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International Journal of Modern Physics D

Entanglement and quantum teleportation in terms of Dirac modes observed by accelerated observers

Yue Dai, Yu Shi

Published Dec 1, 2023• 0 citations
Publisher

Abstract

In this paper, we have studied entanglement between two Dirac modes observed, respectively, by two independently accelerated observers. Due to Unruh effect, the entanglement degrades, but residual entanglement remains in the limit of infinite accelerations. We have also investigated quantum teleportation using entangled Dirac modes, and calculated the fidelities in various cases. In general, the fidelity depends on both the single-qubit state and the Bell state used in the teleportation.

DOI
10.1142/s0218271823501043

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In this paper, we have studied entanglement between two Dirac modes observed, respectively, by two independently accelerated observers. Due to Unruh effect, the entanglement degrades, but residual entanglement remains in the limit of infinite accelerations. We have also investigated quantum teleportation using entangled Dirac modes, and calculated the fidelities in various cases. In general, the fidelity depends on both the single-qubit state and the Bell state used in the teleportation.
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 analyze the entanglement between two modes of a free Dirac field as seen by two relatively accelerated parties. The entanglement is degraded by the Unruh effect and asymptotically reaches a nonvanishing minimum value in the infinite acceleration limit. This means that the state always remains entangled to a degree and can be used in quantum information tasks, such as teleportation, between parties in relative uniform acceleration. We analyze our results from the point of view afforded by the phenomenon of entanglement sharing and in terms of recent results in the area of multiqubit complementarity.
It is commonly believed that the fidelity of quantum teleportation using localized quantum objects with one party or both accelerated in vacuum would be degraded due to the heat up by the Unruh effect. In this paper, we point out that the Unruh effect is not the whole story in accounting for all the relativistic effects in quantum teleportation. First, there could be degradation of fidelity by a common field environment even when both quantum objects are in inertial motion. Second, relativistic effects entering the description of the dynamics, such as frame dependence, time dilation, and Doppler shift, already existent in inertial motion, can compete with or even overwhelm the effect due to uniform acceleration in a quantum field. We show it is not true that larger acceleration of an object would necessarily lead to a faster degradation of fidelity. These claims are based on four cases of quantum teleportation we studied using two Unruh--DeWitt detectors coupled via a common quantum field initially in the Minkowski vacuum. We find the quantum entanglement evaluated around the light cone, rather than the conventional ones evaluated on the Minkowski time slices, is the necessary condition for the averaged fidelity of quantum teleportation beating the classical one. These results are useful as a guide to making judicious choices of states and parameter ranges and estimation of the efficiency of quantum teleportation in relativistic quantum systems under environmental influences.
The interaction of an accelerated observer with a quantum field can modify the entanglement and quantum information shared between observers, thereby affecting quantum communication in non-inertial frames. We formulate the standard teleportation protocol in a relativistic setting where Alice remains inertial while Rob undergoes uniform acceleration and is modeled as an Unruh-DeWitt detector locally coupled to a massive scalar field. The detector-field interaction initially leads to a loss of entanglement and quantum information shared between Alice and Rob. Remarkably, under acceleration, the anti-Unruh regime can reverse this degradation, leading to an increase in both the shared entanglement and the accessible quantum information. We further find that, in the anti-Unruh regime, the teleportation fidelity is independent of the local free-evolution time of Alice's and Rob's states. At high accelerations, the recovered entanglement and quantum information enhance the teleportation fidelity, which approaches unity under appropriate conditions. These results demonstrate that the anti-Unruh effect can protect and recover quantum entanglement and information in a non-inertial frame by reducing the detector's effective temperature and the associated decoherence.
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 use the Unruh effect to investigate how the teleportation of quantum states is affected when one of the entangled qubits used in the process is under the influence of some external force. In order to reach a comprehensive understanding, a detailed analysis of the acceleration effect on such entangled qubit system is performed. In particular, we calculate the mutual information and concurrence between the two qubits and show that the latter has a ``sudden death'' at a finite acceleration, whose value will depend on the time interval along which the detector is accelerated.