Information Bleaching, No-Hiding Theorem and Indefinite Causal Order

TL;DR

This paper explores how indefinite causal order affects quantum information hiding, showing that information can be hidden in correlations without violating the no-hiding theorem, with implications for quantum coherence and entanglement preservation.

Contribution

It demonstrates that quantum information can be hidden in correlations under indefinite causal order without violating the no-hiding theorem and discusses implications for quantum information preservation.

Findings

Quantum information can be hidden in correlations with indefinite causal order.

Entanglement cannot be preserved under hiding maps with indefinite causal order.

Entanglement fidelity remains high despite entanglement loss.

Abstract

The information bleaching refers to any physical process that removes quantum information from the initial state of the physical system. The no-hiding theorem proves that if information is lost from the initial system, then it cannot remain in the bipartite quantum correlation and must be found in the remainder of the Hilbert space. We show that when hiding map acts on the input state in the presence of indefinite causal order, then it is possible to hide quantum information in the correlation. One may ask, does it then violate the no-hiding theorem? We analyse this question and argue that in the extended Hilbert space, it will still respect the no-hiding theorem. We also discuss how to mask quantum information using superposition of two hiding maps. Our results can have interesting implications in preserving the fidelity of information, preservation of quantum coherence and work extraction in the presence of two hiding maps with indefinite causal order. Furthermore, we apply the hiding maps in the presence of indefinite causal order on half of an entangled pair and show that entanglement cannot be preserved. Finally, we discuss that even though quantum entanglement is destroyed, the entanglement fidelity under indefinite causal order is non-zero and can approach close to one.