A Note on Invariants and Entanglements

Abstract

The quantum entanglements are studied in terms of the invariants under local unitary transformations. A generalized formula of concurrence for $N$-dimensional quantum systems is presented. This generalized concurrence has potential applications in studying separability and calculating entanglement of formation for high dimensional mixed quantum states.

Latex, 11 pages

References in corpus (2)

• Teleportation of general finite dimensional quantum systems
• Separability of Rank Two Quantum States

Cited by in corpus (121)

• Concurrence of arbitrary dimensional bipartite quantum states
• Quantifying entanglement resources
• Entanglement monogamy relations of qubit systems
• Black Holes, Qubits and Octonions
• Concurrence Vectors in Arbitrary Multipartite Quantum Systems
• Evolution equation of entanglement for general bipartite systems
• Tighter monogamy relations in multipartite systems
• Further results on entanglement detection and quantification from the correlation matrix criterion
• Tighter entanglement monogamy relations of qubit systems
• A lower bound of concurrence for multipartite quantum states
• Quantify entanglement by concurrence hierarchy
• Generalized Monogamy Relations of Concurrence for N-qubit Systems
• Lower Bound on Entanglement of Formation for the Qubit-Qudit System
• Gisin's Theorem for Arbitrary Dimensional Multipartite States
• Nonlocal Properties and Local Invariants for Bipartite Systems
• Hardy's Paradox for High-Dimensional Systems: Beyond Hardy's Limit
• A Note on Fully Entangled Fraction
• Composite parameterization and Haar measure for all unitary and special unitary groups
• Entanglement of three-qubit random pure states
• Spin-Orbit States of Neutron Wavepackets
• A Note on Entanglement of Formation and Generalized Concurrence
• Concurrence triangle induced genuine multipartite entanglement measure
• Experimental Determination of Entanglement for Arbitrary Pure States
• Quantum Entanglement: Separability, Measure, Fidelity of Teleportation and Distillation
• Concurrence-based entanglement measure for Werner States
• Tighter constraints of multiqubit entanglement
• Partial transpose as a direct link between concurrence and negativity
• Maximizing entanglement in bosonic Josephson junctions using shortcuts to adiabaticity and optimal control
• The invariant-comb approach and its relation to the balancedness of multipartite entangled states
• Identification of three-qubit entanglement
• Tight bounds on the concurrence of quantum superpositions
• Distribution of entanglement and correlations in all finite dimensions
• Quantum information approach to the quantum phase transition in the Kitaev honeycomb model
• A Class of Special Matrices and Quantum Entanglement
• Gate simulation and lower bounds on the simulation time
• Quantifying entanglement of maximal dimension in bipartite mixed states
• Entanglement Cost of Three-Level Antisymmetric States
• Coherence, entanglement and quantumness in closed and open systems with conserved charge, with an application to many-body localisation
• Perspectives for a mixed two-qubit system with binomial quantum states
• Multipartite states under local unitary transformations
• Upper bound of the fully entangled fraction
• General Monogamy Relations of Quantum Entanglement for Multiqubit W-class States
• Entanglement quantification through local observable correlations
• Finer Distribution of Quantum Correlations among Multiqubit Systems
• Inequalities Detecting Quantum Entanglement for $2\otimes d$ Systems
• SLOCC Invariants for Multipartite Mixed States
• Lower Bound of Concurrence and Distillation for Arbitrary Dimensional Bipartite Quantum States
• All Pure Two-Qudit Entangled States Can be Generated via a Universal Yang--Baxter Matrix Assisted by Local Unitary Transformations
• Evolution equation of entanglement for multi-qubit systems
• Complementary Quantum Correlations among Multipartite Systems
• Tighter monogamy relations of quantum entanglement for multiqubit W-class states
• Invariant-based entanglement monotones as expectation values and their experimental detection
• Lower Bound of Concurrence Based on Positive Maps
• Separability of rank two quantum states on multiple quantum spaces
• Three-tangle for high-rank mixed states
• Separability and Entanglement of Quantum States Based on Covariance Matrices
• Genuine Multipartite Entanglement of Superpositions
