Quantum communication using a bounded-size quantum reference frame

TL;DR

This paper investigates how limited quantum reference frames affect quantum communication, characterizing the induced decoherence and proposing near-optimal decoding schemes for different reference frame types.

Contribution

It introduces a near-optimal decoding operation for bounded-size quantum reference frames and compares two implementation methods, with explicit analysis for single-qubit systems.

Findings

Decoding schemes are near-optimal for transmitting information with bounded reference frames.

Two distinct implementations of decoding are identified and analyzed.

Explicit characterizations are provided for single-qubit systems and common reference frame types.

Abstract

Typical quantum communication schemes are such that to achieve perfect decoding the receiver must share a reference frame with the sender. Indeed, if the receiver only possesses a bounded-size quantum token of the sender's reference frame, then the decoding is imperfect, and we can describe this effect as a noisy quantum channel. We seek here to characterize the performance of such schemes, or equivalently, to determine the effective decoherence induced by having a bounded-size reference frame. We assume that the token is prepared in a special state that has particularly nice group-theoretic properties and that is near-optimal for transmitting information about the sender's frame. We present a decoding operation, which can be proven to be near-optimal in this case, and we demonstrate that there are two distinct ways of implementing it (corresponding to two distinct Kraus decompositions). In one, the receiver measures the orientation of the reference frame token and reorients the system appropriately. In the other, the receiver extracts the encoded information from the virtual subsystems that describe the relational degrees of freedom of the system and token. Finally, we provide explicit characterizations of these decoding schemes when the system is a single qubit and for three standard kinds of reference frame: a phase reference, a Cartesian frame (representing an orthogonal triad of spatial directions), and a reference direction (representing a single spatial direction).