arXiv subjects

Hüseyin Talha Şenyaşa

Publications and source records attributed to Hüseyin Talha Şenyaşa.

2 recordsLinked to original sources

arXiv2022

Golden states in resource theory of superposition

One central study that constitutes a major branch of quantum resource theory is the hierarchy of states. This provides a broad understanding of resourcefulness in certain tasks in terms of efficiency. Here, we investigate the maximal superposition states, i.e., golden states, of the resource theory of superposition. Golden states in the resource theory of coherence are very well established; however, it is a very challenging task for superposition due to the nonorthogonality of the basis states. We show that there are sets of inner product settings that admit a golden state in high-dimensional systems. We bridge the gap between the resource theory of superposition and coherence in the context of golden states by establishing a continuous relation by means of a Gram matrix. In addition, immediate corollaries of our framework provide a representation of maximal states which reduces to the maximal state of the coherence in the orthonormal limit of pure basis states.

quant-ph↗

arXiv2021

Resource theory of superposition: State transformations

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.

quant-ph↗