Tripartite entanglement dynamics in the presence of Markovian or non-Markovian environment

Park, DaeKil

doi:10.1007/s11128-016-1331-y

Cited by 15 publications

(6 citation statements)

References 60 publications

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“…Up to now, a number of authors have worked out the bipartite and tripartite systems except for many multipartite systems. [10,[17][18][19][20][21][22][23][24] In recent years, many endeavors were devoted to the inertial quantum properties, and a lot of interesting contributions in the noninertial frames have been made, [21,[25][26][27][28][29][30][31][32][33][34][35][36][37][38][39] in which the general relativity, quantum field theory and quantum information theory have been combined. [13,21] This is because the non-negligible effects of relative motion have occurred in noninertial frame on quantum dynamics.…”

Section: Introductionmentioning

confidence: 99%

Tetrapartite entanglement measures of generalized GHZ state in the noninertial frames

Qian¹,

Carrillo²,

Sun³

et al. 2022

Chinese Phys. B

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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.

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Section: Introductionmentioning

confidence: 99%

Tetrapartite entanglement measures of generalized GHZ state in the noninertial frames

Qian¹,

Carrillo²,

Sun³

et al. 2022

Chinese Phys. B

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“…For example, since several pure multipartite entangled systems was studied [ 25 ], where the Unruh effect was discussed [ 19 , 20 , 21 ], the entanglement has been verified as an observer dependent 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 ].…”

Section: Introductionmentioning

confidence: 99%

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

Zepeda

Rueda-Paz

Aoki

et al. 2022

Entropy

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We study both pentapartite GHZ and W-class states in the noninertial frame and explore their entanglement properties by carrying out the negativities including 1-4, 2-3, and 1-1 tangles, the whole entanglement measures such as algebraic and geometric averages π5 and Π5, and von Neumann entropy. We illustrate graphically the difference between the pentapartite GHZ and W-class states. We find that all 1-4, 2-3 tangles and the whole entanglements, which are observer dependent, degrade more quickly as the number of accelerated qubits increases. The entanglements of these quantities still exist even at the infinite acceleration limit. We also notice that all 1-1 tangles of pentapartite GHZ state Nαβ=NαIβ=NαIβI=0 where α,β∈(A,B,C,D,E), whereas all 1-1 tangles of the W-class state Nαβ,NαIβ and NαIβI are unequal to zero, e.g., Nαβ=0.12111 but NαIβ and NαIβI disappear at r>0.61548 and r>0.38671, respectively. We notice that the entanglement of the pentapartite GHZ and W-class quantum systems decays faster as the number of accelerated particles increases. Moreover, we also illustrate the difference of von Neumann entropy between them and find that the entropy in the pentapartite W-class state is greater than that of GHZ state. The von Neumann entropy in the pentapartite case is more unstable than those of tripartite and tetrapartite subsystems in the noninertial frame.

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“…Sometimes, however, entanglement sudden death (ESD) occurs when the entangled multipartite quantum system is embedded in Markovian environments [14][15][16][17][18][19]. This means that the entanglement is completely disentangled at finite times.…”

Section: Introductionmentioning

confidence: 99%

Thermal entanglement phase transition in coupled harmonic oscillators with arbitrary time-dependent frequencies

Park

2020

Quantum Inf Process

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We derive explicitly the thermal state of the two coupled harmonic oscillator system when the spring and coupling constants are arbitrarily time-dependent. In particular, we focus on the case of sudden change of frequencies. In this case we compute purity function, Rényi and von Neumann entropies, and mutual information analytically and examine their temperature-dependence. We also discuss on the thermal entanglement phase transition by making use of the negativity-like quantity. Our calculation shows that the critical temperature T c increases with increasing the difference between the initial and final frequencies. In this way we can protect the entanglement against the external temperature by introducing large difference of initial and final frequencies.1 arXiv:1903.03297v2 [quant-ph] 29 Jun 2019where the λ i 's are eigenvalues, in decreasing order, of the Hermitian matrixAt nonzero external temperature all eigenvalues are dependent on T . Then, Eq. (1.1) implies that critical temperature T c can be derived by solvingUsing this method the thermal entanglement phase transition and critical temperature were explored[22] recently on the analytical ground in anisotropic Heisenberg XY Z spin model with Dzyaloshinskii-Moriya interaction[23, 24]. 1 see Ref. [12] and web page https://www.computing.co.uk/ctg/news/3065541/european-union-revealstest-projects-for-first-tranche-of-eur1bn-quantum-computing-fund.2The purpose of this paper is to study on the thermal entanglement phase transition in the two-coupled harmonic oscillator system when the spring constant k 0 and coupling constant J are arbitrarily time-dependent. Since this is continuum system with infinite-dimensionalHilbert space, we cannot use Eq. (1.1) for computation of thermal entanglement. However, the behavior of thermal entanglement can be deduced by considering the negativity-like quantity [25].The paper is organized as follows. In section II we derive the thermal state of single harmonic oscillator system when the frequency is arbitrarily time-dependent. We focus on the case of sudden frequency change (SFC). For SFC we derive the purity function and von Neumann entropy of the thermal state analytically. In section III we derive explicitly the thermal state of two coupled harmonic oscillator system when the spring constant k 0 and coupling constant J are arbitrarily time-dependent. In section IV we compute the purity function, Rényi and von Neumann entropies, and mutual information analytically for the thermal state of two coupled harmonic oscillator system in the case of SFC. It is shown that the thermal state is less mixed with increasing the difference between initial and final frequencies at the given external temperature. The mutual information shows that the common information parties A and B share does not completely vanish even in the infinity temperature limit. In section V the entanglement phase transition is discussed for the case of SFC by making use of the negativity-like quantity. It is shown that the critical temperature T c increases with...

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Tripartite entanglement dynamics in the presence of Markovian or non-Markovian environment

Cited by 15 publications

References 60 publications

Tetrapartite entanglement measures of generalized GHZ state in the noninertial frames

Tetrapartite entanglement measures of generalized GHZ state in the noninertial frames

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

Thermal entanglement phase transition in coupled harmonic oscillators with arbitrary time-dependent frequencies

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