Conditions for a class of entanglement transformations

Abstract

Suppose Alice and Bob jointly possess a pure state, $|ψ\ra$. Using local operations on their respective systems and classical communication it may be possible for Alice and Bob to transform $|ψ\ra$ into another joint state $|ϕ\ra$. This Letter gives necessary and sufficient conditions for this process of entanglement transformation to be possible. These conditions reveal a partial ordering on the entangled states, and connect quantum entanglement to the algebraic theory of majorization. As a consequence, we find that there exist essentially different types of entanglement for bipartite quantum systems.

4 pages. Title and some nomenclature changed. Minor errors fixed

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• Quantum entanglement percolation under a realistic restriction
• Identifying families of multipartite states with non-trivial local entanglement transformations
• Spectral Statistics of Non-Hermitian Matrices and Dissipative Quantum Chaos
• Time-reversal frameness and superselection
• Single-shot entanglement manipulation of states and channels revisited
• On the LOCC Classification of Bipartite Density Matrices
• Nonstrict inequality for Schmidt coefficients of three-qubit states
• Entanglement, loss, and quantumness: When balanced beam splitters are best
• Thermodynamic state convertibility is determined by qubit cooling and heating
• Stabilizer states and local realism
• Optimal observables to determine entanglement of a two qubit state
• Inevitable Negativity: Additivity Commands Negative Quantum Channel Entropy
• Correlations, Bell Inequality Violation & Quantum Entanglement
• Classifying Entanglement by Algebraic Geometry
• General entanglement-assisted transformation for bipartite pure quantum states
• Local transformations of superpositions of entangled states
• Probabilistic pure state conversion on the majorization lattice
• Charge-Preserving Operations in Quantum Batteries
• Maximal Entanglement: Applications in Quantum Information and Particle Physics
• Golden states in resource theory of superposition
• Detecting quantum resources in a semi-device independent framework
• Irrversibility of Entanglement Manipulations: Vagueness of the Entanglement of Cost and Entanglement of Distillation
• Random Number Conversion and LOCC Conversion via Restricted Storage
• Multipartite Monogamy of Entanglement for Three Qubit States
• Censorship of quantum resources against catalytic account sharing
• Approximate and ensemble local entanglement transformations for multipartite states
• A combinatorial approach for studying LOCC transformations of multipartite states
• The tightness of multipartite coherence from spectrum estimation
• Entanglement transfer, accumulation and retrieval via quantum-walk-based qubit-qudit dynamics
• Towards the Classical Communication Complexity of Entanglement Distillation Protocols with Incomplete Information
• The landscape of quantum transitions driven by single-qubit unitary transformations with implications for entanglement
• Quantum Circuits for High-Dimensional Absolutely Maximally Entangled States
• Entanglement-Enhanced Classical Communication
• Majorization requires infinitely many second laws
• Stochastic approximate state conversion for entanglement and general quantum resource theories
• Hypergraph-theoretic charaterizations for LOCC incomparable ensembles of multipartite CAT states
• The Existence of Quantum Entanglement Catalysts
• Measurement incompatibility at all remote parties do not always permit Bell nonlocality
• Squashed quantum non-Markovianity: a measure of genuine quantum non-Markovianity in states
• Multipartite entanglement theory with entanglement-nonincreasing operations
• Asymptotic entanglement manipulation of bipartite pure states
• Strong bounds on required resources for quantum channels by local operations and classical communication
• Entanglement percolation in random quantum networks
• Remotely prepared entanglement: a quantum web page
• Complete characterisation of state conversions by work extraction
• Characterising two-sided quantum correlations beyond entanglement via metric-adjusted f-correlations
• Majorization in Quantum Adiabatic Algorithms
• Finite-size catalysis in quantum resource theories
• The role of singular values in entanglement distillation and unambiguous state discrimination
• Generation and Manipulation of Entanglement in Quantum Optical Systems
• Partial Recovery of Quantum Entanglement
• Relative volume of comparable pairs under semigroup majorization
• Probabilistic Coherence Transformation Under Strictly Incoherent Operation
• A Non-Convex Optimization Strategy for Computing Convex-Roof Entanglement
• Certifying entanglement dimensionality by $k$-reduction moments
• A finite sufficient set of conditions for catalytic majorization
• General Classes of Impossible Operations through the Existence of Incomparable States
• Signatures of Environment-Induced Quantum Synchronization Transitions via Two-body Dissipator Engineering
• Witness High-Dimensional Quantum Steering via Majorization Lattice
• Nonlocal sets of orthogonal multipartite product states with less members
• Gauge and diffeomorphism invariance from quantum information principles
• Nonexistence of maximally entangled mixed states for a fixed spectrum
• Analogs of absolutely maximally entangled states in nonlocal correlations via the sheaf-theoretic framework and its applications
• Optimal universal bounds for waves with varied coherence based on supremum and infimum coherence spectra
• Advantage of flexible catalysis for entanglement and quantum thermodynamics
• Distributed variational quantum computing with deterministic entanglement tuning
• Noncooperative Quantum Networks
• Insufficiency of Pure-State Ensembles in Characterizing Transformations of Entangled States under LOCC
• Statistics of Entanglement Transformation with Hierarchies among Catalysts
• Few-body entanglement manipulation
• Geometric Measure of Entanglement and Schmidt Decomposition of Multipartite Systems
• Quantum feedback for measurement and control
• Extracting Quantum Entanglement (General Entanglement Purification Protocols)
• Conditions for local transformations between sets of quantum states
• Nonlocal Generalized Quantum Measurements of Spin Products Without Maximal Entanglement
• Universality of EPR pairs in Entanglement-Assisted Communication Complexity, and the Communication Cost of State Conversion
• Generation and Detection of Quantum Correlations and Entanglement on a Spin-Based Quantum Information Processor
• Universal proofs of entropic continuity bounds via majorization flow
• Sorting of quantum states with respect to amount of entanglement included
• The binegativity of two qubits
• Extremal Steering Assemblages
• Majorization theoretical approach to entanglement enhancement via local filtration
• Analysis of Neural Network Predictions for Entanglement Self-Catalysis
• Joint measurability meets Birkhoff-von Neumann's theorem
• Measurements and majorization
• Entanglement - A Queer In The World Of Quantum : Some Perspectives
• Some properties of n-party entanglement under LOCC operations
• Discrimination of Quantum States under Local Operations and Classical Communication
• A Universal Quantum Certainty Relation for Arbitrary Number of Observables
• Comparing globalness of bipartite unitary operations: delocalization power, entanglement cost, and entangling power
• Introduction to Measurement Space and Application to Operationally Useful Entanglement and Mode Entanglement
• Optimal and covariant single-copy LOCC transformation between two two-qubit states
• Separable Operations, Graph Codes and the Location of Quantum Information
• Efficient decoding of stabilizer code by single-qubit local operations and classical communication
• Quantifying entanglement when measurements are imperfect or restricted
• Information and majorization theory for fermionic phase-space distributions
• The role of local and global geometry in quantum entanglement percolation
• Quantum information processing
• Accounting for gauge symmetries in CHSH experiments
• From Information Theory Puzzles in Deletion Channels to Deniability in Quantum Cryptography