Geometric quantum discord through the Schatten 1-norm

Abstract

It has recently been pointed out that the geometric quantum discord, as defined by the Hilbert-Schmidt norm (2-norm), is not a good measure of quantum correlations, since it may increase under local reversible operations on the unmeasured subsystem. Here, we revisit the geometric discord by considering general Schatten p-norms, explicitly showing that the 1-norm is the only p-norm able to define a consistent quantum correlation measure. In addition, by restricting the optimization to the tetrahedron of two-qubit Bell-diagonal states, we provide an analytical expression for the 1-norm geometric discord, which turns out to be equivalent to the negativity of quantumness. We illustrate the measure by analyzing its monotonicity properties.

v3: published version

References in corpus (13)

• Necessary and sufficient condition for non-zero quantum discord
• On the quantum, classical and total amount of correlations in a quantum state
• Quantum discord for general two--qubit states: Analytical progress
• All non-classical correlations can be activated into distillable entanglement
• Operational Significance of Discord Consumption: Theory and Experiment
• Quantum discord and geometry for a class of two-qubit states
• One-norm geometric quantum discord under decoherence
• Witnessed entanglement and the geometric measure of quantum discord
• Measuring bipartite quantum correlations of an unknown state
• Quantum resources for hybrid communication via qubit-oscillator states
• Quantum-correlating power of local quantum channels
• Tight lower bound on geometric discord of bipartite states
• Comment on "Witnessed entanglement and the geometric measure of quantum discord"

Cited by in corpus (95)

