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arXiv:quant-ph/0608209 · Journal of Physics A Mathematical and Theoretical

Quantum entanglement of electromagnetic field in non-inertial reference frames

Yi Ling, Song Lin He, Weigang Qiu, Hongbao Zhang

Published Jul 12, 2007• 53 citations
arXivHTMLPDF

Abstract

Recently relativistic quantum information has received considerable attention due to its theoretical importance and practical application. In particular, quantum entanglement in non-inertial reference frames has been studied for scalar and Dirac fields. As a further step along this line, we here shall investigate quantum entanglement of electromagnetic field in non-inertial reference frames. In particular, the entanglement of the photon helicity entangled state is extensively analysed. Interestingly, the resultant logarithmic negativity and mutual information remain the same as those for inertial reference frames, which is completely different from that previously obtained for the particle number entangled state.

DOI
10.1088/1751-8113/40/30/024

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•Sep 19, 2008•1 citation
Recently relativistic quantum information has received considerable attention due to its theoretical importance and practical application. In particular, quantum entanglement in non-inertial reference frames has been studied for scalar and Dirac fields. As a further step along this line, we here shall investigate quantum entanglement of electromagnetic field in non-inertial reference frames. In particular, the entanglement of the photon helicity entangled state is extensively analysed. Interestingly, the resultant logarithmic negativity and mutual information remain the same as those for inertial reference frames, which is completely different from that previously obtained for the particle number entangled state.
One of the most fundamental phenomena of quantum physics is entanglement. It describes an inseparable connection between quantum systems, and properties thereof. In a quantum mechanical description even systems far apart from each other can share a common state. This entanglement of the subsystems, although arising from mathematical principles, is no mere abstract concept, but can be tested in experiment, and be utilized in modern quantum information theory procedures, such as quantum teleportation. In particular, entangled states play a crucial role in testing our understanding of reality, by violating Bell inequalities. While the role of entanglement is well studied in the realm of nonrelativistic quantum mechanics, its significance in a relativistic quantum theory is a relatively new field of interest. In this work the consequences of a relativistic description of quantum entanglement are discussed. We analyze the representations of the symmetry groups of special relativity, i.e. of the Lorentz group, and the Poincaré group, on the Hilbert space of states. We describe how unitary, irreducible representations of the Poincaré group for massive spin 1/2 particles are constructed from representations of Wigner's little group. We then proceed to investigate the role of the Wigner rotations in the transformation of quantum states under a change of inertial reference frame. Considering different partitions of the Hilbert space of 2 particles, we find that the entanglement of the quantum states appears different in different inertial frames, depending on the form of the states, the chosen inertial frames, and the particular choice of partition. It is explained, how, despite of this, the maximally possible violation of Bell inequalities is frame independent, when using appropriate spin observables, which are related to the Pauli-Ljubanski vector, a Casimir operator of the Poincaré group.
Given the recent interest in perspectival quantum reference frames (QRFs), we ask how quantum properties in the perspectival picture relate to their global (non-perspectival) counterparts. Such a connection could allow established quantum information to be understood from the perspective of QRFs. Specifically, we find sufficient conditions under which global entanglement decomposes into a combination of perspectival entanglement and coherence -- a phenomenon that we call entanglement transference. We apply this result to non-inertial QRFs, revisiting the problem of acceleration-induced entanglement degradation. We find that entanglement degradation in the perspectival picture can be offset by an increase in coherence resources. This novel insight into (relativistic) quantum resource transformations suggests that QRFs may play a useful role in understanding more general quantum resource and quantum information phenomena.
The majority of current understanding of the quantum correlations is in the field of non-relativistic quantum mechanics. To develop quantum information and computation tasks fully, one must inevitably take into account the relativistic effects. In this regard, the spin is one of the central tools. For this purpose, it is of paramount importance to understand and characterize fully the theory of spin in relativistic quantum information theory where the spin states act as qubit. This area is still far from being resolved. As a result, this article will explore the recent studies of the concepts of the spin and spin quantum correlations in inertial frames and some apparent paradoxes regarding this concept. We will mainly focus on the problem of characterizing the spin, reduced spin density matrices and spin quantum correlations in inertial reference frames and the apparent paradoxes involved therein. Another important aspect is the use of tools of quantum field theory to extend several concepts in non-relativistic domain to relativistic one. In this regard, we analyze the development of the theory of relativistic secret sharing and a correlation measure namely the entanglement of purification.
One of the defining features of quantum theory is entanglement, the notion that quantum systems can display correlations that are impossible from the classical \npoint of view. In quantum information theory entanglement has come to be recognised as a physical resource that enables new technologies that perform information \nprocessing tasks which are beyond the limits of the classical realm. It has been realised only recently that entanglement is dependent on the frame of reference in \nboth inertial and accelerated systems. In this thesis, we investigate the relativistic entanglement of massive spin-1=2 particles in inertial frames by focussing on the \ndependence of entanglement on the geometry of the underlying boost scenario. We first explore the ‘qubit’ of the relativistic setting: a single particle with spin and momentum, with momentum given by a Gaussian distribution. We study the system in a variety of different boost scenarios, analysing the behaviour of entanglement \nfrom a geometric point of view. The spin-spin entanglement of two particle systems is then surveyed for many different discrete product and entangled momenta, with the spins in the Werner state. We also extend the analysis to continuous momentum states and study them in a variety of geometries. The results obtained from the analysis of discrete states are applied to continuous states, leading to a better \nunderstanding of the behaviour of entanglement. We lastly discuss the common view according to which Lorentz boosts leave the total entanglement of the state invariant.
This thesis considers entanglement, an important resource for quantum information processing tasks, while taking into account the theory of relativity. Not only is this a more complete description of quantum information, but it is necessary to fully understand quantum information processing tasks done by systems in arbitrary motion. \n \nIt is shown that accelerated measurements on the vacuum of a free Dirac spinor field results in an entangled state for an inertial observer. The physical mechanism at work is the Davies-Unruh effect. The entanglement produced increases as a function of the acceleration, reaching maximal entanglement in the asymptotic limit of infinite acceleration. \n \nThe dynamics of entanglement between two Unruh-DeWitt detectors, one stationary and the other undergoing non-uniform acceleration, was studied numerically. In the ultraweak coupling limit, the entanglement decreases as a function of time for the parameters considered and decreases faster than if the moving detector had had a uniform acceleration.