No-compressing of quantum phase information

TL;DR

This paper investigates whether quantum phase information can be compressed and retrieved, concluding that quantum mechanics prohibits such compression of phase information from multiple equatorial qubits into fewer general qubits.

Contribution

It provides a theoretical proof that quantum phase information cannot be compressed from multiple equatorial qubits into fewer general qubits.

Findings

Quantum phase information cannot be compressed.

Compression of phase information violates quantum mechanics.

Theoretical proof of non-compressibility.

Abstract

We raise a general question of quantum information theory whether the quantum phase information can be compressed and retrieved. A general qubit contains both amplitude and phase information, while an equatorial qubit contains only a phase information. We study whether it is possible to compress the phase information of n equatorial qubits into m general qubits with m being less than n, and still those information can be retrieved perfectly. We prove that this process is not allowed by quantum mechanics.