Alternative fidelity measure for quantum states

Abstract

We propose an alternative fidelity measure (namely, a measure of the degree of similarity) between quantum states and benchmark it against a number of properties of the standard Uhlmann-Jozsa fidelity. This measure is a simple function of the linear entropy and the Hilbert-Schmidt inner product between the given states and is thus, in comparison, not as computationally demanding. It also features several remarkable properties such as being jointly concave and satisfying all of "Jozsa's axioms". The trade-off, however, is that it is supermultiplicative and does not behave monotonically under quantum operations. In addition, new metrics for the space of density matrices are identified and the joint concavity of the Uhlmann-Jozsa fidelity for qubit states is established.

12 pages, 3 figures. v2 includes minor changes, new references and new numerical results (Sec. IV)

References in corpus (20)

• Quantifying Entanglement
• Entanglement Measures and Purification Procedures
• On the volume of the set of mixed entangled states
• Entanglement monotones
• Distance measures to compare real and ideal quantum processes
• The Quantum Chernoff Bound
• The Bloch Vector for N-Level Systems
• Characterization of the Positivity of the Density Matrix in Terms of the Coherence Vector Representation
• Degrees of concealment and bindingness in quantum bit commitment protocols
• Entanglement measures and the Hilbert-Schmidt distance
• Optimum Quantum Error Recovery using Semidefinite Programming
• Iterative Optimization of Quantum Error Correcting Codes
• A new entanglement measure induced by the Hilbert-Schmidt norm
• Quantum Control of a Single Qubit
• Robust Quantum Error Correction via Convex Optimization
• A Minkowski Type Trace Inequality and Strong Subadditivity of Quantum Entropy II: Convexity and Concavity
• Suboptimal quantum-error-correcting procedure based on semidefinite programming
• "Partial" Fidelities
• Computational approach to quantum encoder design for purity optimization
• Optimal tracking for pairs of qubit states

Cited by in corpus (51)

• Fidelity approach to quantum phase transitions
• Quantum fidelity measures for mixed states
• Uhlmann fidelity between two-mode Gaussian states
• Imperfect measurements settings: implications on quantum state tomography and entanglement witnesses
• Variational Quantum Fidelity Estimation
• Fidelity susceptibility and quantum Fisher information for density operators with arbitrary ranks
• Certifying the building blocks of quantum computers from Bell's theorem
• Charge and spin dynamics driven by ultrashort extreme broadband pulses: a theory perspective
• Transition Probability (Fidelity) and Its Relatives
• Number-resolved photocounter for propagating microwave mode
• GRAPE optimization for open quantum systems with time-dependent decoherence rates driven by coherent and incoherent controls
• An improved bound for quantum speed limit time in open quantum systems by introducing an alternative fidelity
• Quantum Fisher information on two manifolds of two-mode Gaussian states
• Hellinger distance as a measure of Gaussian discord
• Exact resummation of the Holstein-Primakoff expansion and differential equation approach to operator square-roots
• Sub-Quantum Fisher Information
• Direct method for measuring of purity, superfidelity, and subfidelity of photonic two-qubit mixed states
• Bound on trace distance based on superfidelity
• Quantifying non-Gaussianity of quantum-state correlation
• Efficiently computing the Uhlmann fidelity for density matrices
• Looking at Shadows of Entanglement Wedges
• Optimal State Manipulation for a Two-Qubit System Driven by Coherent and Incoherent Controls
• Quantum speed limit based on the bound of Bures angle
• Partitioned trace distances
• Controlled quantum teleportation between discrete and continuous physical systems
• Vibrational exciton-mediated quantum state transfert: a simple model
• Experimentally feasible measures of distance between quantum operations
• Variational Quantum Cloning: Improving Practicality for Quantum Cryptanalysis
• Tight and attainable quantum speed limit for open systems
• Non-Gaussianity and entropy-bounded uncertainty relations: Application to detection of non-Gaussian entangled states
• Controlling NMR spin systems for quantum computation
• Single photon-added coherent states: estimation of parameters and fidelity of the optical homodyne detection
• Natural Metric for Quantum Information Theory
• Designing refrigerators in higher dimensions using quantum spin models
• Measuring distances in Hilbert space by many-particle interference
• Minimal noise subsystems
• Relative purity, speed of fluctuations, and bounds on equilibration times
• Bounds on Shannon distinguishability in terms of partitioned measures
• Experimental characterization of quantum dynamics through many-body interactions
• Shielding quantum discord through continuous dynamical decoupling
• Purification-based metric to measure the distance between quantum states and processes
• Initial-state-dependent quantum speed limit for dissipative state preparation: Framework and optimization
• Probability measure generated by the superfidelity
• Fidelity-based distance bounds for $N$-qubit approximate quantum error correction
• Classifying topological neural network quantum states via diffusion maps
• Tripartite quantum Rabi model with trapped Rydberg ions
• Non-Markovianity in the time evolution of open quantum systems assessed by means of quantum state distance
• Quantifying channels output similarity with applications to quantum control
• Lattice oscillator model, scattering theory and a many-body problem
• Representations of two-qubit and ququart states via discrete Wigner functions
• A unified fidelity-based framework for quantum speed limits in open quantum systems