Entanglement Distillation; A Discourse on Bound Entanglement in Quantum Information Theory

Abstract

PhD thesis (University of York). The thesis covers in a unified way the material presented in quant-ph/0403073, quant-ph/0502040, quant-ph/0504160, quant-ph/0510035, quant-ph/0512012 and quant-ph/0603283. It includes two large review chapters on entanglement and distillation.

192 pages

References in corpus (182)

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• General Entanglement Breaking Channels
• Robustness of entanglement
• Witnessing multipartite entanglement
• Entanglement Measures under Symmetry
• Local Distinguishability of Multipartite Orthogonal Quantum States
• Bound entangled Gaussian states
• Characterizing Entanglement
• Thermodynamics and the Measure of Entanglement
• Bell's inequalities and density matrices. Revealing hidden nonlocality.
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• A Schmidt number for density matrices
• Entanglement of pure states for a single copy
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• Unextendible Product Bases, Uncompletable Product Bases and Bound Entanglement
• The asymptotic entanglement cost of preparing a quantum state
• Limits for entanglement measures
• Secure key from bound entanglement
• An improved bound on distillable entanglement
• Further results on the cross norm criterion for separability
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• Schmidt number witnesses and bound entanglement
• Distillability and partial transposition in bipartite systems
• A rigorous treatment of distillable entanglement
• Minimal conditions for local pure-state entanglement manipulation
• Separability and entanglement of composite quantum systems
• Local indistinguishability and LOCC monotones
• Local indistinguishability: more nonlocality with less entanglement
• Local filtering operations on two qubits
• Reflections upon separability and distillability
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• Optimal entanglement criterion for mixed quantum states
• Characterization of separable states and entanglement witnesses
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• Optimal entanglement purifying via entanglement swapping
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• A uniqueness theorem for entanglement measures
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• Detecting multipartite entanglement
• Multipartite bound entangled states that violate Bell's inequality
• Relations between Entanglement Witnesses and Bell Inequalities
• Irreversibility in asymptotic manipulations of entanglement
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• Quantum entanglement of unitary operators on bi-partite systems
• Local permutations of products of Bell states and entanglement distillation
• Asymptotic Relative Entropy of Entanglement for Orthogonally Invariant States
• Low dimensional bound entanglement with one-way distillable cryptographic key
• Activating bound entanglement in multi-particle systems
• Bound entanglement and continuous variables
• Optimal Entanglement Enhancement for Mixed States
• Remarks on additivity of the Holevo channel capacity and of the entanglement of formation
• Quantum Error-Correcting Codes Need Not Completely Reveal the Error Syndrome
• Distillability via protocols respecting the positivity of partial transpose
• A Method of Areas for Manipulating the Entanglement Properties of One Copy of a Two-Particle Pure State
• Unified approach to quantum capacities: towards quantum noisy coding theorem
• Non-local Operations: Purification, storage, compression, tomography, and probabilistic implementation
• Classical information and distillable entanglement
• Entangled states with positive partial transpose arising from indecomposable positive linear maps
• Interpolation of recurrence and hashing entanglement distillation protocols
• Class of PPT bound entangled states associated to almost any set of pure entangled states
• On Quantum Operations as Quantum States
• Entangling Power of Permutations
• Binegativity and geometry of entangled states in two qubits
• Entanglement Concentration Using Quantum Statistics
• Locally accessible information: How much can the parties gain by cooperating?
• Entanglement purification via separable superoperators
• Entanglement and thermodynamical analogies
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• Connecting the generalized robustness and the geometric measure of entanglement
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• Deterministic entanglement concentration
• Witnessed Entanglement
• A (5,5) and (6,6) PPT edge state
• Characterization of Distillable and Activable States using Entanglement Witnesses
• Entanglement Distillation Protocols and Number Theory
• Recovery of entanglement lost in entanglement manipulation
• Measures of entanglement in multipartite bound entangled states
• A two-way algorithm for the entanglement problem
• Efficient distillation beyond qubits
• General formulas for fixed-length quantum entanglement concentration
• Distillation protocols: Output entanglement and local mutual information
• Construction of $3\otimes 3$ entangled edge states with positive partial transposes
• A class of 2^N x 2^N bound entangled states revealed by non-decomposable maps
• Finding a maximally correlated state - Simultaneous Schmidt decomposition of bipartite pure states
• Asymptotic adaptive bipartite entanglement distillation protocol
• Rates of asymptotic entanglement transformations for bipartite mixed states: Maximally entangled states are not special
• Non-full rank bound entangled states satisfying the range criterion
• Characterization of distillability of entanglement in terms of positive maps
• On quantum channels
• The Minimum Distance Problem for Two-Way Entanglement Purification
• Entanglement Cost of Three-Level Antisymmetric States
• A Class of Bound Entangled States
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• Local transformation of mixed states of two qubits to Bell diagonal states
• On the irreversibility of entanglement distillation
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• When only two thirds of the entanglement can be distilled
• Useful entanglement can be extracted from all nonseparable states
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• Locally Accessible Information and Distillation of Entanglement
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• Calculating the relative entropy of entanglement
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• A note on separability criteria for multipartite state
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• On the continuity of asymptotic measures of entanglement
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• $k$-decomposability of positive maps
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• A simplification of entanglement purification
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Cited by in corpus (9)

• Quantifying Einstein-Podolsky-Rosen steering
• Entanglement witnesses: construction, analysis and classification
• A few steps more towards NPT bound entanglement
• Distillability sudden death in qutrit-qutrit systems under amplitude damping
• A study of separability criteria for mixed three-qubit states
• Nondistillability of distillable qutrit-qutrit states under depolarizing noise
• Algebraic Probability-Theoretic Characterization of Quantum Correlations
• Seven definitions of bipartite bound entanglement
• Non-existence of bipartite bound entanglement with negative partial transposition