• A lower bound of concurrence for multipartite quantum systems
• Separability and entanglement in 2x3xN composite quantum systems
• General pure multipartite entangled states and the Segre variety
• Analytical Expression of Quantum Discord for Rank-2 Two-qubit States
• Entanglement of Multipartite Schmidt-correlated States
• Entanglement measure for general pure multipartite quantum states
• Improved monogamy relations with concurrence of assistance and negativity of assistance for multiqubit W-class states
• Lower Bound of Multipartite Concurrence Based on Sub-quantum State Decomposition
• Quantitative bound entanglement in two-qutrit states
• Monogamy properties of qubit systems
• Entanglement Property and Monogamy Relation of Gerneralized Mixed W
• Faithful geometric measures for genuine tripartite entanglement
• Monogamy relations of concurrence for any dimensional quantum systems
• Monogamy relations of all quantum correlation measures for multipartite quantum systems
• On monogamy and polygamy relations of multipartite systems
• Generalized Entanglement Monogamy and Polygamy Relations for N -Qubit Systems
• Polygamy relations of multipartite systems
• Concurrence classes for general pure multipartite states
• Perfect teleportation with a partially entangled quantum channel
• Tighter monogamy and polygamy relations of quantum entanglement in multi-qubit systems
• Lower bound on concurrence for arbitrary-dimensional tripartite quantum systems
• Method for measuring the entanglement of formation for arbitrary-dimensional pure states
• Bounds for multipartite concurrence
• Concurrence for multipartite states
• Characterizing generalized axisymmetric quantum states in $d\times d$ systems
• Tighter monogamy inequalities of multiqubit entanglement
• Entanglement and entropy in multipartite systems: a useful approach
• Tighter generalized monogamy and polygamy relations for multiqubit systems
• Concurrence classes for an arbitrary multi-qubit state based on positive operator valued measure
• A Note on Quantum Entanglement and PPT
• Spin-momentum entanglement in a Bose-Einstein condensate
• Polygamy relations of multipartite entanglement beyond qubits
• Tighter parameterized monogamy relations
• Note on Product-Form Monogamy Relations for Nonlocality and Other Correlation Measures
• Degree of separability of bipartite quantum states
• Triangle-like inequalities related to coherence and entanglement negativity
• Weighted monogamy and polygamy relations
• Projection based lower bounds of concurrence for multipartite quantum systems
• Entanglement Universality of TGX States in Qubit-Qutrit Systems
• Polygamy Inequalities for Qubit Systems
• Lower bound of multipartite concurrence based on sub-multipartite quantum systems
• A Note on State Decomposition Independent Local Invariants
• Quantum Correlations Induced by Local von Neumann Measurement
• Nonlocality of two-qubit and three-qubit Schmidt-Correlated states
• Quantum Entanglement transfer between spin-pairs
• Concurrence for infinite-dimensional quantum systems
• Separability and Entanglement of Identical Bosonic Systems
• A class of entanglement monotones for general pure multipartite states based on complex projective variety
• Local correlations of mixed two-qubit states
• Alternative Decomposition of Two-Qutrit Pure States and Its Relation with Entanglement Invariants
• A study on the relations between the topological parameter and entanglement
• A note on quantum Bell nonlocality and quantum entanglement for high dimensional quantum systems
• A Note on Pseudo-Hermitian Systems with Point Interactions and Quantum Separability
• A note on lower bounds of concurrence for arbitrary dimensional bipartite quantum states
• Method of constructing braid group representation and entanglement in a Yang-Baxter sysytem
• Entanglement criterion for pure $M\otimes N$ bipartite quantum states
• Lorentz invariants of pure three-qubit states
• Tighter bounds for generalized monogamy and polygamy relations
• Characterizing multipartite entanglement by violation of CHSH inequalities
• Tighter monogamy relations for the Tsallis-q and Rényi-$\alpha$ entanglement in multiqubit systems
• About Factorization of Quantum States with Few Qubits
• Weak Schmidt decomposition and generalized Bell basis related to Hadamard matrices
• The CHSH-type inequalities for infinite-dimensional quantum systems
• Monogamy inequalities of entanglement of assistance in $2\otimes 2\otimes d$ systems