Distance-based approach to quantum coherence and nonclassicality

Abstract

We provide a coherence-based approach to nonclassical behavior by means of distance measures. We develop a quantitative relation between coherence and nonclassicality quantifiers, which establish the nonclassicality as the maximum quantum-coherence achievable. We compute the coherence of several representative examples and discuss whether the theory may be extended to reference observables with continuous spectra.

References in corpus (25)

• Quantifying Coherence
• Quantum Coherence as a Resource
• Quantum Resource Theories
• Many-particle entanglement with Bose--Einstein condensates
• Quantum spin squeezing
• Almost all quantum states have non-classical correlations
• Decoherence, Chaos, and the Correspondence Principle
• Entanglement measures and the Hilbert-Schmidt distance
• Complementarity relations for quantum coherence
• Maximal Coherence and the Resource Theory of Purity
• Quantifying coherence of Gaussian states
• Quantifying Coherence in Infinite Dimensional Systems
• Relative quantum coherence, incompatibility, and quantum correlations of states
• Geometric measures of quantum correlations: characterization, quantification, and comparison by distances and operations
• Quantifying quantum coherence and non-classical correlation based on Hellinger distance
• Frobenius-norm-based measures of quantum coherence and asymmetry
• Basis-independent quantum coherence and its distribution
• A quantum measure of coherence and incompatibility
• Quantum Correlations beyond Entanglement and Discord
• The complementarity relations of quantum coherence in quantum information processing
• Nonclassicality of coherent states: Entanglement of joint statistics
• Intrinsic degree of coherence of classical and quantum states
• Nonclassical states from the joint statistics of simultaneous measurements
• Measuring quantumness: from theory to observability in interferometric setups
• Inequalities for complementarity in observed statistics