Decoherence-full subsystems and the cryptographic power of a private shared reference frame

Bartlett, Stephen D.; Rudolph, Terry; Spekkens, Robert W.

Decoherence-full subsystems and the cryptographic power of a private shared reference frame

Authors

Bartlett, Stephen D.

Rudolph, Terry

Spekkens, Robert W.

Description

We show that private shared reference frames can be used to perform private quantum and private classical communication over a public quantum channel. Such frames constitute a novel type of private shared correlation (distinct from private classical keys or shared entanglement) useful for cryptography. We present optimally efficient schemes for private quantum and classical communication given a finite number of qubits transmitted over an insecure channel and given a private shared Cartesian frame and/or a private shared reference ordering of the qubits. We show that in this context, it is useful to introduce the concept of a decoherence-full subsystem, wherein every state is mapped to the completely mixed state under the action of the decoherence.
13 pages, published version