Abstract
We generalize a quantum communication protocol introduced by Bartlett et al. [New J. Phys. 11, 063013 (2009)], in which two parties communicating do not share a classical reference frame, to the case where changes of their reference frames form a one-dimensional noncompact Lie group. Alice sends to Bob the state , where is the state of the system Alice wishes to communicate and is the state of an ancillary system serving as a token of her reference frame. Because Bob is ignorant of the relationship between his reference frame and Alice's, he will describe the state as an average over all possible reference frames. Bob measures the reference token and applies a correction to the system Alice wished to communicate conditioned on the outcome of the measurement. The recovered state is decohered with respect to , the amount of decoherence depending on the properties of the reference token . We present an example of this protocol when Alice and Bob do not share a reference frame associated with the one-dimensional translation group and use the fidelity between and to quantify the success of the recovery operation.
- Received 2 January 2019
DOI:https://doi.org/10.1103/PhysRevA.99.052315
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