All multipartite entanglements are quantum coherences in locally distinguishable bases

Abstract

We find that the m-separability and k-partite entanglement of a multipartite quantum system is correlated with quantum coherence of the same with respect to complete orthonormal bases, distinguishable under local operations and classical communication in certain partitions. In particular, we show that the geometric measure of m-inseparable entanglement of a multipartite quantum state is equal to the square of minimum fidelity-based quantum coherence of the state with respect to complete orthonormal bases, that are locally distinguishable in a partition into m-parties.

9 pages

References in corpus (92)

• Quantum entanglement
• Quantum Cryptography
• Mixed State Entanglement and Quantum Error Correction
• Quantifying Coherence
• Entanglement detection
• Advances in Quantum Cryptography
• Quantum Coherence as a Resource
• Entanglement Measures and Purification Procedures
• The Role of Relative Entropy in Quantum Information Theory
• Quantum Nonlocality without Entanglement
• Operational Resource Theory of Coherence
• Measuring Quantum Coherence with Entanglement
• The role of quantum information in thermodynamics --- a topical review
• Advances in Quantum Teleportation
• Geometric measure of entanglement and applications to bipartite and multipartite quantum states
• Fisher information and multiparticle entanglement
• Robustness of coherence: An operational and observable measure of quantum coherence
• Vibrations, Quanta and Biology
• Multipartite entanglement and high precision metrology
• Local Distinguishability of Multipartite Orthogonal Quantum States
• Quantum coherence, time-translation symmetry and thermodynamics
• A complete family of separability criteria
• Everything You Always Wanted to Know About LOCC (But Were Afraid to Ask)
• Security in Quantum Cryptography
• Quantum coherence in multipartite systems
• Entanglement Certification $-$ From Theory to Experiment
• Distinguishing separable and entangled states
• A computable measure of nonclassicality for light
• Separability criteria for genuine multiparticle entanglement
• Coherence as a resource in decision problems: The Deutsch-Jozsa algorithm and a variation
• Relating the Resource Theories of Entanglement and Quantum Coherence
• Detection of high-dimensional genuine multi-partite entanglement of mixed states
• Reversible transformations from pure to mixed states, and the unique measure of information
• Bell-type inequalities for partial separability in N-particle systems and quantum mechanical violations
• Local indistinguishability: more nonlocality with less entanglement
• Local indistinguishability and LOCC monotones
• Converting Nonclassicality into Entanglement
• Coherence depletion in the Grover quantum search algorithm
• Maximal Coherence and the Resource Theory of Purity
• Strong Quantum Nonlocality without Entanglement
• Measuring Coherence with Entanglement Concurrence
• Operational one-to-one mapping between coherence and entanglement measures
• The geometric measure of entanglement for symmetric states
• Entanglement and coherence in quantum state merging
• Channel Capacities versus Entanglement Measures in Multiparty Quantum States
• Detecting multipartite entanglement
• Thermodynamic resource theories, non-commutativity and maximum entropy principles
• Hierarchies of Geometric Entanglement
• Spin squeezing inequalities for arbitrary spin
• The entropy vector formalism and the structure of multidimensional entanglement in multipartite systems
• On the permutationally invariant part of a density matrix and nonseparability of N-qubit states
• Energy Cost of Creating Quantum Coherence
• Measure of multipartite entanglement with computable lower bounds
• Determining lower bounds on a measure of multipartite entanglement from few local observables
• Metrological Detection of Multipartite Entanglement from Young Diagrams
• Advances in quantum dense coding
• Efficient entanglement criteria for discrete, continuous, and hybrid variables
• Multipartite Entanglement in Stabilizer Tensor Networks
• Characterizing multipartite entanglement without shared reference frames
• Geometric measure of entanglement for pure multipartite states
• Improved lower bounds on genuine-multipartite-entanglement concurrence
• Detection of genuinely entangled and non-separable $n$-partite quantum states
• Demonstrating quantum coherence and metrology that is resilient to transversal noise
• Indistinguishability-enabled coherence for quantum metrology
• Multiparticle covariance matrices and the impossibility of detecting graph state entanglement with two-particle correlations
• Efficient $k$-separability criteria for mixed multipartite quantum states
• Axiomatic and operational connections between the $l_1$-norm of coherence and negativity
• A new coherence measure based on fidelity
• Genuine Multipartite Entanglement Trends in Gapless-gapped Transitions of Quantum Spin Systems
• Coherence orders, decoherence and quantum metrology
• A new type of complementarity between quantum and classical information
• Separability criteria for several classes of $n$-partite quantum states
• Generalized Geometric Measure of Entanglement for Multiparty Mixed States
• Coherence number as a discrete quantum resource
• Detection of $k$-partite entanglement and $k$-nonseparability of multipartite quantum states
• k-stretchability of entanglement, and the duality of k-separability and k-producibility
• Multipartite entanglement outperforming bipartite entanglement under limited quantum system sizes
• Geometric coherence and quantum state discrimination
• Measuring coherence of quantum measurements
• Of Local Operations and Physical Wires
• Relation between Quantum Coherence and Quantum Entanglement in Quantum Measurements
• Entanglement and communication-reducing properties of noisy N-qubit states
• Coherence Depletion in Quantum Algorithms
• Experimental quantum phase discrimination enhanced by controllable indistinguishability-based coherence
• Quantification of Entanglement and Coherence with Purity Detection
• Criteria for non-$k$-separability of $n$-partite quantum states
• Protocol for unambiguous quantum state discrimination using quantum coherence
• All entangled states are quantum coherent with locally distinguishable bases
• Accessible quantification of multiparticle entanglement
• Stretching the limits of multiparticle entanglement
• Correlation between resource-generating capacities of quantum gates
• Critical behaviour in the optimal generation of multipartite entanglement

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