Quantum Information Masking of Hadamard Sets

TL;DR

This paper investigates quantum information masking for Hadamard sets, demonstrating that any such set can be deterministically masked by a unitary operation and analyzing the conditions for masking combined states.

Contribution

It introduces the concept of Hadamard sets in quantum states and proves their maskability via unitary operations, expanding understanding of quantum masking.

Findings

Hadamard sets can be deterministically masked by unitary operations

Conditions for masking linear combinations of fixed states are characterized

Examples illustrate the masking process and its limitations

Abstract

We study quantum information masking of arbitrary dimensional states. Given a set of fixed reducing pure states, we study the linear combinations of them, such that they all have the same marginal states with the given ones. We define the so called Hadamard set of quantum states whose Gram-Schmidt matrix can be diagonalized by Hadamard unitary matrices. We show that any Hadamard set can be deterministically masked by a unitary operation. We analyze the states which can be masked together with the given Hadamard set using the result about the linear combinations of fixed reducing states. Detailed examples are given to illustrate our results.