Symmetrizing Cost of Quantum States

Abstract

We introduce and analyze a task that we call symmetrization, in which a state of a quantum system, associated with a symmetry group, is transformed by a random unitary operation to a symmetric state. Each element of the unitary ensemble is required to be symmetry preserving, in the sense that it keeps the set of symmetric states invariant. We consider an asymptotic limit of infinitely many copies and vanishingly small error, and analyze the symmetrizing cost, that is, the minimum cost of randomness per copy required for symmetrization. We prove that the symmetrizing cost of an arbitrary quantum state is equal to the relative entropy of frameness, thereby providing it with a direct operational meaning.

9 pages, 2 figures. Sections are restructured, presentations improved, result unchanged, proofs modified. Comments are welcome

References in corpus (8)

• Reference frames, superselection rules, and quantum information
• On the quantum, classical and total amount of correlations in a quantum state
• The resource theory of quantum reference frames: manipulations and monotones
• Extending Noether's theorem by quantifying the asymmetry of quantum states
• Measuring the quality of a quantum reference frame: the relative entropy of frameness
• The WAY theorem and the quantum resource theory of asymmetry
• Does nonlinear metrology offer improved resolution? Answers from quantum information theory
• Random subspaces for encryption based on a private shared Cartesian frame

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• Superdense Coding in Resource Theory of Asymmetry
• Randomness cost of symmetric twirling
• Quantifying Algebraic Asymmetry of Hamiltonian Systems
• When quantum memory is useful for dense coding
• Mathematical methods for resource-based type theories