Quantum Coherence via Skew Information and Its Polygamy

Abstract

Quantifying coherence is a key task in both quantum mechanical theory and practical applications. Here, a reliable quantum coherence measure is presented by utilizing the quantum skew information of the state of interest subject to a certain broken observable. This coherence measure is proven to fulfill all the criteria (especially the strong monotonicity) recently introduced in the resource theories of quantum coherence. The coherence measure has an analytic expression and an obvious operational meaning related to quantum metrology. In terms of this coherence measure, the distribution of the quantum coherence, i.e., how the quantum coherence is distributed among the multiple parties is studied and a corresponding polygamy relation is proposed. As a further application, it is found that the coherence measure forms the natural upper bounds for quantum correlations prepared by incoherent operations. The experimental measurement of our coherence measure as well as the relative-entropy coherence, $l_p$-norm coherence is studied finally.

14 pages, 4 figures; accepted by PRA

References in corpus (13)

• Scalable multi-particle entanglement of trapped ions
• Measuring Quantum Coherence with Entanglement
• Dephasing assisted transport: Quantum networks and biomolecules
• General Monogamy Inequality for Bipartite Qubit Entanglement
• Description of quantum coherence in thermodynamic processes requires constraints beyond free energy
• Observable measure of quantum coherence in finite dimensional systems
• Optimal Quantum Phase Estimation
• Quantum coherence, time-translation symmetry and thermodynamics
• Role of quantum coherence in chromophoric energy transport
• Witnessing Quantum Coherence: from solid-state to biological systems
• Entanglement Monogamy of Tripartite Quantum States
• Measurable entanglement for tripartite quantum pure states of qubits
• Novel Schemes for Directly Measuring Entanglement of General States

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• Quantum Fisher information and skew information correlations in dipolar spin system
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• Superadditivity of convex roof coherence measures
• Resource Theory of Total Quantum Coherence
• Coherence and complementarity based on modified generalized skew information
• Coherence, Asymmetry, and Quantum Macroscopicity
• Quantifying coherence in terms of Fisher information
• Skew information-based coherence generating power of quantum channels
• Average skew information-based coherence and its typicality for random quantum states
• Generalized-mean Cramér-Rao Bounds for Multiparameter Quantum Metrology
• Quantum Speed Limit in Terms of Coherence Variations
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• Tsallis relative $\alpha$ entropy of coherence dynamics in Grover's search algorithm
• Experimental tests of density matrix's properties-based complementarity relations
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• Coherence-mixedness trade-offs
• Coherence and imaginarity of quantum states
• Coherence dynamics in quantum algorithm for linear systems of equations
• Quantifying quantum coherence based on the Tsallis relative operator entropy
• Monogamy and trade-off relations for correlated quantum coherence
• Physiological search for quantum biological effects based on the Wigner-Yanase connection between coherence and uncertainty
• Thermally-induced qubit coherence in quantum electromechanics
• The optimal approximation of qubit states with limited quantum states
• A Compendious Review of Majorization-Based Resource Theories: Quantum Information and Quantum Thermodynamics
• Action in Hamiltonian Models Constructed by Yang-Baxter Equation: Entanglement and Measures of Correlation
• Measurement-induced nonlocality in arbitrary dimensions in terms of the inverse approximate joint diagonalization
• Estimating coherence with respect to general quantum measurements
• Coherence and Imaginarity as Resources in Quantum Circuit Complexity
• Quantifying coherence of quantum channels based on the generalized $\alpha$-$z$-relative Rényi entropy
• Enhanced quantum channel uncertainty relations by skew information
• Quantum coherence of an orbital angular momentum multiplexed continuous-variable entangled state
• Analytically Computable Symmetric Quantum Correlations
• Coherence and entanglement dynamics in Shor's algorithm
• Multipartite entanglement detection via generalized Wigner-Yanase skew information
• Quantum dynamical speedup for correlated initial states
• Complete complementarity relations in system-environment decoherent dynamics
• A note on Wigner-Yanase skew information-based uncertainty of quantum channels
• Generalized entropic uncertainty relation and non-classicality in Schwarzschild black hole
• Creation of superposition of arbitrary states encoded in two three-dimensional cavities
• Quantifying quantum non-Markovianity based on quantum coherence via skew information
• The best approximation of a given qubit state with the limited pure-state set
• The best approximation of an objective state with a given set of quantum states
• The $n$-th decay rate of coherence for Bell-diagonal states under quantum channels
• Coherence monotones of quantum channels based on two generalized quantum relative entropies
• Experimental demonstration of robustness of Gaussian quantum coherence
• Quantum Dynamical Resource Theory under Resource Non-increasing Framework
• Experimental demonstration of complementarity relations between quantum steering criteria
• Comparing coherence measures for X states: Can quantum states be ordered based on quantum coherence?
• Characterizing quantum ensemble using geometric measure of quantum coherence
• Behavior of quantum coherence in the ultrastrong and deep strong coupling regimes of light-matter system
• Coherence measures in the strictly incoherent operation framework and its application in the multi-path interferometer
• Quantifying Dynamical Total Coherence in a Resource Non-increasing Framework
• Phase-sensitive superposition of quantum states