Entanglement versus Bell violations and their behaviour under local filtering operations

Abstract

We discuss the relations between the violation of the CHSH Bell inequality for systems of two qubits on the one side and entanglement of formation, local filtering operations, and the entropy and purity on the other. We calculate the extremal Bell violations for a given amount of entanglement of formation and characterize the respective states, which turn out to have extremal properties also with respect to the entropy, purity and several entanglement monotones. The optimal local filtering operations leading to the maximal Bell violation for a given state are provided and the special role of the resulting Bell diagonal states in the context of Bell inequalities is discussed.

5 pages, 1 figure, revtex4

References in corpus (4)

• A computable measure of entanglement
• Local filtering operations on two qubits
• A comparison of the entanglement measures negativity and concurrence
• The Lorentz singular value decomposition and its applications to pure states of 3 qubits

Cited by in corpus (134)

• Bell nonlocality
• Entanglement detection
• Device-independent security of quantum cryptography against collective attacks
• Device-independent quantum key distribution secure against collective attacks
• Research on Hidden Variable Theories: a review of recent progresses
• Deterministic Quantum State Transfer and Generation of Remote Entanglement using Microwave Photons
• Maximal entanglement versus entropy for mixed quantum states
• Qubit Disentanglement and Decoherence via Dephasing
• Quantitative entanglement witnesses
• Quantifying entanglement resources
• Device-independent entanglement quantification and related applications
• Estimating entanglement measures in experiments
• Unbounded violation of tripartite Bell inequalities
• Genuine hidden quantum nonlocality
• All bipartite entangled states display some hidden nonlocality
• Diagnosis, prescription and prognosis of a Bell-state filter by quantum process tomography
• Preserving entanglement and nonlocality in solid-state qubits by dynamical decoupling
• Evaluation of convex roof entanglement measures
• Entanglement estimation from Bell inequality violation
• On experimental procedures for entanglement verification
• Family of Bell-like inequalities as device-independent witnesses for entanglement depth
• Semi-device-independent bounds on entanglement
• Two-qubit mixed states more entangled than pure states: Comparison of the relative entropy of entanglement for a given nonlocality
• Entanglement or separability: The choice of how to factorize the algebra of a density matrix
• Bell inequalities and entanglement at quantum phase transition in the XXZ Model
• Sudden Death of Entanglement induced by Polarization Mode Dispersion
• Key distillation from quantum channels using two-way communication protocols
• Entanglement swapping of noisy states: A kind of superadditivity in nonclassicality
• Relations between entanglement, Bell-inequality violation and teleportation fidelity for the two-qubit X states
• Revealing Hidden Coherence in Partially Coherent Light
• Nonlocality and entanglement in qubit systems
• Connection among entanglement, mixedness and nonlocality in a dynamical context
• Quantum state tomography with quantum shotnoise
• Entangled de Sitter from Stringy Axionic Bell pair I: An analysis using Bunch Davies vacuum
• Entanglement without hidden nonlocality
• Necessary and sufficient detection efficiency for the Mermin inequalities
• Experimental Entanglement Distillation of Two-qubit Mixed States Under Local filtering Operations
• Synthesizing arbitrary two-photon polarization mixed states
• Lower bounds on entanglement measures from incomplete information
• Entanglement degradation in the solid state: interplay of adiabatic and quantum noise
• Ensemble averaged entanglement of two-particle states in Fock space
• All entangled states display some hidden nonlocality
• Dynamics of Non Classically Reproducible Entanglement
• Monolithic Semiconductor Chips as a Source for Broadband Wavelength-Multiplexed Polarization Entangled Photons
• Revealing of hidden quantum steerability using local filtering operations
• Quantum correlations of two-qubit states with one maximally mixed marginal
• Control the entanglement of two atoms in an optical cavity via white noise
• Measurement-device-independent quantification of entanglement for given Hilbert space dimension
• Quantifying entanglement of a two-qubit system via measurable and invariant moments of its partially transposed density matrix
• Bell inequality violation versus entanglement in presence of local decoherence
• Experimental construction of a W-superposition state and its equivalence to the GHZ state under local filtration
• Shareability of Quantum Steering and its Relation with Entanglement
• CHSH violation and entropy - concurrence plane
• Reduced and projected two-particle entanglement at finite temperatures
• Efficiency of photonic state tomography affected by fiber attenuation
• Complete characterization of quantum correlations by randomized measurements
• High-concurrence time-bin entangled photon pairs from optimized Bragg-reflection waveguides
• Bell inequalities for three systems and arbitrarily many measurement outcomes
• Probing the geometry of correlation matrices with randomized measurements
• Practical measurement-device-independent entanglement quantification
• Entanglement as upper bounded for the nonlocality of a general two-qubit system
• Einstein-Podolsky-Rosen correlations and Bell correlations in the simplest scenario
