A resource theory of superposition

Abstract

The superposition principle lies at the heart of many non-classical properties of quantum mechanics. Motivated by this, we introduce a rigorous resource theory framework for the quantification of superposition of a finite number of linear independent states. This theory is a generalization of resource theories of coherence. We determine the general structure of operations which do not create superposition, find an elementary connection to unambiguous state discrimination, and propose several general quantitative superposition measures. We show that several main results from resource theories of coherence still hold in our more general setting. Of special importance are two results about the free completion of trace decreasing operations and the free probabilistic transformation between pure states that are also valid for the special case of coherence.

Close to published version. Connection to entanglement theory added. 5+16 pages

References in corpus (5)

• The resource theory of quantum reference frames: manipulations and monotones
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Cited by in corpus (102)

• Quantum Resource Theories
• Quantum coherence and geometric quantum discord
• Resource theory of quantum non-Gaussianity and Wigner negativity
• Quantifying the Imaginarity of Quantum Mechanics
• Quantifying Operations with an Application to Coherence
• Gaussian quantum resource theories
• One-Shot Operational Quantum Resource Theory
• Convex geometry of quantum resource quantification
• Resource theory of coherence based on positive-operator-valued measures
• Resource theory of non-Gaussian operations
• Asymmetry and coherence weight of quantum states
• Experimental progress on quantum coherence: detection, quantification, and manipulation
• Operational interpretation of weight-based resource quantifiers in convex quantum resource theories of states
• Quantifying the resource content of quantum channels: An operational approach
• Coherence, Quantum Fisher Information, Superradiance and Entanglement are Interconvertible Resources
• Quantum coherence and state conversion: theory and experiment
• Converting multilevel nonclassicality into genuine multipartite entanglement
• Coherence measures with respect to general quantum measurements
• Measures of imaginarity and quantum state order
• Experimental quantification of coherence of a tunable quantum detector
• Partial coherence and quantum correlation with fidelity and affinity distances
• Complete characterization of qubit masking
• Activation of entanglement from quantum coherence and superposition
• An uncertainty view on complementarity and a complementarity view on uncertainty
• Quantitative wave-particle duality relations from the density matrix properties
• Quantum coherence in a compass chain under an alternating magnetic field
• Coherence of quantum channels
• Quantifying dynamical coherence with dynamical entanglement
• Quantum coherence as asymmetry from complex weak values
• Coherence measure: Logarithmic coherence number
• Measuring coherence of quantum measurements
• Genuine Distributed Coherence
• Of Local Operations and Physical Wires
• Relation between Quantum Coherence and Quantum Entanglement in Quantum Measurements
• Coherence of operations and interferometry
• Teleportation of quantum coherence
• Inequalities witnessing coherence, nonlocality, and contextuality
• Resource theory of superposition: State transformations
• Some notes on the robustness of k-coherence and k-entanglement
• Multi-object operational tasks for convex quantum resource theories
• Quantum Process Capability
• Coherence makes quantum systems 'magical'
• Resource theory of quantum coherence with probabilistically non-distinguishable pointers and corresponding wave-particle duality
• Coherence generating power of unitary transformations via probabilistic average
• Simulation of quantum optics by coherent state decomposition
• Assisted harvesting and catalysis of coherence from scalar fields
• Quantum Mean Embedding of Probability Distributions
• Wave-particle duality employing quantum coherence in superposition with non-orthogonal pointers
• Generalized coherence vector applied to coherence transformations and quantifiers
• Generalized-mean Cramér-Rao Bounds for Multiparameter Quantum Metrology
• One-shot manipulation of entanglement for quantum channels
• Impossibility of Cloning of Quantum Coherence
• Quantum Models of Consciousness from a Quantum Information Science Perspective
• Unification of quantum resources in distributed scenarios
• Optimal approximations of available states and a triple uncertainty relation
• Estimating quantum coherence by noncommutativity of any observable and its incoherent part
• Complete Optimal Convex Approximations of Qubit States under $B_2$ Distance
• The block-coherence measures and the coherence measures based on positive-operator-valued measures
• Geometric-Like imaginarity: quantification and state conversion
• Statistical distribution of quantum correlation induced by multiple scattering in the disordered medium
• Exclusion principle for nonlocal advantage of quantum coherence
• Cohering and decohering power of massive scalar fields under instantaneous interactions
• Accessible bounds for general quantum resources
• Quantifying Superpositions Between Quantum Evolutions
• A no-go theorem for superpositions of causal orders
• Sudden death of entanglement in fermionic systems under collective decoherence
• Violating the Leggett-Garg inequalities with classical light
• Quantum Causal Structure and Quantum Thermodynamics
• Quantum coherence between subspaces: State transformation, Cohering Power, $k$-coherence and other properties
• A Compendious Review of Majorization-Based Resource Theories: Quantum Information and Quantum Thermodynamics
• Hardy-like Quantum Pigeonhole Paradox and the Projected-Coloring Graph State
• Theory of Quantum Path Computing with Fourier Optics and Future Applications for Quantum Supremacy, Neural Networks and Nonlinear Schrödinger Equations
• The optimal approximation of qubit states with limited quantum states
• Coherence and Imaginarity as Resources in Quantum Circuit Complexity
• Manifestation of Superposition and Coherence in $\mathcal{P}\mathcal{T}$-symmetry through the $\eta$-inner Product
• One-shot manipulation of coherence in dynamic quantum resource theory
• Coherence, superposition, and Löwdin symmetric orthogonalization
• Correlation between resource-generating capacities of quantum gates
• Experimental implementation of Hardy-like quantum pigeonhole paradoxes
• Spread and asymmetry of typical quantum coherence and their inhibition in response to glassy disorder
• Quantifying the phase of quantum states
• Quantum coherence with incomplete set of pointers and corresponding wave-particle duality
• Noncommutative coherence and quantum phase estimation algorithm
• The best approximation of a given qubit state with the limited pure-state set
• Multi-object operational tasks for measurement incompatibility
• The best approximation of an objective state with a given set of quantum states
• Improving quantum channel discrimination with resourceful states
• Geometric measures of quantum nonlocality: characterization, quantification, and comparison by distances and operations
• Off-resonant preservation and generation of imaginarity in distributed scenarios
• Deterministic all-versus-nothing proofs of Bell nonlocality based on non-stabilizer states
• Generating quantum dissonance via local operations
• Quantifying Algebraic Asymmetry of Hamiltonian Systems
• Methods of constructing superposition measures
• A note on robustness of coherence for multipartite quantum states
• Golden states in resource theory of superposition
• Continuity of measurement outcomes
• Graphene Josephson Junctions for Engineering Motional Quanta
• Electron dynamics induced by quantum cat-state light
• The coherent measurement cost of coherence distillation
• Phase-sensitive superposition of quantum states
• The reduction of the number of incoherent Kraus operations for qutrit systems
• Frame-dependent coherence of a quantum state