Entanglement and Quantum Correlation Measures from a Minimum Distance Principle

Abstract

Entanglement, and quantum correlation, are precious resources for quantum technologies implementation based on quantum information science, such as, for instance, quantum communication, quantum computing, and quantum interferometry. Nevertheless, to our best knowledge, a directly computable measure for the entanglement of multipartite mixed-states is still lacking. In this work, {\it i)} we derive from a minimum distance principle, an explicit measure able to quantify the degree of quantum correlation for pure or mixed multipartite states; {\it ii)} through a regularization process of the density matrix, we derive an entanglement measure from such quantum correlation measure; {\it iii)} we prove that our entanglement measure is \textit{faithful} in the sense that it vanishes only on the set of separable states. Then, a comparison of the proposed measures, of quantum correlation and entanglement, allows one to distinguish between quantum correlation detached from entanglement and the one induced by entanglement, hence to define the set of separable but non-classical states. Since all the relevant quantities in our approach, descend from the geometry structure of the projective Hilbert space, the proposed method is of general application. Finally, we apply the derived measures as an example to a general Bell diagonal state and to the Werner states, for which our regularization procedure is easily tractable.

arXiv comment7 Pages, 3 Figures

References in corpus (32)

• Quantum entanglement
• Entanglement of Formation of an Arbitrary State of Two Qubits
• Mixed State Entanglement and Quantum Error Correction
• Separability Criterion for Density Matrices
• Separability of Mixed States: Necessary and Sufficient Conditions
• Introducing Quantum Discord
• Three qubits can be entangled in two inequivalent ways
• Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
• Distributed Entanglement
• Entanglement detection
• Quantifying Entanglement
• Persistent entanglement in arrays of interacting particles
• Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
• Entanglement, Non-linear Dynamics, and the Heisenberg Limit
• Fisher information and multiparticle entanglement
• Information-theoretic aspects of quantum inseparability of mixed states
• Multipartite entanglement and high precision metrology
• Thermodynamics and the Measure of Entanglement
• Decoherence and multipartite entanglement
• Measures and applications of quantum correlations
• Separability criteria for genuine multiparticle entanglement
• Classification of multi-qubit mixed states: separability and distillability properties
• The Schmidt Measure as a Tool for Quantifying Multi-Particle Entanglement
• Characterizing the entanglement of bipartite quantum systems
• Comparative investigation of the freezing phenomena for quantum correlations under nondissipative decoherence
• Entanglement of three-qubit Greenberger-Horne-Zeilinger-symmetric states
• Note on Separability of the Werner states in arbitrary dimensions
• Explicit product ensembles for separable quantum states
• Entanglement in macroscopic systems
• Entanglement distance for arbitrary $M$-qudit hybrid systems
• Entanglement distance for an arbitrary state of M qubits
• Entanglement estimation in non-optimal qubit states

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