Relativistic entanglement of single and two particle systems

One of the defining features of quantum theory is entanglement, the notion that quantum systems can display correlations that are impossible from the classical point of view. In quantum information theory entanglement has come to be recognised as a physical resource that enables new technologies that perform information processing 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 both 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 dependence 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 from 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 understanding of the behaviour of entanglement. We lastly discuss the common view according to which Lorentz boosts leave the total entanglement of the state invariant

Thomas--Wigner rotation as a holonomy for spin-1/21/2 particles

The Thomas--Wigner rotation (TWR) results from the fact that a combination of boosts leads to a non-trivial rotation of a physical system. Its origin lies in the structure of the Lorentz group. In this article we discuss the idea that the TWR can be understood in the geometric manner, being caused by the non-trivially curved relativistic momentum space, i.e. the mass shell, seen as a Riemannian manifold. We show explicitly how the TWR for a massive spin-$1/2$ particle can be calculated as a holonomy of the mass shell. To reach this conclusion we recall how to construct the spin bundle over the mass shell manifold.Comment: 25 pages, 3 figure

Generation of maximally entangled states with sub-luminal Lorentz boost

Recent work has studied entanglement between the spin and momentum components of a single spin-1/2 particle and showed that maximal entanglement is obtained only when boosts approach the speed of light. Here we extend the boost scenario to general geometries and show that, intriguingly, maximal entanglement can be achieved with boosts less than the speed of light. Boosts approaching the speed of light may even decrease entanglement. We also provide a geometric explanation for this behavior

Entanglement and nonlocality of a single relativistic particle

Recent work has argued that the concepts of entanglement and nonlocality must be taken seriously even in systems consisting of only a single particle. These treatments, however, are nonrelativistic and, if single particle entanglement is fundamental, it should also persist in a relativistic description. Here we consider a spin-1/2 particle in a superposition of two different velocities as viewed by an observer in a different relativistically-boosted inertial frame. We show that the entanglement survives right up to the speed of light and that the boosted observer would see single-particle violations of Bell's inequality. We also discuss how quantum gates could be implemented in this way and the possible implications for quantum information processing.Comment: 4 page

Maps generated by entangled momenta: exploring spin entanglement in relativity

We study relativistic entanglement of a bipartite system consisting of massive spin-1=2 particles with momenta. The spin state is described by the maximally entangled Bell state and momenta are given by entangled Gaussian distributions. We conceptualize the dependency between spin and momentum in relativity along the lines of controlled operations in quantum information theory. This leads to a systematic study of maps that Wigner rotations generate on the spin degree of freedom of the total system in different boost scenarios. We use a visualization tool from quantum information theory in order to get better insight into how and why the entanglement changes in different boost geometries

Behaviour of entanglement and Cooper pairs under relativistic boosts

Recent work has shown how single-particle entangled states are transformed when boosted in relativistic frames for certain restricted geometries. Here we extend that work to consider completely general inertial boosts. We then apply our single particle results to multiparticle entanglements by focussing on Cooper pairs of electrons. We show that a standard Cooper pair state consisting of a spin-singlet acquires spin-triplet components in a relativistically boosted inertial frame, regardless of the geometry. We also show that, if we start with a spin-triplet pair, two out of the three triplet states acquire a singlet component, the size of which depends on the geometry. This transformation between the different singlet and triplet superconducting pairs may lead to a better understanding of unconventional superconductivity.Comment: 5 pages, 2 figure

Relativistic entanglement of two particles driven by continuous product momenta

In this paper we explore the entanglement of two relativistic spin-1/2 particles with continuous momenta. The spin state is described by the Bell state and the momenta are given by Gaussian distributions of product form. Transformations of the spins are systematically investigated in different boost scenarios by calculating the orbits and concurrence of the spin degree of freedom. By visualizing the behavior of the spin state we get further insight into how and why the entanglement changes in different boost situations

Behavior of Werner states under relativistic boosts

We study the structure of maps that Lorentz boosts induce on the spin degree of freedom of a system consisting of two massive spin-1/2 particles. We consider the case where the spin state is described by the Werner state and the momenta are discrete. Transformations on the spins are systematically investigated in various boost scenarios by calculating the orbit and concurrence of the bipartite spin state with different kinds of product and entangled momenta. We confirm the general conclusion that Lorentz boosts causes non-trivial behaviour of bipartite spin entanglement. Visualization of the evolution of the spin state is shown to be valuable in explaining the pattern of concurrence. The idealized model provides a basis of explanation in terms of which phenomena in systems involving continuous momenta can be understood