Real quantum operations and state transformations

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 singl...

Full description

Saved in:
Bibliographic Details
Published in:New journal of physics 2023-09, Vol.25 (9), p.93043
Main Authors: Varun Kondra, Tulja, Datta, Chandan, Streltsov, Alexander
Format: Article
Language:English
Subjects:
Accuracy
Complex numbers
Control theory
Hilbert space
Physics
Quantum entanglement
Quantum mechanics
Quantum physics
real quantum operations
resource theory of imaginarity
stochastic approximate state conversion
Transformations
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:1367-2630
1367-2630
DOI:10.1088/1367-2630/acf9c4