Designing Quantum Information Processing via Structural Physical Approximation

TL;DR

This paper reviews how structural physical approximation can be used to implement and analyze non-physical quantum maps, aiding in entanglement detection and advancing quantum information processing techniques.

Contribution

It provides a comprehensive overview of the properties and applications of structural physical approximation in quantum information processing, highlighting recent progress.

Findings

Efficient methods for detecting entangled states have been developed.

Structural physical approximation enables approximation of non-physical maps with quantum channels.

Experimental demonstrations with photonic qubits validate practical applications.

Abstract

In quantum information processing it may be possible to have efficient computation and secure communication beyond the limitations of classical systems. In a fundamental point of view, however, evolution of quantum systems by the laws of quantum mechanics is more restrictive than classical systems, identified to a specific form of dynamics, that is, unitary transformations and, consequently, positive and completely positive maps to subsystems. This also characterizes classes of disallowed transformations on quantum systems, among which positive but not completely maps are of particular interest as they characterize entangled states, a general resource in quantum information processing. Structural physical approximation offers a systematic way of approximating those non-physical maps, positive but not completely positive maps, with quantum channels. Since it has been proposed as a method of detecting entangled states, it has stimulated fundamental problems on classifications of positive maps and the structure of Hermitian operators and quantum states, as well as on quantum measurement such as quantum design in quantum information theory. It has developed efficient and feasible methods of directly detecting entangled states in practice, for which proof-of-principle experimental demonstrations have also been performed with photonic qubit states. Here, we present a comprehensive review on quantum information processing with structural physical approximations and the related progress. The review mainly focuses on properties of structural physical approximations and their applications toward practical information applications.