling
- Optimized maximum-confidence discrimination of N mixed quantum states and application to symmetric states
- Designing the unambiguous discriminator from the one -photon interferometer
- Generalized quantum process discrimination problems
- Local unambiguous discrimination of symmetric ternary states
- Quantum State Detector Design: Optimal Worst-Case a posteriori Performance
- Quantum-state filtering applied to the discrimination of Boolean functions
- Quantum nonlocality without entanglement depending on nonzero prior probabilities in optimal unambiguous discrimination
- Parametrization of quantum states and the quantum state discrimination problem
- Generalized bipartite quantum state discrimination problems with sequential measurements
- Geometric Bloch Vector Solution to Minimum Error Discriminations of Mixed Qubit States
- Degree of separability of bipartite quantum states
- Violating the Modified Helstrom Bound with Nonprojective Measurements
- Quantum coherence with incomplete set of pointers and corresponding wave-particle duality
- Bound on optimal local discrimination of multipartite quantum states
- Quantum Detection with Unknown States
- POVMs are equivalent to projections for perfect state exclusion of three pure states in three dimensions
- Optimal discrimination of quantum sequences
- Quantum Minimax Theorem
- Adaptive Procedures for Discrimination Between Arbitrary Tensor-Product Quantum States
- Locking and unlocking of quantum nonlocality without entanglement in local discrimination of quantum states
- Quantum state discrimination