Amplifying asymmetry with correlated catalysts

Abstract

We investigate the basic constraint on amplifying the asymmetry in quantum states with correlated catalysts. Here a correlated catalyst is a finite-dimensional auxiliary, which exactly preserves its reduced state while allowed to become correlated to the quantum system. Interestingly, we prove that under translationally invariant operations, catalysts in pure states are useless in any state transformation, while with a correlated catalyst in a mixed state, one can enlarge the set of accessible states from an initially asymmetric state. Moreover, we show that the power of a catalyst increases with its dimension, and further, with a large enough catalyst, a qubit state with arbitrarily small amount of asymmetry can be converted to any mixed qubit state. In doing so, we build a bridge between two important results concerning the restrictions on coherence conversion, the no-broadcasting theorem and the catalytic coherence. Our results may also apply to the constraints on coherence evolution in quantum thermodynamics, and to the distribution of timing information between quantum clocks.

arXiv commentAlmost published version

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Cited by in corpus (14)

• Catalytic quantum teleportation and beyond
• Catalysis of entanglement and other quantum resources
• Correlation in Catalysts Enables Arbitrary Manipulation of Quantum Coherence
• Arbitrary Amplification of Quantum Coherence in Asymptotic and Catalytic Transformation
• Catalysis in Action via Elementary Thermal Operations
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• Experimental Catalytic Amplification of Asymmetry
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• Unspeakable Coherence Concentration