Continuity bounds for entanglement

Abstract

This note quantifies the continuity properties of entanglement: how much does entanglement vary if we change the entangled quantum state just a little? This question is studied for the pure state entanglement of a bipartite system and for the entanglement of formation of a bipartite system in a mixed state.

5 pages, submitted to Physical Review A Brief Reports. Minor typo in equation (25) corrected in resubmission

Cited by in corpus (70)

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• Fundamentals of Quantum Information Theory
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• Tight uniform continuity bounds for quantum entropies: conditional entropy, relative entropy distance and energy constraints
• The entanglement of purification
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• The Uniqueness Theorem for Entanglement Measures
• Quantum dynamics as a physical resource
• Irreversibility for all bound entangled states
• A uniqueness theorem for entanglement measures
• Local symmetry properties of pure 3-qubit states
• Irreversibility in asymptotic manipulations of entanglement
• A Quantum to Classical Phase Transition in Noisy Quantum Computers
• Continuity of quantum channel capacities
• Squashed entanglement for multipartite states and entanglement measures based on the mixed convex roof
• Principles of Quantum Communication Theory: A Modern Approach
• Entanglement Cost of Quantum Channels
• Applications of coherent classical communication and the Schur transform to quantum information theory
• Entanglement universality of two-qubit X-states
• Squashed entanglement, k-extendibility, quantum Markov chains, and recovery maps
• On asymptotic continuity of functions of quantum states
• Criteria for measures of quantum correlations
• Communication Capacity of Quantum Computation
• Activating NPPT distillation with an infinitesimal amount of bound entanglement
• A Survey of Quantum Property Testing
• Entanglement Rényi $\alpha$-entropy
• An Introduction to Quantum Entanglement: a Geometric Approach
• Optimal superdense coding of entangled states
• On Shor's channel extension and constrained channels
• Continuity of the quantum Fisher information
• Entanglement in quantum information theory
• Flag Additivity in Quantum Resource Theories
• Squashed entanglement in infinite dimensions
• Relation between classical communication capacity and entanglement capability for two-qubit unitary operations
• Continuity of quantum entropic quantities via almost convexity
• Quantum states representing perfectly secure bits are always distillable
• Exponential clustering of bipartite quantum entanglement at arbitrary temperatures
• A Coding Theorem for Bipartite Unitaries in Distributed Quantum Computation
• On the Optimality of Quantum Encryption Schemes
• Quantum Side Information: Uncertainty Relations, Extractors, Channel Simulations
• Local geometry and quantum geometric tensor of mixed states
• Persistence of entanglement in thermal states of spin systems
• Many-body entropies and entanglement from polynomially-many local measurements
• An order-unity correction to Hawking radiation
• Continuity of characteristics of composite quantum systems
• Entanglement in Finitely Correlated Spin States
• Remarks on the equivalence of full additivity and monotonicity for the entanglement cost
• Close-to-optimal continuity bound for the von Neumann entropy and other quasi-classical applications of the Alicki-Fannes-Winter technique
• On the units of bipartite entanglement: Is sixteen ounces of entanglement always equal to one pound?
• Uniform continuity bounds for characteristics of multipartite quantum systems
• Continuity of entropies via integral representations
• Vacuum selection by inflation as the origin of the dark energy
• Entanglement theory with limited computational resources
• Two-dimensional local Hamiltonian problem with area laws is QMA-complete
• Allowed and Forbidden Bipartite Correlations from Thermal States
• Device-independent characterizations of a shared quantum state independent of any Bell inequalities
• Entanglement cost for infinite-dimensional physical systems
• Analytic Semi-device-independent Entanglement Quantification for Bipartite Quantum States
• Counting atypical black hole microstates from entanglement wedges
• On the strong superadditivity of entanglement of formation -- Conditions and examples
• Chemical bonding concepts emerge naturally from maximally entangled atomic orbitals
• Geometrically Taming Dynamical Entanglement Growth in Purified Quantum States
• Analysis of the Entanglement Cost and Calculation of the Holevo Capacity
• Some aspects of the interplay between bipartite correlations and quantum channels
• Convex Hulls of Varieties and Entanglement Measures Based on the Roof Construction