Resource theory of superposition: State transformations

Torun G., Şenyaşa H. T., Yıldız A.

PHYSICAL REVIEW A, vol.103, no.3, 2021 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 103 Issue: 3
  • Publication Date: 2021
  • Doi Number: 10.1103/physreva.103.032416
  • Journal Name: PHYSICAL REVIEW A
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Chemical Abstracts Core, Compendex, INSPEC, zbMATH, DIALNET
  • Istanbul Technical University Affiliated: Yes


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 >= 3, scalar products of the pure superposition-free states have a greater place in seeking maximally resourceful states. Various explicit examples illustrate our findings.