Minimum-error discrimination between mixed quantum states
arXiv:0707.3970 · doi:10.1103/PhysRevA.77.012328
Abstract
We derive a general lower bound on the minimum-error probability for {\it ambiguous discrimination} between arbitrary mixed quantum states with given prior probabilities. When , this bound is precisely the well-known Helstrom limit. Also, we give a general lower bound on the minimum-error probability for discriminating quantum operations. Then we further analyze how this lower bound is attainable for ambiguous discrimination of mixed quantum states by presenting necessary and sufficient conditions related to it. Furthermore, with a restricted condition, we work out a upper bound on the minimum-error probability for ambiguous discrimination of mixed quantum states. Therefore, some sufficient conditions are obtained for the minimum-error probability attaining this bound. Finally, under the condition of the minimum-error probability attaining this bound, we compare the minimum-error probability for {\it ambiguously} discriminating arbitrary mixed quantum states with the optimal failure probability for {\it unambiguously} discriminating the same states.
A further revised version, and some results have been added
References in corpus (27)
- Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling
- Unknown Quantum States and Operations, a Bayesian View
- Noncommuting mixed states cannot be broadcast
- Probabilistic cloning and identification of linearly independent quantum states
- Quantum State Discrimination
- Unambiguous Discrimination Between Linearly-Independent Quantum States
- Optimum Unambiguous Discrimination Between Linearly Independent Symmetric States
- Optimal discrimination of quantum operations
- Designing Optimal Quantum Detectors Via Semidefinite Programming
- Unambiguous discrimination of mixed states
- A Semidefinite Programming Approach to Optimal Unambiguous Discrimination of Quantum States
- Optimum unambiguous discrimination of two mixed quantum states
- Optimal discrimination of mixed quantum states involving inconclusive results
- Optimal distinction between non-orthogonal quantum states
- Minimum-error discrimination between three mirror-symmetric states
- A universal programmable quantum state discriminator that is optimal for unambiguously distinguishing between unknown states
- Minimum-error discrimination between symmetric mixed quantum states
- Reduction Theorems for Optimal Unambiguous State Discrimination of Density Matrices
- Mixed quantum state detection with inconclusive results
- Optimal unambiguous discrimination between subsets of non-orthogonal quantum states
- General Strategies for Discrimination of Quantum States
- Distinguishing mixed quantum states: Minimum-error discrimination versus optimum unambiguous discrimination
- Minimum-error discrimination between subsets of linearly dependent quantum states
- Minimax quantum state discrimination
- Optimum unambiguous discrimination of two mixed states and application to a class of similar states
- Unambiguous discrimination of mixed states: A description based on system-ancilla coupling
- Condition and capability of quantum state separation
Cited by in corpus (32)
- Relations between coherence and path information
- Quantum Cloning Machines and the Applications
- Optimum Unambiguous Discrimination of Linearly Independent Pure States
- Probe incompatibility in multiparameter noisy quantum metrology
- Discriminating quantum states: the multiple Chernoff distance
- Monitoring of the process of system information broadcasting in time
- Two-sided bounds on minimum-error quantum measurement, on the reversibility of quantum dynamics, and on the maximum overlap problem using directional iterates
- Two-sided estimates of minimum-error distinguishability of mixed quantum states via generalized Holevo-Curlander bounds
- Upper bounds on the error probabilities and asymptotic error exponents in quantum multiple state discrimination
- A lower bound on the probability of error in quantum state discrimination
- Estimating distinguishability measures on quantum computers
- Discriminating single-photon states unambiguously in high dimensions
- Generalized quantum state discrimination problems
- Simultaneously sorting overlapping quantum states of light
- Wave-particle duality of many-body quantum states
- Error rates of Belavkin weighted quantum measurements and a converse to Holevo's asymptotic optimality theorem
- Minimum-error multiple state discrimination constrained by the no-signaling principle
- Optimal discrimination between quantum operations
- New general lower and upper bounds under minimum-error quantum state discrimination
- One-shot conclusive multiport quantum dense coding capacities
- Entanglement cost of discriminating noisy Bell states by local operations and classical communication
- Simple upper and lower bounds on the ultimate success probability for discriminating arbitrary finite-dimensional quantum processes
- Contextuality witness inspired by optimal state discrimination
- Generalized bipartite quantum state discrimination problems with sequential measurements
- Discrimination of unitary transformations in the Deutsch-Jozsa algorithm
- Any four orthogonal ququad-ququad maximally entangled states are locally markable
- Upper and Lower Bounds on Optimal Success Probability of Quantum State Discrimination with and without Inconclusive Results
- Minimum-error discrimination of quantum states: New bounds and comparison
- Minimal-error quantum state discrimination versus robustness of entanglement:More indistinguishability with less entanglement
- Error-Tolerant Quantum State Discrimination: Optimization and Quantum Circuit Synthesis
- Unbounded entanglement-sustaining sequential local quantum state discrimination
- Characterizations of one-way general quantum finite automata