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Annalen der Physik

Genuine Entanglement of a Multipartite GHZ State in Non‐Inertial Frame

Reza Hamzehofi, Mehrzad Ashrafpour, Davood Afshar

Published Aug 12, 2025• 3 citations
Publisher

Abstract

Abstract This research investigates the entanglement properties of multipartite GHZ states of bosonic and fermionic fields, particularly in scenarios where some parties are uniformly accelerated. The analysis incorporates perspectives from both inertial and non‐inertial observers. Entanglement is quantified using the Π‐tangle for GHZ states and the one‐tangle for multipartite GHZ states. To facilitate this analysis, the study derives the density matrices for the multipartite GHZ states with m uniformly accelerated parties (). The results reveal that entanglement diminishes as the acceleration parameter increases, with accelerated observers experiencing less entanglement compared to their inertial counterparts. In the bosonic case, genuine entanglement is entirely lost for non‐inertial observers at high accelerations, whereas inertial observers still experience it. In the fermionic case, however, genuine entanglement is not completely eliminated when the number of accelerated parties is limited. Furthermore, the decrease in entanglement is proportional to the number of accelerated parties, approaching zero as m tends to infinity ().

DOI
10.1002/andp.202500206

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Physica Scripta•Dec 1, 2021•0 citations
Abstract This research investigates the entanglement properties of multipartite GHZ states of bosonic and fermionic fields, particularly in scenarios where some parties are uniformly accelerated. The analysis incorporates perspectives from both inertial and non‐inertial observers. Entanglement is quantified using the Π‐tangle for GHZ states and the one‐tangle for multipartite GHZ states. To facilitate this analysis, the study derives the density matrices for the multipartite GHZ states with m uniformly accelerated parties (). The results reveal that entanglement diminishes as the acceleration parameter increases, with accelerated observers experiencing less entanglement compared to their inertial counterparts. In the bosonic case, genuine entanglement is entirely lost for non‐inertial observers at high accelerations, whereas inertial observers still experience it. In the fermionic case, however, genuine entanglement is not completely eliminated when the number of accelerated parties is limited. Furthermore, the decrease in entanglement is proportional to the number of accelerated parties, approaching zero as m tends to infinity ().
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.
Abstract Using the single-mode approximation, we calculate entanglement measures such as negativity (1 − 3, 1 − 1 and 2 − 2 tangles) and von Neumann entropy for a tetrapartite Greenberger–Horne–Zeilinger system in a non-inertial frame. We then analyze the whole entanglement measures, the residual π 4 and geometric Π 4 average of tangles. We find that the difference between them is very small or disappears with the increasing accelerated observers. The entanglement properties are compared among the different cases from one accelerated observer and others remaining stationary to all four accelerated observers. The results presented here show that entanglement still exists for the complete system even when acceleration r tends to infinity. The degree of entanglement is always equal to zero for the 1 − 1 tangle case. We also study the negativity 2 − 2 tangle for completeness. We reexamine the existence of the Unruh effect in non-inertial frames. It is also found that the von Neumann entropy increases with the increasing accelerated observers, and S κ I ζ I and S κ I ζ I δ I first increase and then decrease with the acceleration parameter r , e.g. S κ ζ ( max ) = 1.65853 at r = 0.599881 and S κ ζ δ ( max ) = 2.28231 at r = 0.676196. This implies that the subsystems ρ κ I ζ I and ρ κ I ζ I δ I are at first more disordered and then the disorder is reduced with the increasing acceleration parameter r .
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.
Using a single-mode approximation, we carry out the entanglement measures, e.g., the negativity and von Neumann entropy when a tetrapartite generalized GHZ state is treated in a noninertial frame, but only uniform acceleration is considered for simplicity. In terms of explicit negativity calculated, we notice that the difference between the algebraic average π 4 and geometric average Π 4 is very small with the increasing accelerated observers and they are totally equal when all four qubits are accelerated simultaneously. The entanglement properties are discussed from one accelerated observer to all four accelerated observers. It is shown that the entanglement still exists even if the acceleration parameter r goes to infinity. It is interesting to discover that all 1-1 tangles are equal to zero, but 1-3 and 2-2 tangles always decrease when the acceleration parameter r increases. We also study the von Neumann entropy and find that it increases with the number of the accelerated observers. In addition, we find that the von Neumann entropy S ABCDI, S ABCIDI, S ABICIDI and S AIBICIDI always decrease with the controllable angle θ, while the entropies S 3 – 3 non, S 3 – 2 non, S 3 – 1 non and S 3 – 0 non first increase with the angle θ and then decrease with it.
The decoherence effect on multipartite entanglement in non-inertial frames is investigated. The GHZ state is considered to be shared between partners with one partner in the inertial frame whereas the other two are in accelerated frames. One-tangle and π-tangles are used to quantify the entanglement of the multipartite system influenced by phase damping and phase flip channels. It is seen that for the phase damping channel, entanglement sudden death (ESD) occurs for p > 0.5 in the infinite acceleration limit. On the other hand, in the case of the phase flip channel, ESD behavior occurs at p = 0.5. It is also seen that entanglement sudden birth (ESB) occurs in the case of phase flip channel just after ESD, i.e. p > 0.5. Furthermore, it is seen that the effect of the environment on multipartite entanglement is much stronger than that of the acceleration of non-inertial frames.
Abstract We investigate robustness of bipartite and tripartite entangled states for fermionic systems in non-inertial frames, which are under noisy channels. We consider two Bell states and two Greenberger-Horne-Zeilinger (GHZ) states, which possess initially the same amount of entanglement, respectively. By using genuine multipartite (GM) concurrence, we analytically derive the equations that determine the difference between the robustness of these locally unitarily equivalent states under the amplitude-damping channel. We find that tendency of the robustness for two GHZ states evaluated by using three-tangle τ and GM concurrence as measures of genuine tripartite entanglement is equal to each other. We also find that the robustness of two Bell states is equal to each other under the depolarizing, phase damping and bit flip channels, and that the same is true for two GHZ states.