Irreversibility for all bound entangled states

Abstract

We derive a new inequality for entanglement for a mixed four-partite state. Employing this inequality, we present a one-shot lower bound for entanglement cost and prove that entanglement cost is strictly larger than zero for any entangled state. We demonstrate that irreversibility occurs in the process of formation for all non-distillable entangled states. In this way we solve a long standing problem, of how "real" is entanglement of bound entangled states. Using the new inequality we also prove impossibility of local-cloning of a known entangled state.

The publication version. As noted in quant-ph/0510035, the result also implies that the mathematical definition of entangled states is equivalent to the physical definition in the sense of states preparation by LOCC

References in corpus (1)

• Distillation of secret key and entanglement from quantum states

Cited by in corpus (63)

• Quantum entanglement
• Operational Resource Theory of Coherence
• Entanglement in continuous variable systems: Recent advances and current perspectives
• No-local-broadcasting theorem for quantum correlations
• Quantum discord and its allies: a review
• Faithful Squashed Entanglement
• Entanglement Theory and the Second Law of Thermodynamics
• A Generalization of Quantum Stein's Lemma
• Entanglement irreversibility from quantum discord and quantum deficit
• A reversible theory of entanglement and its relation to the second law
• Quantum nonlocality does not imply entanglement distillability
• Experimental bound entanglement in a four-photon state
• Squashed entanglement for multipartite states and entanglement measures based on the mixed convex roof
• A few steps more towards NPT bound entanglement
• Relative Entropy of Entanglement and Restricted Measurements
• Broadcast copies reveal the quantumness of correlations
• Entanglement Cost of Quantum Channels
• Analytical characterization of the genuine multiparticle negativity
• Quantum discord of two-qubit rank-two states
• A measure of physical reality
• A simple proof of monogamy of entanglement
• Entanglement cost and quantum channel simulation
• Sudden death of distillability in qutrit-qutrit systems
• Distillability sudden death in qutrit-qutrit systems under global decoherence
• An Introduction to Quantum Entanglement: a Geometric Approach
• Quantum discord for a two-parameter class of states in $2\otimes d$ quantum systems
• Distillability sudden death in qutrit-qutrit systems under amplitude damping
• Potential capacities of quantum channels
• Testing product states, quantum Merlin-Arthur games and tensor optimisation
• Irreversibility of Asymptotic Entanglement Manipulation Under Quantum Operations Completely Preserving Positivity of Partial Transpose
• "Pretty strong" converse for the quantum capacity of degradable channels
• Entanglement quantification by local unitaries
• Exponential clustering of bipartite quantum entanglement at arbitrary temperatures
• Multipartite unlockable bound entanglement in the stabilizer formalism
• Entangled inputs cannot make imperfect quantum channels perfect
• Work and Heat Value of Bound Entanglement
• Work extraction from tripartite entanglement
• Quantum Side Information: Uncertainty Relations, Extractors, Channel Simulations
• Entanglement Distillation; A Discourse on Bound Entanglement in Quantum Information Theory
• Enhancement of quantum correlations for the system of cavity QED by applying bang-bang pulses
• Attainability and lower semi-continuity of the relative entropy of entanglement, and variations on the theme
• Delayed birth of distillable entanglement in the evolution of bound entangled states
• No-go theorem for entanglement distillation using catalysis
• Entanglement manipulation and distillability beyond LOCC
• Quantum Earth mover's distance, No-go Quantum Kantorovich-Rubinstein theorem, and Quantum Marginal Problem
• Quantum Bell Nonlocality is Entanglement
• Diagonal quantum discord
• Coherence distribution in multipartite systems
• Asymptotic Compatibility between LOCC Conversion and Recovery
• Geometric characterization of separability and entanglement in pure Gaussian states by single-mode unitary operations
• Bipartite bound entanglement in continuous variables through deGaussification
• Continuity of entropies via integral representations
• Bipartite Bound Entanglement
• Entanglement cost for infinite-dimensional physical systems
• Computable entanglement cost under positive partial transpose operations
• Distributing long-distance trust in optomechanics
• On the state space structure of tripartite quantum systems
• One-way Unlocalizable Information Deficit
• One-shot rates for entanglement manipulation under non-entangling maps
• No-local-broadcasting theorem for non-signalling behaviours and assemblages
• Thermodynamics of bipartite entanglement
• Local Hidden Variable Theoretic Measure of Quantumness of Mutual Information
• Strong monotonicity in mixed-state entanglement manipulation