Randomness cost of masking quantum information and the information conservation law

TL;DR

This paper investigates the fundamental randomness requirements for quantum information masking, disproves a previous geometric conjecture, and establishes a lower bound on the randomness cost based on information conservation laws.

Contribution

It provides an algebraic analysis of quantum masking, disproves a geometric conjecture, and derives a lower bound on the randomness cost related to information distribution.

Findings

Disproved the geometric conjecture about unitarily maskable states.

Established a lower bound on the randomness cost of quantum masking.

Linked the randomness cost to the evenness of information distribution and conservation laws.

Abstract

Masking quantum information, which is impossible without randomness as a resource, is a task that encodes quantum information into bipartite quantum state while forbidding local parties from accessing to that information. In this work, we disprove the geometric conjecture about unitarily maskable states [K. Modi et al., Phys. Rev. Lett. 120, 230501 (2018)], and make an algebraic analysis of quantum masking. First, we show a general result on quantum channel mixing that a subchannel's mixing probability should be suppressed if its classical capacity is larger than the mixed channel's capacity. This constraint combined with the well-known information conservation law, a law that does not exist in classical information theory, gives a lower bound of randomness cost of masking quantum information as a monotone decreasing function of evenness of information distribution. This result provides a consistency test for various scenarios of fast scrambling conjecture on the black hole evaporation process. The results given here are robust to incompleteness of quantum masking.