Entanglement sharing in one-particle states

Lakshminarayan, Arul; Subrahmanyam, V.

doi:10.1103/physreva.67.052304

Cited by 67 publications

(86 citation statements)

References 32 publications

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“…We therefore expect an intimate relationship between the dynamics and the multipartite entanglement induced amongst the qubits. Using different approaches, the dynamics of entanglement in qubit bases was recently investigated in [23,24].…”

Section: Introductionmentioning

confidence: 99%

Entangling power of the quantum baker s map

Scott

Caves

2003

J. Phys. A: Math. Gen.

133

193

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We investigate entanglement production in a class of quantum baker's maps. The dynamics of these maps is constructed using strings of qubits, providing a natural tensor-product structure for application of various entanglement measures. We find that, in general, the quantum baker's maps are good at generating entanglement, producing multipartite entanglement amongst the qubits close to that expected in random states. We investigate the evolution of several entanglement measures: the subsystem linear entropy, the concurrence to characterize entanglement between pairs of qubits, and two proposals for a measure of multipartite entanglement. Also derived are some new analytical formulae describing the levels of entanglement expected in random pure states.

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Section: Introductionmentioning

confidence: 99%

Entangling power of the quantum baker s map

Scott

Caves

2003

J. Phys. A: Math. Gen.

133

193

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“…Recently, pairwise entanglement sharing in one-particle states was studied [14] using the concurrence [15] in the Harper model [16]. Here, we study another type of entanglement of one-particle states, the bipartite entanglement, which refers to entanglement between two subsystems when a whole system is divided into two parts.…”

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confidence: 99%

Bipartite entanglement and localization of one-particle states

Li¹,

Wang²,

Hu³

2004

J. Phys. A: Math. Gen.

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We study bipartite entanglement in a general one-particle state, and find that the linear entropy, quantifying the bipartite entanglement, is directly connected to the paricitpation ratio, charaterizing the state localization. The more extended the state is, the more entangled the state. We apply the general formalism to investigate ground-state and dynamical properties of entanglement in the onedimensional Harper model. [5]. On the other hand, entanglement has been proved to be playing an important role in condensed matter physics. There are many studies on entanglement in the Heisenberg spin models [6,7,8], Ising models in a transverse magnetic field [9,10], and related itinerant fermionic systems [11]. In the context of quantum phase transition, entanglment is also an indicator of the transition which can not be captured by common statistical physics [12,13].Recently, pairwise entanglement sharing in one-particle states was studied [14] using the concurrence [15] in the Harper model [16]. Here, we study another type of entanglement of one-particle states, the bipartite entanglement, which refers to entanglement between two subsystems when a whole system is divided into two parts. We reveal that the average bipartite entanglement directly connects to state localization.The one-particle states permeate many physics systems. For examples, for one electron moving on a substrate potential, the eigenfunctins are one-particle states. In quantum spin chain models with only one spin up (down) and all other spins down (up), the eigenfuntions of the model are one-magnon states.We consider a system containing N two-level systems (qubits) with |0 being the excited state and |1 the ground state. A general one-particle state is then written asHere, {|ψ n | 2 } is a probability distribution, satisfying the normalization condition N n=1 |ψ n | 2 = 1. When |ψ n | = 1/ √ N , state |Ψ reduces to the W state [8,17], one representative state in quantum information theory. We now consider bipartite entanglement between a block of L qubits and the rest N − L qubits. Bipartite entanglement of a pure state can be measured by the linear entropy of reduced density matrices [18].where ρ i is the reduced density matrix for subsystem i.To calcualte bipartite entanglement, we first consider a simple situation, namely, the entanglement between the first qubit and the rest N − 1 qubits. The one-particle state can be written in the following form:

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“…Let be given an ensemble of wavefunctions of the form (6). With each of the basis vectors ψ n is associated a couple of reduced density matrices ρ A and ρ B .…”

Section: Resultsmentioning

confidence: 99%

“…This time-dependence has been analysed recently in chaotic systems [1], in experimental spectra of triatomic molecules [2], and in Rydberg atoms [3]. Timedependent entanglement has been studied in theoretical models, like the Dicke model [4], a model of coupled kicked tops [5], the Harper Hamiltonian [6], a dimer model [7], Bose-Einstein condensates [8]. In these papers, the notions of time-averaged entanglement and ensemble-averaged entanglement have been shown to be useful in monitoring phase transitions, although the generality of this relationship has been questioned, see e.g.…”

Section: Introductionmentioning

confidence: 99%