A limit formula for the quantum fidelity

Abstract

Quantum fidelity is a central tool in quantum information, quantifying how much two quantum states are similar. Here we propose a limit formula for the quantum fidelity between a mixed state and a pure state. As an example of an application, we apply this formula to the case of multimode Gaussian states, achieving a simple expression in terms of their first and second-order statistical moments.

Error corrected in the proof of Theorem 1. Results remain valid

References in corpus (16)

• Gaussian Quantum Information
• Quantum teleportation between light and matter
• Quantum Illumination with Gaussian States
• The Quantum Chernoff Bound
• Computable bounds for the discrimination of Gaussian states
• The quantum Chernoff bound as a measure of distinguishability between density matrices: application to qubit and Gaussian states
• Uhlmann fidelity between two-mode Gaussian states
• Correlation Matrices of Two-Mode Bosonic Systems
• Quantum Teleportation with Continuous Variables: a survey
• Quantum Teleportation of Optical Quantum Gates
• Cloning of Gaussian states by linear optics
• Experimental implementation of unambiguous quantum reading
• Symmetric M-ary phase discrimination using quantum-optical probe states
• Quantum reading under a local energy constraint
• A Quantum Teleportation Game
• Error free Quantum Reading by Quasi Bell State of Entangled Coherent States

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• Optimal measurements for quantum fidelity between Gaussian states and its relevance to quantum metrology
• Dissipative engineering of Gaussian entangled states in harmonic lattices with a single-site squeezed reservoir
• Asymmetric quantum hypothesis testing with Gaussian states
• Quantum reading of digital memory with non-Gaussian entangled light
• Quantum master equations for entangled qubit environments
• Anonymous broadcasting of classical information with a continuous-variable topological quantum code
• Cryptographic aspects of quantum reading
• Correcting finite squeezing errors in continuous-variable cluster states
• Minimum resources for versatile continuous variable entanglement in integrated nonlinear waveguides
• Energy-dependent barren plateau in bosonic variational quantum circuits
• Classical simulation and quantum resource theory of non-Gaussian optics
• Generation of stable Gaussian cluster states in optomechanical systems with multifrequency drives
• Classical simulation of bosonic linear-optical random circuits beyond linear light cone
• Spectral and temporal properties of type-II parametric down-conversion: The impact of losses during state generation
• Symmetric and asymmetric discrimination of bosonic loss: Toy applications to biological samples and photo-degradable materials
• Discriminating quantum field theories in non-inertial frames
• Noise-reduction of multimode Gaussian Boson Sampling circuits via Unitary Averaging
• Multimode Gaussian steady state engineering in optomechanical systems with a squeezed reservoir