Changepoint Problem in Quantumn Setting

Abstract

In the changepoint problem, we determine when the distribution observed has changed to another one. We expand this problem to the quantum case where copies of an unknown pure state are being distributed. We study the fundamental case, which has only two candidates to choose. This problem is equal to identifying a given state with one of the two unknown states when multiple copies of the states are provided. In this paper, we assume that two candidate states are distributed independently and uniformly in the space of the whole pure states. The minimum of the averaged error probability is given and the optimal POVM is defined as to obtain it. Using this POVM, we also compute the error probability which depends on the inner product. These analytical results allow us to calculate the value in the asymptotic case, where this problem approaches to the usual discrimination problem.

References in corpus (6)

• The Quantum Chernoff Bound
• The quantum Chernoff bound as a measure of distinguishability between density matrices: application to qubit and Gaussian states
• Comparison of two unknown pure quantum states
• Quantum pure-state identification
• Unambiguous pure state identification without classical knowledge
• Multi-copy programmable discrimination of general qubit states

Cited by in corpus (16)

• Quantum change point
• Ultimate limits for quickest quantum change-point detection
• Programmable discrimination with an error margin
• Success probabilities for universal unambiguous discriminators between unknown pure states
• Recoupling coefficients and quantum entropies
• An agnostic-Dolinar receiver for coherent states classification
• Optimal quantum state identification with qudit-encoded unknown states
• Universal algorithms for quantum data learning
• Experimentally detecting a quantum change point via Bayesian inference
• Optimal programmable unambiguous discriminator between two unknown latitudinal states
• Quantum change point and entanglement distillation
• An Exponential Quantum Projection Filter for Open Quantum Systems
• Fundamental Limits Of Quickest Change-point Detection With Continuous-Variable Quantum States
• Testing identity of collections of quantum states: sample complexity analysis
• Measurement disturbance tradeoffs in three-qubit unsupervised quantum classification
• Dealing with ignorance: universal discrimination, learning and quantum correlations