• Estimating multipartite entanglement measures
• A geometric comparison of entanglement and quantum nonlocality in discrete systems
• Measuring the Entanglement between Double Quantum Dot Charge Qubits
• Experimental hierarchy of two-qubit quantum correlations without state tomography
• Quantum tomography of entangled qubits by time-resolved single-photon counting with time-continuous measurements
• Absolute Non-Violation of a Three-Setting Steering Inequality by Two-Qubit States
• Violation of Bell's inequalities implies distillability for N qubits
• Measure-independent anomaly of nonlocality
• Quantum Information Processing with Adversarial Devices
• Bell's Inequality and Entanglement in Qubits
• Entanglement at finite temperatures in the electronic two-particle interferometer
• Bell inequalities versus entanglement and mixedness for a class of two - qubit states
• Entanglement localization after a coupling to incoherent noisy system
• Bell violation versus geometric measure of quantum discord and their dynamical behavior
• Certifying the purity of quantum states with temporal correlations
• Near-maximal two-photon entanglement for quantum communications at 2.1 $\mu$m
• Strengthened Bell Inequalities for Entanglement Verification
• Complementarity-Entanglement Tradeoff in Quantum Gravity
• Generation of maximally entangled mixed states of two atoms via on-resonance asymmetric atom-cavity couplings
• Measurement-based local quantum filters and their ability to transform quantum entanglement
• Transition from pure-state to mixed-state entanglement by random scattering
• Quantifying necessary quantum resources for nonlocality
• Emergence of Intra-Particle Entanglement and Time-Varying Violation of Bell's Inequality in Dirac Matter
• More Nonlocality with Less Entanglement in CHSH Experiments using Inefficient Detectors
• Bell-CHSH Violation Under Global Unitary Operations: Necessary and Sufficient conditions
• Absolute fully entangled fraction from spectrum
• Interplay among entanglement, measurement incompatibility, and nonlocality
• Entanglement with phase decoherence
• How quantum correlations enhance prediction of complementary measurements
• Quantifying Bell nonlocality of a pure two-qudit state via its entanglement
• Effects of decoherence and errors on Bell-inequality violation
• Device-independent quantum authorization based on the Clauser-Horne-Shimony-Holt game
• Entanglement dynamics and Bell Violations of two atoms in Tavis-Cummings model with phase decoherence
• On the Activation of Quantum Nonlocality
• The Degree of Quantum Contextuality in terms of Concurrence for the KCBS Scenario
• Purification and redistribution of entanglement via single local filtering
• Emergence of maximal hidden quantum correlations and its trade-off with the filtering probability in dissipative two-qubit systems
• Entanglement characterization by single-photon counting with random noise
• Programmable Bell State Generation in an Integrated Thin Film Lithium Niobate Circuit
• Entanglement versus Bell nonlocality of quantum nonequilibrium steady states
• Violation of Bell-CHSH inequalities through optimal local filters in the vacuum
• Maximal Clauser-Horne-Shimony-Holt violation for qubit-qudit states
• Complete analysis of measurement-induced entanglement localization on a three-photon system
• Quantum State Tomography of Four-Level Systems with Noisy Measurements
• Maximally Entangled State and Bell's Inequality in Qubits
• Interferometric distillation and determination of unknown two-qubit entanglement
• Non-Locality$\ne$Quantum Entanglement
• Quantum channels and some absolute properties of quantum states
• Generalized Entropy with Clustering and Quantum Entangled States
• Generalized Entropy from Mixing: Thermodynamics, Mutual Information and Symmetry Breaking
• Correlations, Bell Inequality Violation & Quantum Entanglement
• Entangling ability of a beam splitter in the presence of temporal which-path information
• Locally inaccessible hidden quantum correlations
• Quantum steering ellipsoids and quantum obesity in critical systems
• Deterministic construction of arbitrary $W$ states with quadratically increasing number of two-qubit gates
• Testing the Structure of Multipartite Entanglement with Hardy's Nonlocality
• Specifying nonlocality of a pure bipartite state and analytical relations between measures for bipartite nonlocality and entanglement
• A note on quantum Bell nonlocality and quantum entanglement for high dimensional quantum systems
• Role of Steering Inequality In Quantum Key Distribution Protocol
• Swapping of quantum correlations and the role of local filtering operations
• Interplay of Quantum Resources in Nonlocality Tests
• Gigahertz-rate thin-film lithium niobate receiver for time-bin quantum communication
• Nonviolation of the CHSH inequality under local spin-1 measurements on two spin qutrits
• W-class states-identification and quantification of Bell-CHSH inequalities' violation
• Bipartite entanglement purification with neutral atoms
• Revealing hidden standard tripartite nonlocality by local filtering
• A closed-form necessary and sufficient condition for any two-qubit state to show hidden nonlocality w.r.t the Bell-CHSH inequality
• Dynamical redistribution of quantum resources in tree-level Bhabha scattering
• Topological Tenfold Classification and the Entanglement of Two Qubits
• High-spin measurements in an arbitrary two-qudit state
• Maximal violation of Bell inequalities under local filtering
• Characterizing multipartite entanglement by violation of CHSH inequalities