Resource theory of superposition : State transformations

Author / Creator

Quantum 2020 (2020)

Conferences

Quantum 2020 QF-1: Quantum Foundations (2020)

Available as

Online

Summary

A combination of a finite number of linear independent states forms superposition in a way that cannot be conceived classically. We give the conditions for a class of superposition state transforma...

A combination of a finite number of linear independent states forms superposition in a way that cannot be conceived classically. We give the conditions for a class of superposition state transformations by using the tools of resource theory of superposition. 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 scalar products of the pure superposition-free states have a greater place in seeking maximally resourceful states for d > 2.

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