The masking condition for quantum state in two-dimensional Hilbert space

TL;DR

This paper investigates the conditions under which quantum information in a single qubit can be masked within two-dimensional Hilbert space, providing mathematical criteria and analyzing special cases.

Contribution

It establishes the necessary and sufficient conditions for quantum state masking in two-dimensional space and characterizes properties of maskable states, including non-orthogonal and orthogonal cases.

Findings

Quantum information can be masked if state coefficients satisfy specific equations.

Non-orthogonal maskable states share the same number of terms and basis.

Orthogonal maskable states are exemplified with detailed images.

Abstract

This paper focuses on quantum information masking for quantum state in two-dimensional Hilbert space. We present a system of equations as the condition of quantum information masking. It is shown that quantum information contained in a single qubit state can be masked, if and only if the coefficients of quantum state satisfy the given system of equations. By observing the characteristics of non-orthogonal maskable quantum states, we obtain a related conclusion, namely, if two non-orthogonal two-qubit quantum states can mask a single qubit state, they have the same number of terms and the same basis. Finally, for maskable orthogonal quantum states, we analyze two special examples and give their images for an intuitive description.