Real quantum operations and state transformations

Abstract

Resource theory of imaginarity provides a useful framework to understand the role of complex numbers, which are essential in the formulation of quantum mechanics, in a mathematically rigorous way. In the first part of this article, we study the properties of ``real'' (quantum) operations both in single-party and bipartite settings. As a consequence, we provide necessary and sufficient conditions for state transformations under real operations and show the existence of ``real entanglement'' monotones. In the second part of this article, we focus on the problem of single copy state transformation via real quantum operations. When starting from pure initial states, we completely solve this problem by finding an analytical expression for the optimal fidelity of transformation, for a given probability of transformation and vice versa. Moreover, for state transformations involving arbitrary initial states and pure final states, we provide a semidefinite program to compute the optimal achievable fidelity, for a given probability of transformation.

9 pages. Close to published version

References in corpus (5)

• QuTiP 2: A Python framework for the dynamics of open quantum systems
• The resource theory of quantum reference frames: manipulations and monotones
• Resource theory of imaginarity: Quantification and state conversion
• Linking a distance measure of entanglement to its convex roof
• Positive maps and entanglement in real Hilbert spaces

Cited by in corpus (17)

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• Resource Theory of Imaginarity: New Distributed Scenarios
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• Quantifying imaginarity in terms of pure-state imaginarity
• Coherence manipulation in asymmetry and thermodynamics
• Coherence and imaginarity of quantum states
• Geometric-Like imaginarity: quantification and state conversion
• Quantifying the imaginarity via different distance measures
• Real randomized measurements for analyzing properties of quantum states
• Imaginarity measures induced by real part states and the complementarity relations
• Detecting quantum resources in a semi-device independent framework
• Off-resonant preservation and generation of imaginarity in distributed scenarios
• Strict advantage of complex quantum theory in a communication task
• Experimental certification of the nonlocal advantages of quantum imaginarity
• Measure of set imaginarity