Accessing inaccessible information via quantum indistinguishability

In this paper we present and analyze an information-theoretic task that consists in learning a bit of information by spatially moving the "target" particle that encodes it. We show that, on one hand, the task can be solved with the use of additional independently prepared quantum particles, only if these are indistinguishable from the target particle. On the other hand, the task can be solved with the use of distinguishable quantum particles, only if they are entangled with the target particle. Our task thus provides a new example in which the entanglement apparently inherent to independently prepared indistinguishable quantum particles is put into use for information processing. Importantly, a novelty of our protocol lies in that it does not require any spatial overlap between the involved particles. Besides analyzing the class of quantum-mechanical protocols that solve our task, we gesture towards possible ways of generalizing our results and of applying them in cryptography.