• Measures and applications of quantum correlations
• Frozen Quantum Coherence
• Quantum coherence and geometric quantum discord
• Quantum discord and its allies: a review
• Toward computability of trace distance discord
• Comparative investigation of the freezing phenomena for quantum correlations under nondissipative decoherence
• Monogamy of quantum correlations - a review
• Genuine quantum coherence
• Measurement-induced nonlocality based on the trace norm
• Uncertainty-induced quantum nonlocality
• Local Detection of Quantum Correlations with a Single Trapped Ion
• Hierarchy and dynamics of trace distance correlations
• Evolution equation for quantum coherence
• Universal freezing of quantum correlations within the geometric approach
• Observation of environment-induced double sudden transitions in geometric quantum correlations
• Strong Quantum Darwinism and Strong Independence is equivalent to Spectrum Broadcast Structure
• Geometric measures of quantum correlations: characterization, quantification, and comparison by distances and operations
• Evolution equation for geometric quantum correlation measures
• Experimental entanglement activation from discord in a programmable quantum measurement
• The dynamics of local quantum uncertainty and trace distance discord for two-qubit X states under decoherence: a comparative study
• Geometric classical and total correlations via trace distance
• Circuit Complexity and 2D Bosonisation
• Preservation of the geometric quantum discord in noisy environments
• Trace-distance correlations for X states and emergence of the pointer basis in Markovian and non-Markovian regimes
• Quantumness of correlations, quantumness of ensembles and quantum data hiding
• Geometric quantum discord and non-Markovianity of structured reservoirs
• Building separable approximations for quantum states via neural networks
• Carboxylate based molecular magnet: one path toward achieving stable quantum correlations at room temperature
• Equivalence of qubit-environment entanglement and discord generation via pure dephasing interactions and the consequences thereof
• The dynamic behaviors of local quantum uncertainty for three-qubit X states under decoherence channels
• Universal evolution of non-classical correlations due to collective spontaneous emission
• Gaussian Discriminating Strength
• Effects of DM and KSEA interactions on entanglement, Fisher and Wigner-Yanase information correlations of two XYZ-Heisenberg-qubit states under a magnetic field
• Local quantum uncertainty guarantees the measurement precision for two coupled two-level systems in non-Markovian environment
• Sudden change of geometric quantum discord in finite temperature reservoirs
• Quantum correlation measure in arbitrary bipartite systems
• Overcoming ambiguities in classical and quantum correlation measures
• Enhancing the estimation precision of an unknown phase shift in multipartite Glauber coherent states via skew information correlations and local quantum Fisher information
• Qutrit geometric discord
• Effect of local filtering on Freezing Phenomena of Quantum Correlation
• Quantifying quantum coherence in a metal-silicate framework
• Progress towards a unified approach to entanglement distribution
• Single and double changes of Entanglement
• Broadcasting of Quantum Correlations: Possibilities & Impossibilities
• Hierarchy of efficiently computable and faithful lower bounds to quantum discord
• Detecting non-decomposability of time evolution via extreme gain of correlations
• Many-body localization transition through pairwise correlations
• Quantum discord protection from amplitude damping decoherence
• Reducing Computational Complexity of Quantum Correlations
• Influence of the external pressure on the quantum correlations of molecular magnets
• One-body information loss in fermion systems
• Enhancing the geometric quantum discord in the Heisenberg {\it XX} chain by Dzyaloshinsky-Moriya interaction
• Sudden transitions of trace distance discord of dipole-dipole coupled two qubits
• Dissipative dynamics of quantum correlation quantifiers under decoherence channels
• The relation between the quantum discord and quantum teleportation: the physical interpretation of the transition point between different quantum discord decay regimes
• Generalized conditional entropy optimization for qudit-qubit states
• Generalized conditional entropy in bipartite quantum systems
• Spontaneous emission and quantum discord: comparison of Hilbert-Schmidt and trace distance discord
• Computable measure of the quantum correlation
• Non-Markovianity through Multipartite Correlation Measures
• Entanglement-Coherence and Discord-Coherence analytical relations for X states
• Quantum discord and information deficit in spin chains
• Geometric quantum discord and coherence in a dipolar interacting magnetic system
• Determining quantum correlations in bipartite systems - from qubit to qutrit and beyond
• Quantum correlations in Ising-XYZ diamond chain structure under an external magnetic field
• Negativity of quantumness and non-Markovianity in a qubit coupled to a thermal Ising spin bath system
• Measurement - induced qudit geometric discord
• Investigation of the Quantum Correlations for a S=1/2 Ising- Heisenberg Model on a Symmetrical Diamond Chain
• Two-qubit trace-norm geometric discord: the complete solution
• Correlation Minor Norms, Entanglement Detection and Discord
• Direct-dynamical entanglement-discord relations
• Non-monotonicity of trace distance under tensor products
• Correlation evolution and monogamy of two geometric quantum discords in multipartite systems
• The sudden change phenomenon of quantum discord
• A recursive approach for geometric quantifiers of quantum correlations in multiqubit Schrödinger cat states
• Problem of quantifying quantum correlations with non-commutative discord
• Geometric quantum discord of an arbitrary two-qudit state: the exact value and general upper bounds
• The Geometric Structure of Quantum Resources for Bell-diagonal states
• The local detection method: Dynamical detection of quantum discord with local operations
• Quantum correlations and coherence between two particles interacting with a thermal bath
• Quantum correlation cost of the weak measurement
• Affinity-based geometric discord and quantum speed limits of its creation and decay
• Non-commutative measure of quantum correlations under local operations
• Multipartite Generalization of Geometric measure of Discord
• Local available quantum correlations of non-symmetric X states
• Quantifying Nonclassicality of Correlations based on the Concept of Nondisruptive Local State Identification
• Pairwise quantum and classical correlations in multi-qubits states via linear relative entropy
• Unified scheme for correlations using linear relative entropy
• Characterising two-sided quantum correlations beyond entanglement via metric-adjusted f-correlations
• Fidelity based Measurement Induced Nonlocality over two-sided measurements
• Computable Measure of Total Quantum Correlation of Multipartite Systems
• Quantum discord and one-norm geometric quantum discord for XXX Heisenberg spin chain under noisy channels
• Correlation and Entanglement dynamics for two atoms distributed in two isolated thermal cavities
• Non-commutativity measure of quantum discord
• Connes spectral distances, quantum discord and coherence of qubits