Genuine activation of nonlocality: From locally available to locally hidden information

TL;DR

This paper demonstrates that certain orthogonal quantum states, initially distinguishable by local operations, can have their nonlocality activated through local measurements, enabling the hiding of information that requires entanglement to retrieve.

Contribution

It introduces the concept of activating nonlocality from locally distinguishable states without local redundancy, revealing new ways to hide information using local measurements.

Findings

Existence of orthogonal sets that become nonorthogonal when subsystems are discarded.

Local measurements can convert distinguishable states into indistinguishable ones.

Information can be hidden locally and retrieved only with entanglement.

Abstract

Quantum nonlocality has different manifestations that, in general, are revealed by local measurements of the parts of a composite system. In this paper, we study nonlocality arising from a set of orthogonal states that cannot be perfectly distinguished by local operations and classical communication (LOCC). Such a set is deemed nonlocal, for a joint measurement on the whole system is necessary for perfect discrimination of the states with certainty. On the other hand, a set of orthogonal states that can be perfectly distinguished by LOCC is believed to be devoid of nonlocal properties. Here, we show that there exist orthogonal sets that are locally distinguishable but without local redundancy (i.e., they become nonorthogonal on discarding one or more subsystems) whose nonlocality can be activated by local measurements. In particular, a state chosen from such a set can be locally converted, with certainty, into another state, the identity of which can now only be ascertained by global measurement and no longer by LOCC. In other words, a locally distinguishable set without local redundancy may be locally converted into a locally indistinguishable set with certainty. We also suggest an application, namely, local hiding of information, that allows us to locally hide locally available information without losing any part. Once hidden, the information in its entirety can only be retrieved using entanglement.