Multiple-copy state discrimination: Thinking globally, acting locally

Abstract

We theoretically investigate schemes to discriminate between two nonorthogonal quantum states given multiple copies. We consider a number of state discrimination schemes as applied to nonorthogonal, mixed states of a qubit. In particular, we examine the difference that local and global optimization of local measurements makes to the probability of obtaining an erroneous result, in the regime of finite numbers of copies $N$, and in the asymptotic limit as $N\to \infty$. Five schemes are considered: optimal collective measurements over all copies, locally optimal local measurements in a fixed single-qubit measurement basis, globally optimal fixed local measurements, locally optimal adaptive local measurements, and globally optimal adaptive local measurements. Here, adaptive measurements are those for which the measurement basis can depend on prior measurement results. For each of these measurement schemes we determine the probability of error (for finite $N$) and scaling of this error in the asymptotic limit. In the asymptotic limit, adaptive schemes have no advantage over the optimal fixed local scheme, and except for states with less than 2% mixture, the most naive scheme (locally optimal fixed local measurements) is as good as any noncollective scheme. For finite $N$, however, the most sophisticated local scheme (globally optimal adaptive local measurements) is better than any other noncollective scheme, for any degree of mixture.

11 pages, 14 figures

References in corpus (4)

• The Quantum Chernoff Bound
• The quantum Chernoff bound as a measure of distinguishability between density matrices: application to qubit and Gaussian states
• Local discrimination of mixed states
• Mixed state discrimination using optimal control

Cited by in corpus (26)

• Revisiting the Dolinar Receiver through Multiple-Copy State Discrimination Theory
• Realizable receivers for discriminating arbitrary coherent-state waveforms and multi-copy quantum states near the quantum limit
• Difficulty of distinguishing product states locally
• Quantum State Discrimination Using the Minimum Average Number of Copies
• Optimized mitigation of random-telegraph-noise dephasing by spectator-qubit sensing and control
• Discriminating mixed qubit states with collective measurements
• Detecting magnetic fields using Nitrogen-Vacancy Centers
• Programmable discrimination with an error margin
• Discriminating qubit amplitude damping channels
• Local unambiguous discrimination of symmetric ternary states
• Multiple-copy state discrimination of noisy qubits
• Experimental Realization of Genuine Three-copy Collective Measurements for Optimal Information Extraction
• Quantum State Discrimination Circuits Inspired by Deutschian Closed Timelike Curves
• Attainability of quantum state discrimination bounds with collective measurements on finite copies
• Optimal discrimination of quantum sequences
• Quantum entanglement percolation under a realistic restriction
• Theory of Single Photon Detection by a Photoreceptive Molecule and a Quantum Coherent Spin Center
• Adaptive Procedures for Discrimination Between Arbitrary Tensor-Product Quantum States
• Quantum hypothesis testing via robust quantum control
• Dealing with ignorance: universal discrimination, learning and quantum correlations
• Bayesian and Markovian classical feedforward for discriminating qubit channels
• Measurement disturbance tradeoffs in three-qubit unsupervised quantum classification
• Factorizability of optimal quantum sequence discrimination under maximum-confidence measurements
• Reinforcement Learning with Neural Networks for Quantum Multiple Hypothesis Testing
• Optimal estimation of three parallel spins with genuine and restricted collective measurements
• Simulating and Optimising Quantum Thermometry Using Single Photons