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arXiv:1210.3040 · Physical Review A

Higher entanglement and fidelity with a uniformly accelerated partner via nonorthogonal states

Graham White

Published Sep 27, 2012• 0 citations
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Abstract

We show that nonorthogonal states achieve a higher level of entanglement when one party undergoes uniform acceleration. We also show that in this regime nonorthogonal states achieve a higher fidelity for teleportation. A quantum field as observed by an observer confined to a Rindler wedge acts as an open system. When one traces over the field modes in the causally disconnected region of space time, one finds that, for a qubit derived from the modes of a scalar field, the effective state space of a qubit is deformed. In order to show this we numerically calculate the Bures angle between states as seen by an accelerating observer. We also derive the Bures metric of an effective qubit in the limit of low accelerations. In order to show that the deformation is not just a coordinate transform, we calculate the scalar curvature of the effective Bures metric. We see that the effective Bures metric loses its isotropic nature. Despite taking the limit of low accelerations, our results are also relevant to large gravitational fields.

DOI
10.1103/physreva.86.032340

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We show that nonorthogonal states achieve a higher level of entanglement when one party undergoes uniform acceleration. We also show that in this regime nonorthogonal states achieve a higher fidelity for teleportation. A quantum field as observed by an observer confined to a Rindler wedge acts as an open system. When one traces over the field modes in the causally disconnected region of space time, one finds that, for a qubit derived from the modes of a scalar field, the effective state space of a qubit is deformed. In order to show this we numerically calculate the Bures angle between states as seen by an accelerating observer. We also derive the Bures metric of an effective qubit in the limit of low accelerations. In order to show that the deformation is not just a coordinate transform, we calculate the scalar curvature of the effective Bures metric. We see that the effective Bures metric loses its isotropic nature. Despite taking the limit of low accelerations, our results are also relevant to large gravitational fields.
A central aim of relativistic quantum information (RQI) is the investigation of quantum information tasks and resources taking into account the relativistic aspects of nature. More precisely, it is of fundamental interest to understand how the storage, manipulation, and transmission of information utilizing quantum systems are influenced by the fact that these processes take place in a relativistic spacetime. In particular, many studies in RQI have been focused on the effects of non-uniform motion on entanglement, the main resource of quantum information protocols. Early investigations in this direction were performed in highly idealized settings that prompted questions as to the practical accessibility of these results. To overcome these limitations it is necessary to consider quantum systems that are in principle accessible to localized observers. In this thesis we present such a model, the rigid relativistic cavity, and its extensions, focusing on the effects of motion on entanglement and applications such as quantum teleportation. We study cavities in (1+1) dimensions undergoing non-uniform motion, consisting of segments of uniform acceleration and inertial motion of arbitrary duration that allow the involved velocities to become relativistic. The transitions between segments can be sharp or smooth and higher dimensions can be incorporated. The primary focus lies in the Bogoliubov transformations of the quantum fields, real scalar fields or Dirac fields, confined to the cavities. The Bogoliubov transformations change the particle content and the occupation of the energy levels of the cavity. We show how these effects generate entanglement between the modes of the quantum fields inside a single cavity for various initial states. The entanglement between several cavities, on the other hand, is degraded by the non-uniform motion, influencing the fidelity of tasks such as teleportation.
We consider a continuous-variable quantum teleportation protocol between a uniformly accelerated sender in the right Rindler wedge, a conformal receiver restricted to the future light cone, and an inertial observer in the Minkowski vacuum. Using a nonperturbative quantum circuit model, the accelerated observer interacts unitarily with the Rindler modes of the field, thereby accessing entanglement of the vacuum as a resource. We find that a Rindler-displaced Minkowski vacuum state prepared and teleported by the accelerated observer appears mixed according to the inertial observer, despite a reduction of the quadrature variances below classical limits. This is a surprising result, since the same state transmitted directly from the accelerated observer appears as a pure coherent state to the inertial observer. The decoherence of the state is caused by an interplay of opposing effects as the acceleration increases: the reduction of vacuum noise in the output state for a stronger entanglement resource, constrained by the amplification of thermal noise due to the presence of Unruh radiation.
The entanglement between two modes of free scalar and Dirac fields as seen by two relatively accelerated observers has been investigated. It is found that the same initial entanglement for an initial state parameter $\ensuremath{\alpha}$ and its ``normalized partner'' $\sqrt{1\ensuremath{-}{\ensuremath{\alpha}}^{2}}$ will be degraded by the Unruh effect along two different trajectories except for the maximally entangled state, which just shows the inequivalence of the quantization for a free field in Minkowski and Rindler coordinates. In the infinite-acceleration limit, the state does not have distillable entanglement for any $\ensuremath{\alpha}$ for the scalar field, but always remains entangled to a degree that is dependent on $\ensuremath{\alpha}$ for the Dirac field. It is also interesting to note that in this limit the mutual information equals just half of the initial mutual information; this result is independent of $\ensuremath{\alpha}$ and the type of field.
We have studied entanglement between two Dirac modes respectively observed by two independently accelerated observers. Due to Unruh effect, the entanglement degrades, but residual nonzero entanglement remains even when the accelerations of both observers are infinite. We have also investigated quantum teleportation using entangled Dirac modes, and calculated the fidelities in various cases. In general, the fidelity depends on the single-qubit state γ∣0⟩+δ∣1⟩γ|0\rangle +δ|1\rangleγ∣0⟩+δ∣1⟩ to be teleported, as well as which Bell state to use. In the limit that both accelerations are infinite, the average fidelity in using $|ϕ^\pm\rangle\equiv\frac{1}{2}(|00\rangle\pm |11\rangle) $ is 34\frac{3}{4}43​, while that in using $|ψ^\pm\rangle\equiv \frac{1}{2} (|01\rangle\pm |10\rangle) $ is 12+∣γ∣2∣δ∣2\frac{1}{2} + |γ|^2 |δ|^221​+∣γ∣2∣δ∣2.
We study how an arbitrary Gaussian state of two localized wave packets, prepared in an inertial frame of reference, is described by a pair of uniformly accelerated observers. We explicitly compute the resulting state for arbitrarily chosen proper accelerations of the observers and independently tuned distance between them. To do so, we introduce a generalized Rindler frame of reference and analytically derive the corresponding state transformation as a Gaussian channel. Our approach provides several new insights into the phenomenon of vacuum entanglement such as the highly nontrivial effect of spatial separation between the observers including sudden death of entanglement. We also calculate the fidelity of the two-mode channel for nonvacuum Gaussian states and obtain bounds on classical and quantum capacities of a single-mode channel. Our framework can be directly applied to any continuous variable quantum information protocol in which the effects of acceleration or gravity cannot be neglected.
Emission of photons by atoms can occur into modes which extend into a region causally disconnected with the emitter.For example, a uniformly accelerated ground-state atom emits a photon into the Unruh-Minkowski mode which is exponentially larger in the causally disconnected region.This makes an impression that photon emission is acausal.Here we show that conventional quantum optical analysis yields that a detector atom will not detect the emitted photon in the region noncausally connected with the emitter.However, joint excitation probability of atoms in the causally disconnected regions can be correlated due to entanglement of Minkowski vacuum and be much larger than the product of independent excitation probabilities.Moreover, atoms uniformly accelerated in the same Rindler wedge cannot become simultaneously excited without changing the state of the field, that is, the Unruh-Minkowski photon emitted by one atom cannot be absorbed by the other atom.We discuss examples demonstrating interesting features of Minkowski vacuum entanglement.