Communicating without shared reference frames

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 ${\rho }_R\otimes {\rho }_S$, where ${\rho }_S$ is the state of the system Alice wishes to communicate and ${\rho }_R$ 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 ${\rho }_R\otimes {\rho }_S$ 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 ${\rho }_S^{\prime }$ is decohered with respect to ${\rho }_S$, the amount of decoherence depending on the properties of the reference token ${\rho }_R$. 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 ${\rho }_S$ and ${\rho }_S^{\prime }$ to quantify the success of the recovery operation.

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References in corpus (10)

• Reference frames, superselection rules, and quantum information
• Quantum mechanics and the covariance of physical laws in quantum reference frames
• Classical and quantum communication without a shared reference frame
• Quantum communication using a bounded-size quantum reference frame
• Relativistically invariant quantum information
• Changing quantum reference frames
• Quantum reference frames associated with non-compact groups: the case of translations and boosts, and the role of mass
• Communication between inertial observers with partially correlated reference frames
• Teleportation transfers only speakable quantum information
• Perfect tight quantum teleportation without a shared reference frame

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