Bounding the benefit of adaptivity in quantum metrology using the relative fidelity

Abstract

Protocols for discriminating between a pair of channels or for estimating a channel parameter can often be aided by adaptivity or by entanglement between the probe states. This can make it difficult to bound the best possible performance for such protocols. In this paper, we introduce a quantity that we call the relative fidelity of a given pair of channels and a pair of input states to those channels. Constraining the allowed input states to all pairs of states whose fidelity is greater than some minimum "input fidelity" and minimising this quantity over the valid pairs of states, we get the minimum relative fidelity for that input fidelity constraint. We are then able to lower bound the fidelity between the possible output states of any protocol acting on one of two possible channels in terms of the minimum relative fidelity. This allows us to bound the performance of the most general, adaptive discrimination and parameter estimation protocols. By finding a continuity bound for the relative fidelity, we also provide a simple confirmation that the quantum Fisher information (QFI) of the output of an $N$-use protocol is no more than $N^2$ times the one-shot QFI.

arXiv comment13 pages, 3 figures, supplementary files available at https://doi.org/10.5281/zenodo.5498138. Similar to published version

References in corpus (30)

• Advances in Quantum Metrology
• Quantum metrology with nonclassical states of atomic ensembles
• General Benchmarks for Quantum Repeaters
• Fundamental Limits of Repeaterless Quantum Communications
• Advances in Photonic Quantum Sensing
• Quantum enhanced measurements without entanglement
• Quantum State Discrimination
• Quantum Circuits Architecture
• Statistical distinguishability between unitary operations
• Using entanglement improves precision of quantum measurements
• A Geometric Perspective on Quantum Parameter Estimation
• Quantum information and precision measurement
• Entanglement can enhance the distinguishability of entanglement-breaking channels
• The Perfect Distinguishability of Quantum Operations
• Fundamental limits to quantum channel discrimination
• Unambiguous discrimination among quantum operations
• Adaptive versus non-adaptive strategies for quantum channel discrimination
• Amortized Channel Divergence for Asymptotic Quantum Channel Discrimination
• Discrimination of two channels by adaptive methods and its application to quantum system
• Optimal estimation of quantum dynamics
• Optimum unambiguous discrimination among linearly-independent non-orthogonal quantum states and its optical realization
• Fidelity susceptibility and quantum Fisher information for density operators with arbitrary ranks
• Asymptotic theory of quantum channel estimation
• Ultimate limits for multiple quantum channel discrimination
• Entanglement-enhanced testing of multiple quantum hypotheses
• Geometric distinguishability measures limit quantum channel estimation and discrimination
• Quantum speedup in the identification of cause-effect relations
• Quantum-enhanced barcode decoding and pattern recognition
• Ultimate Limits of Thermal Pattern Recognition
• Idler-free channel position finding