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.

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

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Cited by in corpus (104)

• Quantum Coherence as a Resource
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• Quantum coherence and geometric quantum discord
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• Quantifying the Imaginarity of Quantum Mechanics
• Quantifying Operations with an Application to Coherence
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• 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
• Complete characterization of qubit masking
• Partial coherence and quantum correlation with fidelity and affinity distances
• 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
• Coherence of quantum channels
• Quantum coherence in a compass chain under an alternating magnetic field
• Generalized concurrence in boson sampling
• Quantifying dynamical coherence with dynamical entanglement
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• Measuring coherence of quantum measurements
• Genuine Distributed Coherence
• Of Local Operations and Physical Wires
• Coherence of operations and interferometry
• Relation between Quantum Coherence and Quantum Entanglement in Quantum Measurements
• Inequalities witnessing coherence, nonlocality, and contextuality
• Teleportation of quantum coherence
• Resource theory of superposition: State transformations
• Some notes on the robustness of k-coherence and k-entanglement
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• Simulation of quantum optics by coherent state decomposition
• Quantum Mean Embedding of Probability Distributions
• Wave-particle duality employing quantum coherence in superposition with non-orthogonal pointers
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• Quantifying Algebraic Asymmetry of Hamiltonian Systems
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