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arXiv:2107.02490 · Physical Review A

Accessible and inaccessible quantum coherence in relativistic quantum systems

Saveetha Harikrishnan, Segar Jambulingam, Peter P. Rohde, Chandrashekar Radhakrishnan

Published May 3, 2022• 43 citations
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Abstract

The quantum coherence of a multipartite system is investigated when some of the parties are moving with uniform acceleration and the analysis is carried out using the single-mode approximation. Due to acceleration the quantum coherence is divided into two parts as accessible and inaccessible coherence. First we investigate tripartite systems, considering both GHZ and $W$ states. We find that the quantum coherence of these states does not vanish in the limit of infinite acceleration, rather asymptoting to a nonzero value. These results hold for both single- and two-qubit acceleration. In the GHZ and $W$ states the coherence is distributed as correlations between the qubits and is known as global coherence. However, quantum coherence can also exist due to the superposition within a qubit, the local coherence. To study the properties of local coherence we investigate a separable state. The GHZ state, $W$ state, and separable states contain only one type of coherence. Next we consider the $W\overline{W}$ and star states in which both local and global coherences coexist. We find that under uniform acceleration both local and global coherence show similar qualitative behavior. Finally, we derive analytic expressions for the quantum coherence of $N$-partite GHZ and $W$ states for $n<N$ accelerating qubits. We find that the quantum coherence of a multipartite GHZ state falls exponentially with the number of accelerated qubits, whereas for multipartite $W$ states the quantum coherence decreases only polynomially. We conclude that $W$ states are more robust to Unruh decoherence and discuss some potential applications in satellite-based quantum communication and black-hole physics.

