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arXiv · 2008.07811

Resource theory of superposition: State transformations

Gokhan Torun·Hüseyin Talha Şenyaşa·Ali Yildiz
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Abstract

A combination of a finite number of linear independent states forms superposition in a way that cannot be conceived classically. Here, using the tools of resource theory of superposition, we give the conditions for a class of superposition state transformations. These conditions strictly depend on the scalar products of the basis states and reduce to the well-known majorization condition for quantum coherence in the limit of orthonormal basis. To further superposition-free transformations of $d$-dimensional systems, we provide superposition-free operators for a deterministic transformation of superposition states. The linear independence of a finite number of basis states requires a relation between the scalar products of these states. With this information in hand, we determine the maximal superposition states which are valid over a certain range of scalar products. Notably, we show that, for $d\geq3$, scalar products of the pure superposition-free states have a greater place in seeking maximally resourceful states. Various explicit examples illustrate our findings.

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Gokhan Torun, Hüseyin Talha Şenyaşa, Ali Yildiz. 2021-03-17. Resource theory of superposition: State transformations. https://doi.org/10.1103/physreva.103.032416

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