Must We Hide?

Lawrence M. Krauss

David Peter Divincenzo, Debbie Leung, Barbara M. Terhal

We expand on our work on quantum data hiding - hiding classical data among parties who are restricted to performing only local quantum operations and classical communication (LOCC). We review our scheme that hides one bit between two parties using Bell (1964) states, and we derive upper and lower bounds on the secrecy of the hiding scheme. We provide an explicit bound showing that multiple bits can be hidden bitwise with our scheme. We give a preparation of the hiding states as an efficient quantum computation that uses at most one ebit of entanglement. A candidate data-hiding scheme that does not use entanglement is presented. We show how our scheme for quantum data hiding can be used in a conditionally secure quantum bit commitment scheme.

Yi-Kai Liu

Yun Li

David Peter Divincenzo, Debbie Leung, Barbara M. Terhal

Abstract — We expand on our work on Quantum Data Hiding [1] – hiding classical data among parties who are restricted to performing only local quantum operations and classical communication (LOCC). We review our scheme that hides one bit between two parties using Bell states, and we derive upper and lower bounds on the secrecy of the hiding scheme. We provide an explicit bound showing that multiple bits can be hidden bitwise with our scheme. We give a preparation of the hiding states as an efficient quantum computation that uses at most one ebit of entanglement. A candidate data hiding scheme that does not use entanglement is presented. We show how our scheme for quantum data hiding can be used in a conditionally secure quantum bit commitment scheme.

Abhay Srivastav, Arun Kumar Pati

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.