DOI
10.1103/physreva.105.052403

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arXiv:1906.07267•May 27, 2019•1 citation
The quantum coherence of a multipartite system is investigated when some of the parties are moving with uniform acceleration and the analysis is carried out using the single-mode approximation. Due to acceleration the quantum coherence is divided into two parts as accessible and inaccessible coherence. First we investigate tripartite systems, considering both GHZ and WWW states. We find that the quantum coherence of these states does not vanish in the limit of infinite acceleration, rather asymptoting to a nonzero value. These results hold for both single- and two-qubit acceleration. In the GHZ and WWW states the coherence is distributed as correlations between the qubits and is known as global coherence. However, quantum coherence can also exist due to the superposition within a qubit, the local coherence. To study the properties of local coherence we investigate a separable state. The GHZ state, WWW state, and separable states contain only one type of coherence. Next we consider the WW‾W\overline{W}WW and star states in which both local and global coherences coexist. We find that under uniform acceleration both local and global coherence show similar qualitative behavior. Finally, we derive analytic expressions for the quantum coherence of NNN-partite GHZ and WWW states for n<Nn<Nn<N accelerating qubits. We find that the quantum coherence of a multipartite GHZ state falls exponentially with the number of accelerated qubits, whereas for multipartite WWW states the quantum coherence decreases only polynomially. We conclude that WWW states are more robust to Unruh decoherence and discuss some potential applications in satellite-based quantum communication and black-hole physics.
Abstract We study the quantum coherence and its distribution of N -partite GHZ and W states of bosonic fields in the noninertial frames with arbitrary number of acceleration observers. We find that the coherence of both GHZ and W state reduces with accelerations and freezes in the limit of infinite accelerations. The freezing value of coherence depends on the number of accelerated observers. The coherence of N -partite GHZ state is genuinely global and no coherence exists in any subsystems. For the N -partite W state, however, the coherence is essentially bipartite types, and the total coherence is equal to the sum of coherence of all the bipartite subsystems.
Tripartite entanglement is examined when one of the three parties moves with a uniform acceleration with respect to other parties. As the Unruh effect indicates, tripartite entanglement exhibits a decreasing behavior with increasing acceleration. Unlike bipartite entanglement, however, tripartite entanglement does not completely vanish in the infinite acceleration limit. If the three parties, for example, share the Greenberger-Horne-Zeilinger or WWW state initially, the corresponding $\ensuremath{\pi}$-tangle, one of the measures of tripartite entanglement, is shown to be $\ensuremath{\pi}/6~0.524$ or 0.1760.1760.176 in this limit, respectively. This fact indicates that tripartite quantum-information processing may be possible even if one of the parties approaches the Rindler horizon. The physical implications of this striking result are discussed in the context of black-hole physics.
In this work, we generalize the entanglement of three-qbit Bosonic systems beyond the single-mode approximation when one of the observers is accelerated. For this purpose, we review the effects of acceleration on field modes and quantum states. The single-mode approximation and beyond the single-mode approximation methods are introduced. After this brief introduction, the main problem of this paper, tripartite entanglement of bosonic systems in a noninertial frame beyond the single- mode approximation is investigated. The tripartite entangled states have different classes with GHZ and W states being most important. Here, we choose &pi-tangle as a measure of tripartite entanglement. If the three parties share GHZ state, the corresponding &pi-tangle will increase by increasing acceleration for some Unruh modes. This phenomenon, increasing entanglement, has never been observed in the single-mode approximation for bosonic case. Moreover, the &pi-tangle dose not exhibit a monotonic behavior with increasing acceleration. In the infinite acceleration limit, the &pi-tangle goes to different nonzero values for distinct Unruh modes. Unlike GHZ state, the entanglement of the W state shows only monotonically increasing and decreasing behaviors with increasing acceleration. Also, the entanglement for all possible choices of Unruh modes approaches only 0.176 in the high acceleration limit. Therefore, according to the quantum entanglement, there is no distinction between the single-mode approximation and beyond the single-mode approximation methods in this limit.
Abstract In this paper quantum teleportation of an unknown quantum state via noisy maximally bipartite (Bell) and maximally tripartite (Greenberger–Horne–Zeilinger (GHZ)) entangled states are investigated. We suppose that one of the observers who would receive the sent state accelerates uniformly with respect to the sender. The interactions of the quantum system with its environment during the teleportation process impose noises. These (unital and nonunital) noises are: phase damping, phase flip, amplitude damping and bit flip. In expressing the modes of the Dirac field used as qubits, in the accelerating frame, the so-called single mode approximation is not imposed. We calculate the fidelities of teleportation, and discuss their behaviors using suitable plots. The effects of noise, acceleration and going beyond the single mode approximation are discussed. Although the Bell states bring higher fidelities than GHZ states, the global behaviors of the two quantum systems with respect to some noise types, and therefore their fidelities, are different.
Entanglement degradation caused by the Unruh effect is discussed for the tripartite GHZ or W states constructed by modes of a non-interacting quantum field viewed by one inertial observer and two uniformly accelerated observers. For fermionic states, the Unruh effect even for infinite accelerations cannot completely remove the entanglement. However, for the bosonic states, the situation is different and the entanglement vanishes asymptotically. Also, the entanglement is studied for the bipartite subsystems. While for the GHZ states all the bipartite subsystems are identically disentangled, for the W states the bipartite subsystems are somewhat entangled, though, this entanglement can be removed for appropriately accelerated observers. Interestingly, logarithmic negativity as a measure for determining the entanglement of one part of the system relative to the other two parts, is not generally the same for different parts. This means that we encounter tripartite systems where each part is differently entangled to the other two parts.
We investigate the entanglement measures of tripartite W-State and GHZ-state in noninertial frame through the coordinate transformation between Minkowski and Rindler. First it is shown that all three qubits undergo in a uniform acceleration aaa of W-State, we find that the one-tangle, two-tangle, and πππ-tangle decrease when the acceleration parameter rrr increases, and the two-tangle cannot arrive to infinity of the acceleration. Next we show that the one qubit goes in a uniform acceleration a1a_{1}a1​ and the other two undergo in a uniform acceleration aaa of GHZ-state, we find that the two-tangle is equal to zero and NBI(AICI)=NCI(AIBI)≠NAI(BICI)N_{B_I (A_I C_I)} = N_{C_I (A_I B_I)}\neq N_{A_I (B_I C_I)}NBI​(AI​CI​)​=NCI​(AI​BI​)​=NAI​(BI​CI​)​, but one-tangle and πππ-tangle never reduce to zero for any acceleration.