Convex ordering and quantification of quantumness

Abstract

The characterization of physical systems requires a comprehensive understanding of quantum effects. One aspect is a proper quantification of the strength of such quantum phenomena. Here, a general convex ordering of quantum states will be introduced which is based on the algebraic definition of classical states. This definition resolves the ambiguity of the quantumness quantification using topological distance measures. Classical operations on quantum states will be considered to further generalize the ordering prescription. Our technique can be used for a natural and unambiguous quantification of general quantum properties whose classical reference has a convex structure. We apply this method to typical scenarios in quantum optics and quantum information theory to study measures which are based on the fundamental quantum superposition principle.

9 pages, 2 figures, revised version; published in special issue "150 years of Margarita and Vladimir Man'ko"

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• Gaussian quantum resource theories
• Convex geometry of quantum resource quantification
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• Nonclassical Light and Metrological Power: An Introductory Review
• Measuring nonclassicality of bosonic field quantum states via operator ordering sensitivity
• Quasiprobability representation of quantum coherence
• Converting multilevel nonclassicality into genuine multipartite entanglement
• Quasiprobability distributions for quantum-optical coherence and beyond
• Roughness as Classicality Indicator of a Quantum State
• Fisher information universally identifies quantum resources
• Quantum non-Gaussianity and quantification of nonclassicality
• Quantifying nonclassicality by characteristic functions
• Validating and controlling quantum enhancement against noise by motion of a qubit
• Quantumness of spin-1 states
• Measuring coherence of quantum measurements
• Mode-independent quantum entanglement for light
• Asymptotic state transformations of continuous variable resources
• Quantifying quantum coherence in polariton condensates
• Quadrature coherence scale driven fast decoherence of bosonic quantum field states
• Relating the Entanglement and Optical Nonclassicality of Multimode States of a Bosonic Quantum Field
• Some notes on the robustness of k-coherence and k-entanglement
• Monotones in General Resource Theories
• Decoherence and nonclassicality of photon-added/subtracted multi-mode Gaussian states
• Tracking quantum coherence in polariton condensates with time-resolved tomography
• Quantum correlations in composite systems
• Resource Theory of Total Quantum Coherence
• Quantum coherences of indistinguishable particles
• Attainability and lower semi-continuity of the relative entropy of entanglement, and variations on the theme
• Deterministic transformations of multilevel coherent states under incoherence-preserving operations
• Tight bounds for antidistinguishability and circulant sets of pure quantum states
• Classical evolution in quantum systems
• Convex roofs witnessing Kirkwood-Dirac nonpositivity
• Entanglement-assisted quantum speedup: Beating local quantum speed limits
• An introductory review on resource theories of generalized nonclassical light
• Quantum coherence between subspaces: State transformation, Cohering Power, $k$-coherence and other properties
• Interferometric measurement of the quadrature coherence scale using two replicas of a quantum optical state
• Unbreakable and breakable quantum censorship
• Polarization monotones of two-dimensional and three-dimensional random electromagnetic fields
• Quadrature Coherence Scale of Linear Combinations of Gaussian Functions in Phase Space
• Certifying Multilevel Coherence in the Motional State of a Trapped Ion
• Retrodiction of measurement outcomes on a single quantum system reveals entanglement with its environment
• Censorship of quantum resources against catalytic account sharing
• Exact Quantum Capacity of Decohering Channels in Arbitrary Dimensions
• The entangling power of non-entangling channels