Resource Theory of Superposition

2017/03/31 by T. Theurer, Thomas Theurer, Nathan Killoran +5 · 6 citations
Computer Science · Mathematics · Physics and Astronomy · #Artificial intelligence #Coherence (philosophical gambling strategy) #Computer science #Connection (principal bundle) #Generalization #Mathematical analysis #Mathematics #Physics #Probabilistic logic #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum entanglement #Quantum mechanics #Statistical physics #Superposition principle #Theoretical physics #quant-ph

paper · pdf · doi:10.1103/physrevlett.119.230401

published as Phys. Rev. Lett. 119, 230401 (2017) · Close to published version. Connection to entanglement theory added. 5+16 pages

openalex publication_date 2017/12/05 · arxiv created 2017/12/18 · arxiv updated 2017/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The superposition principle lies at the heart of many nonclassical 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 a fundamental connection to unambiguous state discrimination, and propose several quantitative superposition measures. Using this theory, we show that trace decreasing operations can be completed for free which, when specialized to the theory of coherence, resolves an outstanding open question and is used to address the free probabilistic transformation between pure states. Finally, we prove that linearly independent superposition is a necessary and sufficient condition for the faithful creation of entanglement in discrete settings, establishing a strong structural connection between our theory of superposition and entanglement theory.

Citations

• Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels
• Unambiguous discrimination between linearly independent quantum states
• Quantum cryptography based on Bell’s theorem
• Computable Measure of Nonclassicality for Light
• The resource theory of quantum reference frames: manipulations and monotones
• Completely positive linear maps on complex matrices
• Convex ordering and quantification of quantumness
• Measures and applications of quantum correlations
• Quantum Computation and Quantum Information
• Quantifying Entanglement
• Quantum entanglement

Cited by

• Theory of quantum path computing with Fourier optics and future applications for quantum supremacy, neural networks and nonlinear Schrödinger equations
• Partial coherence and quantum correlation with fidelity and affinity distances
• Resource theory of quantum coherence with probabilistically nondistinguishable pointers and corresponding wave-particle duality
• An uncertainty view on complementarity and a complementarity view on uncertainty
• Resource theory of superposition: State transformations
• Quantum resource theories