Witnessing quantum discord in 2 x N systems

Abstract

Bipartite states with vanishing quantum discord are necessarily separable and hence positive partial transpose (PPT). We show that 2 x N states satisfy additional property: the positivity of their partial transposition is recognized with respect to the canonical factorization of the original density operator. We call such states SPPT (for strong PPT). Therefore, we provide a natural witness for a quantum discord: if a 2 x N state is not SPPT it must contain nonclassical correlations measured by quantum discord. It is an analog of the celebrated Peres-Horodecki criterion: if a state is not PPT it must be entangled.

5 pages

References in corpus (22)

• Quantum discord and the power of one qubit
• Necessary and sufficient condition for non-zero quantum discord
• Experimental quantum computing without entanglement
• Quantum discord for two-qubit X-states
• Unified View of Quantum and Classical Correlations
• Robustness of quantum discord to sudden death
• Classical and quantum correlations under decoherence
• Almost all quantum states have non-classical correlations
• Quantum versus classical correlations in Gaussian states
• Gaussian quantum discord
• Non-Markovian Dynamics of Quantum Discord
• No-local-broadcasting theorem for quantum correlations
• Vanishing quantum discord is necessary and sufficient for completely positive maps
• Quantum discord of two-qubit X-states
• System-reservoir dynamics of quantum and classical correlations
• Completely Positive Maps and Classical Correlations
• Correlations in local measurements on a quantum state, and complementarity as an explanation of nonclassicality
• Quantum discord and local demons
• Broadcast copies reveal the quantumness of correlations
• On circulant states with positive partial transpose
• Quantum states with strong positive partial transpose
• Generalized Circulant Densities and a Sufficient Condition for Separability

Cited by in corpus (49)

• The classical-quantum boundary for correlations: discord and related measures
• Quantum discord for general two--qubit states: Analytical progress
• Quantum discord and its allies: a review
• Quantum discord and geometry for a class of two-qubit states
• Optimal measurements to access classical correlations of two-qubit states
• Calculation of quantum discord for qubit-qudit or N qubits
• Theoretical and experimental aspects of quantum discord and related measures
• Tight lower bound to the geometric measure of quantum discord
• Frozen discord in non-Markovian dephasing channels
• Quantum discord and multipartite correlations
• Quantum Dissension: Generalizing Quantum Discord for Three-Qubit States
• Detecting Multipartite Classical States and their Resemblances
• Gaussian geometric discord
• Measuring geometric quantum discord using one bit of quantum information
• Quantum discord for a two-parameter class of states in $2\otimes d$ quantum systems
• Entanglement and Discord of superposition of Greenberger-Horne-Zeilinger states
• Quantum discord and non-Markovianity of quantum dynamics
• Nonclassical correlations in continuous-variable non-Gaussian Werner states
• Qubit-qudit states with positive partial transpose
• Detecting the quantum discord of an unknown state by a single observable
• Direct scheme for measuring the geometric quantum discord
• Witnessing nonclassical multipartite states
• Quantum Discord in the Ground and Thermal States of Spin Clusters
• Maximally dense coding capable quantum states
• Verification of quantum discord
• Observable estimation of entanglement of formation and quantum discord for bipartite mixed quantum states
• Classicality witness for two-qubit states
• Inequalities Detecting Quantum Entanglement for $2\otimes d$ Systems
• Geometric measure of quantum discord over two-sided projective measurements
• Measuring nonclassical correlations of two-photon states
• Experimental Verification of Quantum Discord in Continuous-Variable States
• No-activation theorem for Gaussian nonclassical correlations by Gaussian operations
• Quantum discord of SU(2) invariant states
• Separability of Multipartite Quantum States with Strong Positive Partial Transpose
• Geometric measure of quantum discord and total quantum correlations in a N-partite quantum state
• Tomographic characterisation of correlations in a photonic tripartite state
• Generalizations of Quantum Discord
• Quantum dissonance provide power to deterministic quantum computation with single qubit
• Separability of qubit-qudit quantum states with strong positive partial transposes
• Geometric measure of quantum discord and the geometry of a class of two-qubit states
• Quantum discord of 2n-dimensional Bell-diagonal states
• Maximal Clauser-Horne-Shimony-Holt violation for qubit-qudit states
• Quantum Discord Witness With Uncharacterized Devices
• Propagation of local excitations through strongly correlated quantum chains
• On separable decompositions of quantum states with strong positive partial transposes
• Detecting Two Qubit Both-Way Positive Discord States
• Complete condition for nonzero quantum correlation in continuous variable systems
• Any Two Qubit State Has Non Zero Quantum Discord Under Global Unitary Operations
• Some aspects of the interplay between bipartite correlations and quantum channels