Optimal environment localization

Abstract

Quantum channels model many physical processes. For this reason, hypothesis testing between quantum channels is a fundamental task in quantum information theory. Here we consider the paradigmatic case of channel position finding, where the aim is to determine the position of a target quantum channel within a sequence of background channels. We explore this model in the setting of bosonic systems, considering Gaussian channels with the same transmissivity (or gain) but different levels of environmental noise. Thus the goal of the problem becomes detecting the position of a target environment among a number of identical background environments, all acting on an input multi-mode system. We derive bounds for the ultimate error probability affecting this multi-ary discrimination problem and find an analytic condition for quantum advantage over protocols involving classical input states. We also design an explicit protocol that gives numerical bounds on the ultimate error probability and often achieves quantum advantage. Finally, we consider direct applications of the model for tasks of thermal imaging (finding a warmer pixel in a colder background) and quantum communication (for localizing a different level of noise in a sequence of lines or a frequency spectrum).

arXiv comment11 pages, 7 figures. Similar to published version

References in corpus (20)

• Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
• Quantum cryptography: Public key distribution and coin tossing
• Gaussian Quantum Information
• General Benchmarks for Quantum Repeaters
• Fundamental Limits of Repeaterless Quantum Communications
• Quantum computation over continuous variables
• Advances in Photonic Quantum Sensing
• Quantum Circuits Architecture
• Statistical distinguishability between unitary operations
• Reversing quantum dynamics with near-optimal quantum and classical fidelity
• Quantum fidelity for arbitrary Gaussian states
• Optimal discrimination of quantum operations
• Uhlmann fidelity between two-mode Gaussian states
• Entanglement can enhance the distinguishability of entanglement-breaking channels
• Fundamental limits to quantum channel discrimination
• Unambiguous discrimination among quantum operations
• Ultimate Precision of Adaptive Noise Estimation
• Optimal estimation of quantum dynamics
• Practical route to entanglement-assisted communication over noisy bosonic channels
• Entanglement-enhanced testing of multiple quantum hypotheses

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• Analytical Bounds for Dynamic Multi-Channel Discrimination
• Idler-Free Multi-Channel Discrimination via Multipartite Probe States