Restoration of Quantum State in Dephasing Channel

TL;DR

This paper presents a scheme to fully restore unknown multi-qubit quantum states affected by phase damping noise, using a universal reversal operation, with potential extensions beyond standard methods.

Contribution

It introduces an explicit recovery scheme for multi-qubit states under phase damping, including a universal unitary reversal operation and non-RU methods for certain entangled states.

Findings

Success probability of 1 for state recovery

Explicit construction of RU Kraus decomposition for common bath

Non-RU methods can restore some entangled states

Abstract

In this paper, we propose an explicit scheme to fully recover a multiple-qubit state subject to a phase damping noise. We establish the theoretical framework and the operational procedure to restore an unknown initial quantum state for an N-qubit model interacting with either individual baths or a common bath. We give an explicit construction of the random unitary (RU) Kraus decomposition for an N-qubit model interacting with a common bath. We also demonstrate how to use only one unitary reversal operation to restore an arbitrary state with phase damping noise. In principle, the initial state can always be recovered with a success probability of 1. Interestingly, we found that non-RU decomposition can also be used to restore some particular entangled states. This may open a new path to restore a quantum state beyond the standard RU scheme.