Tripartite Entanglement Measures of Generalized GHZ State in Uniform Acceleration^*

Abstract

Using the single-mode approximation, we study entanglement measures including two independent quantities; i.e., negativity and von Neumann entropy for a tripartite generalized Greenberger–Horne–Zeilinger (GHZ) state in noninertial frames. Based on the calculated negativity, we study the whole entanglement measures named as the algebraic average π 3 -tangle and geometric average Π 3 -tangle. We find that the difference between them is very small or disappears with the increase of the number of accelerated qubits. The entanglement properties are discussed from one accelerated observer and others remaining stationary to all three accelerated observers. The results show that there will always exist entanglement, even if acceleration r arrives to infinity. The degree of entanglement for all 1–1 tangles are always equal to zero, but 1–2 tangles always decrease with the acceleration parameter r. We notice that the von Neumann entropy increases with the number of the accelerated observers and S κ I ζ I (κ, ζ ∈ (A, B, C)) first increases and then decreases with the acceleration parameter r. This implies that the subsystem ρ κ I ζ I is first more disorder and then the disorder will be reduced as the acceleration parameter r increases. Moreover, it is found that the von Neumann entropies S ABCI, S ABICI and S AIBICI always decrease with the controllable angle θ, while the entropies of the bipartite subsystems S 2−2non (two accelerated qubits), S 2-1non (one accelerated qubit) and S 2-0non (without accelerated qubit) first increase with the angle θ and then decrease with it.

Tetrapartite entanglement measures of generalized GHZ state in the noninertial frames

“…For the acceleration a i ∈ [0, ∞), one has r i ∈ [0, π/4). As treated in our recent work about the tripartite case, [44] only monochromatic mode case w A, B, C, D = w and uniform acceleration a A, B, C, D = a are considered for simplicity. Thus, we have r A = r B = r C = r D ≡ r. To show how to expand the ψ g ABCD in the Rindler coordinates, let us give an explicit expression for the accelerated observer, say David, i.e.,…”

“…Along with this line, we have carried out the entanglement measures of the tripartite and tetrapartite systems initialed in the pure or mixed states such as the GHZ, the W-class and the Werner states in noninertial frame. [40][41][42][43][44][45][46][47] Among them, the tripartite entanglement measures for a generalized GHZ state including a polar angle θ have been explored in the noninertial frame. [44] In this work, we are going to investigate the tetrapartite entanglement measures of a generalized GHZ state when the observers are moving in a uniform acceleration.…”

“…[40][41][42][43][44][45][46][47] Among them, the tripartite entanglement measures for a generalized GHZ state including a polar angle θ have been explored in the noninertial frame. [44] In this work, we are going to investigate the tetrapartite entanglement measures of a generalized GHZ state when the observers are moving in a uniform acceleration. Four different cases, i.e., the observer accelerated from one to four will be studied.…”

Pentapartite Entanglement Measures of GHZ and W-Class State in the Noninertial Frame

“…Compared with the well-known entangled stated-GHZ state [ 15 , 36 , 37 , 38 , 39 , 40 , 41 ], the authors paid less attention to the W-class state because its density matrix cannot be written as an X matrix form. Nevertheless, we have employed a special technique to study the density matrix in the non-X matrix form and carried out the tripartite and tetrapartite W-class state cases [ 42 , 43 , 44 ], except for the generalized GHZ state in the noninertial frame [ 45 , 46 , 47 , 48 ]. After studying, we find that the degree of entanglement of the W-class state is more robust than the GHZ and generalized GHZ states.…”

One-step direct measurement of the entangled W states with cross-Kerr nonlinearity

“…In the field of quantum information, theories based on quantum mechanics have many interesting developments [1][2][3][4][5][6][7][8]. The preparation and measurement [9][10][11][12] of entangled states are important in practical applications [13,14].…”