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arXiv:1508.03341 · Physical Review A

Communication between inertial observers with partially correlated reference frames

Mehdi Ahmadi, Alexander R. H. Smith, Andrzej Dragan

Published Dec 10, 2015• 24 citations
arXivHTMLPDF

Abstract

In quantum communication protocols the existence of a shared reference frame between two spatially separated parties is normally presumed. However, in many practical situations we are faced with the problem of misaligned reference frames. In this paper, we study communication between two inertial observers who have partial knowledge about the Lorentz transformation that relates their frames of reference. Since every Lorentz transformation can be decomposed into a pure boost followed by a rotation, we begin by analyzing the effects on communication when the parties have partial knowledge about the transformation relating their frames, when the transformation is either a rotation or a pure boost. This then enables us to investigate how the efficiency of communication is affected due to partially correlated inertial reference frames related by an arbitrary Lorentz transformation. Furthermore, we show how the results of previous studies where reference frames are completely uncorrelated are recovered from our results in appropriate limits.

DOI
10.1103/physreva.92.062319

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In quantum communication protocols the existence of a shared reference frame between two spatially separated parties is normally presumed. However, in many practical situations we are faced with the problem of misaligned reference frames. In this paper, we study communication between two inertial observers who have partial knowledge about the Lorentz transformation that relates their frames of reference. Since every Lorentz transformation can be decomposed into a pure boost followed by a rotation, we begin by analyzing the effects on communication when the parties have partial knowledge about the transformation relating their frames, when the transformation is either a rotation or a pure boost. This then enables us to investigate how the efficiency of communication is affected due to partially correlated inertial reference frames related by an arbitrary Lorentz transformation. Furthermore, we show how the results of previous studies where reference frames are completely uncorrelated are recovered from our results in appropriate limits.
We show how to reliably encode quantum information and send it between two arbitrary general-relativistic observers without a shared reference frame. Information stored in a quantum field will inevitably be destroyed by an unknown Bogoliubov transformation relating the observers. However, certain quantum correlations between different, independent fields will be preserved, no matter what transformation is applied. We show how to efficiently use these correlations in communication between arbitrary observers.
In this paper we show that the quantum channel between two inertial observers who transmit quantum information by sending realistic photonic wave packets is a well-studied channel in quantum Shannon theory: the Pauli channel. The parameters of the Pauli channel and therefore its classical and quantum capacity depend on the magnitude of the Lorentz boost relating the two observers. The most striking consequence is that two inertial observers whose Pauli channel has initially zero quantum capacity can achieve nonzero quantum communication rates (reaching, in principle, its maximal value, equal to 1) by applying a boost in the right direction. This points to a fundamental connection between quantum channel capacities and special relativity.
Abstract Quantum reference frame as in the example of observing a quantum particle from another has been a topic of much recent interest. Quantum spatial translations, quantum rotations, and quantum Lorentz boosts in the sense have been studied to some extent. The article aims at using a consistent formulation of all that to give a full picture of what would be the symmetry of Special Quantum Relativity as special relativity as seen from quantum particles. We first look at a direct formulation of the mathematical quantum analog of any classical one-parameter Lie group of such transformations suggested by our Heisenberg picture thinking of quantum mechanics. A quantum rotation and a quantum Lorentz boost are presented. Analysis of the compositions of two such transformations shows unnatural results with various problems, especially with their commutators. From a physical point of view, we argue for a modified formulation. A quantum reference frame transformation, as the description of firstly the spacetime position of an object, idealized as a particle, as seen from another has to involve a full set of four-coordinate quantum quantities instead of one in a single coordinate only. Unlike the classical case, we illustrate that the analog of a change by the zero classical coordinate values has nontrivial effects in the transformation. A consistent full picture of the symmetry is then obtained. Results that could be interpreted essentially as the quantum analogs of the translation of a single coordinate observable, including angular ones for a rotation or a boost, can be retrieved from that but only as approximations. Under the traditional perspective of relativity symmetry being about spacetime reference frames, our task is then completed. We further look at the quantum version of Heisenberg–Weyl symmetry and perspectives on its relation with the subject matter and argue for the necessity of our background noncommutative geometric perspective for a conceptual consistent story.
This paper was concerned with the spin-momentum correlation in single-particle quantum states, which is described by the mixed states under Lorentz transformations. For convenience, instead of using the superposition of momenta we use only two momentum eigen states (p1 and p2) that are perpendicular to the Lorentz boost direction. Consequently, in 2D momentum subspace we show that the entanglement of spin-momentum in the moving frame depends on the angle between them. Therefore, when spin and momentum are perpendicular the measure of entanglement is not observer-dependent quantity in inertial frame. Likewise, we have calculated the measure of entanglement (by using the concurrence) and has shown that entanglement decreases with respect to the increasing of observer velocity. Finally, we argue that, Wigner rotation is induced by Lorentz transformations can be realized as controlling operator.