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arXiv:1003.2201 · Physical Review A

Entanglement of two qubits in a relativistic orbit

Jason Doukas, B. J. Carson

Published Jun 16, 2010• 40 citations
arXivHTMLPDF

Abstract

The creation and destruction of entanglement between a pair of interacting two-level detectors accelerating about diametrically opposite points of a circular path is investigated. It is found that any nonzero acceleration has the effect of suppressing the vacuum entanglement and enhancing the acceleration radiation, thereby reducing the entangling capacity of the detectors. Given that for large accelerations the acceleration radiation is the dominant effect, we investigate the evolution of a two-detector system initially prepared in a Bell state using a perturbative master equation and treating the vacuum fluctuations as an unobserved environment. A general function for the concurrence is obtained for stationary and symmetric world lines in flat space. The entanglement sudden-death time is computed.

DOI
10.1103/physreva.81.062320

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The creation and destruction of entanglement between a pair of interacting two-level detectors accelerating about diametrically opposite points of a circular path is investigated. It is found that any nonzero acceleration has the effect of suppressing the vacuum entanglement and enhancing the acceleration radiation, thereby reducing the entangling capacity of the detectors. Given that for large accelerations the acceleration radiation is the dominant effect, we investigate the evolution of a two-detector system initially prepared in a Bell state using a perturbative master equation and treating the vacuum fluctuations as an unobserved environment. A general function for the concurrence is obtained for stationary and symmetric world lines in flat space. The entanglement sudden-death time is computed.
We study the dynamics of quantum entanglement between two Unruh-DeWitt detectors, one stationary (Alice), and another uniformly accelerating (Rob), with no direct interaction but coupled to a common quantum field in (3+1)D(3+1)\mathrm{D}(3+1)D Minkowski space. We find that for all cases studied the initial entanglement between the detectors disappears in a finite time (``sudden death''). After the moment of total disentanglement the correlations between the two detectors remain nonzero until late times. The relation between the disentanglement time and Rob's proper acceleration is observer dependent. The larger the acceleration is, the longer the disentanglement time in Alice's coordinate, but the shorter in Rob's coordinate.
We study the full entanglement dynamics of two uniformly accelerated Unruh-DeWitt detectors with no direct interaction in between but each coupled to a common quantum field and moving back-to-back in the field vacuum. For two detectors initially prepared in a separable state our exact results show that quantum entanglement between the detectors can be created by the quantum field under some specific circumstances, though each detector never enters the other's light cone in this setup. In the weak coupling limit, this entanglement creation can occur only if the initial moment is placed early enough and the proper acceleration of the detectors is not too large or too small compared to the natural frequency of the detectors. Once entanglement is created it lasts only a finite duration, and always disappears at late times. Prior result by Reznik [B. Reznik, Found. Phys. 33, 167 (2003).] derived using the time-dependent perturbation theory with extended integration domain is shown to be a limiting case of our exact solutions at some specific moment. In the strong coupling and high acceleration regime, vacuum fluctuations experienced by each detector locally always dominate over the cross correlations between the detectors, so entanglement between the detectors will never be generated.
It is well known that the quantum fluctuation of entanglement (QFE) between Unruh–De Witt detector (modeled by a two-level atom) is always investigated in a relativistic setting. However, both of the Unruh radiation and quantum fluctuation effects play an important role in precise measurements of quantum entanglement. In this paper, we have quantitatively analyzed how the relativistic motion affects the QFE for two entangled Unruh–De Witt detectors, one of which is accelerated and interacting with the neighbor external scalar field. Our results show that the QFE, which initially increases by the Unruh thermal noise, will suddenly decay when the acceleration reaches to a considerably large value. Therefore, the relativistic effect will lead to non-negligible QFE effect. We also find that the initial QFE (without acceleration effect) reaches its minimum value at the maximally entangled state and the separable state. More importantly, our analysis demonstrates that although the QFE has a huge decay when the acceleration is greater than ∼0.96, the ratio of ΔE/C is still very large, due to the simultaneous decay of concurrence to a very low value. Finally, enlightened by the well-known equivalence principle, we discuss the possibility of applying the above findings to the dynamics of QFE under the influence of gravitation field.
We study, in the paradigm of open quantum systems, the entanglement dynamics of two uniformly accelerated atoms with the same acceleration perpendicular to the separation. The two-atom system is treated as an open system coupled with a bath of fluctuating massless scalar fields in the Minkowski vacuum, and the master equation that governs its evolution is derived. It has been found that, for accelerated atoms with a nonvanishing separation, entanglement sudden death is a general feature when the initial state is entangled, while for those in a separable initial state, entanglement sudden birth only happens for atoms with an appropriate interatomic separation and sufficiently small acceleration. Remarkably, accelerated atoms can get entangled in certain circumstances while the inertial ones in the Minkowski vacuum cannot. A comparison between the results of accelerated atoms and those of static ones in a thermal bath shows that uniformly accelerated atoms exhibit features distinct from those immersed in a thermal bath at the Unruh temperature in terms of entanglement dynamics.
We show that vacuum-induced coherence in three-level atomic systems can lead to preservation of bipartite entanglement when two such atoms are prepared as two initially entangled qubits, each independently interacting with their respective vacuum reservoirs. We explicitly calculate the time evolution of concurrence for two different Bell states and show that a large amount of entanglement can survive in the long time limit. The amount of entanglement left between the two qubits depends strongly on the ratio of the nonorthogonal transitions in each qubit and can be more than 5050%50. Moreover, we find that as a consequence of vacuum-induced coherence, sudden death of entanglement is prevented for an initial mixed entangled state of the qubits.
We derive a general Gorini-Kossakowski-Lindblad-Sudarshan master equation for two co-located, uniformly accelerated two-level detectors weakly coupled to scalar fields in the Minkowski vacuum, retaining coherent and dissipative contributions for arbitrary orientations, field masses, and spacetime dimensions. For equal orientations, we determine stationary states and their entanglement for two couplings to massless fields in four dimensions: symmetric coupling yields acceleration-dependent concurrence, whereas rotating-wave coupling gives acceleration-independent concurrence.