No-masking theorem for observables

TL;DR

This paper extends the no-masking theorem to quantum observables, showing the impossibility of universally masking an observable and revealing implications for quantum information security and conservation laws.

Contribution

It introduces the concept of masking observables, proves the non-existence of a universal masking operation for observables, and links this to quantum information conservation and cryptography.

Findings

Universal masking of arbitrary observables is impossible.

For qubits, masking relates to the SWAP operation.

No-bit commitment follows from the no-masking theorem.

Abstract

The no-masking theorem for quantum information proves that it is impossible to encode an arbitrary input state into a larger bipartite entangled state such that the full information is stored in the correlation but the individual subsystems have no information about the input state. Here, we ask the question: Is it possible to mask an observable such that the information about the observable is available in the joint system, but individual subsystems reveal nothing about the imprints of the observable? This generalizes the notion of masking to observables. We show that a universal unitary that can mask an arbitrary observable in any dimension does not exist. For a qubit system, we show that the masking operation for a given observable is locally unitarily connected to the SWAP operation. This suggests a conservation law for information content of observables that goes beyond the conservation laws under symmetry operations. Furthermore, we prove that the unconditional no-bit commitment result follows from the no-masking theorem for observables. Our results can have important applications in quantum information and quantum communication where we encode information not in states but in observables.