Entanglement transfer from continuous variables to qubits

Son, Wonmin; Kim, M. S.; Lee, Jinhyoung; Ahn, Doyeol

doi:10.1080/09500340110120941

Cited by 78 publications

(78 citation statements)

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“…In Refs. [21,22,23,24] entanglement swapping between qubits and continuous variables has been investigated in detail. Here we are particularily interested in the role of energy in the entanglement transfer process.…”

Section: Entanglement Transfer: 2 Modes To 2 Qubitsmentioning

confidence: 99%

Entanglement, purity, and energy: Two qubits versus two modes

2006

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We study the relationship between the entanglement, mixedness and energy of two-qubit and twomode Gaussian quantum states. We parametrize the set of allowed states of these two fundamentally different physical systems using measures of entanglement, mixedness and energy that allow us to compare and contrast the two systems using a phase diagram. This phase diagram enables one to clearly identify not only the physically allowed states, but the set of states connected under an arbitrary quantum operation. We pay particular attention to the maximally entangled mixed states (MEMS) of each system. Following this we investigate how efficiently one may transfer entanglement from two-mode to two-qubit states.

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Section: Entanglement Transfer: 2 Modes To 2 Qubitsmentioning

confidence: 99%

Entanglement, purity, and energy: Two qubits versus two modes

2006

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“…In the limit of 2 1, the Poissonian distribution is replaced by a Gaussian distribution over the variable n with mean value and variance equal to 2 [9] so that C 2 n e ÿ 2 2n n! 1 2 2 p e ÿ nÿ 2 2 =2 2 .…”

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confidence: 99%

Entanglement Reciprocation between Qubits and Continuous Variables

et al. 2006

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We investigate how entanglement can be transferred between qubits and continuous-variable (CV) systems. We find that one ebit borne in maximally entangled qubits can be fully transferred to two CV systems which are initially prepared in a pure separable Gaussian field with high excitation. We show that it is possible to retrieve the entanglement back to qubits from the entangled CV systems. The deposition of multiple ebits from qubits to the initially separable CV systems is also pointed out. We show that the entanglement transfer and retrieval are done at a quasisteady state. DOI: 10.1103/PhysRevLett.96.080501 PACS numbers: 03.67.Mn, 03.67.Hk, 42.50.Ct Quantum information processing (QIP) has been extensively studied for a qubit system which is a quantum extension of a bit, spanning two-dimensional Hilbert space. A qubit is realized by a spin, a two-level atom, the polarization of a photon, and a superconductor among others. A two-dimensional system is mathematically handy and logically easy to treat. On the other hand, many continuous-variable (CV) physical systems such as a harmonic oscillator and a light field, which are defined in infinite-dimensional Hilbert space, have also attracted considerable attention for other practical reasons. While qubit and CV systems are nearly always treated separately, there is a good reason to believe that a study of their interface may result in synergy for the implementation of QIP. There have been some pilot works on how to entangle two separate qubits by an entangled Gaussian field [1][2][3]. In this Letter, we ask the interesting questions of how easy it is to deposit the entanglement of two qubits to two coherent states and retrieve quantum entanglement back to the qubits.When two maximally entangled two-level atoms are sent to two respective cavities initially prepared in vacuum, after the Rabi time the maximal entanglement is fully transferred to the cavity fields [4,5]. Here the interaction is assumed resonant and the cavities are lossless. Essentially, in the above transfer the cavity does not behave as a true CV system, as only cavity states j0i and j1i play a part. Adding an extra excitation in a cavity initially in vacuum will be noticeable. However, if the cavities are prepared with coherent fields of large amplitudes, will the atom's depositing extra excitation still be visible to show the entanglement of ebit? Can the entanglement be retrieved by the next set of atoms? Answering the questions, we find that it is possible to perfectly deposit entanglement to initial coherent fields and retrieve them back at a quasisteady state. We also show the possibility to extend the memory to multidimensional states. The cavities thus act as a memory for entanglement, differently from the usual perspective where the atoms are designed to memorize the quantum state. Our approach is based on the use of the resonant Jaynes-Cummings (JC) model [6]. This is not a limitation, as this model has been proven to be naturally valid in many physical situations in which coherent ex...

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“…Methods of extracting the entanglement from a squeezed continuousvariable state into a pair of two-level system were previously studied in [18,19,20] Using our mapping to an effective two-qubit system, we can swap the entanglement in a small region of the continuous wavefunction to local qubits (i.e. true two-level systems).…”

Section: Example: Entanglement Of Gaussian Statesmentioning

confidence: 99%

Entanglement in general two-mode continuous-variable states: Local approach and mapping to a two-qubit system

Lin

Fisher

2007

Phys. Rev. A

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We present a new approach to the analysis of entanglement in smooth bipartite continuousvariable states. One or both parties perform projective filterings via preliminary measurements to determine whether the system is located in some region of space; we study the entanglement remaining after filtering. For small regions, a two-mode system can be approximated by a pair of qubits and its entanglement fully characterized, even for mixed states. Our approach may be extended to any smooth bipartite pure state or two-mode mixed state, leading to natural definitions of concurrence and negativity densities. For Gaussian states both these quantities are constant throughout configuration space.There has been growing interest in the quantification of entanglement in quantum systems. However, many systems of interest have continuous, rather than discrete, degrees of freedom [1]. The general characterization of entanglement in such continous-variable systems is a very difficult problem; most of the known results are for Gaussian states, where the logarithmic negativity [2] can be calculated for arbitrary bipartite divisions [3]. The entanglement of formation [4] is known exactly only for symmetric bipartite Gaussian states [5], and further measures of entanglement in multipartite Gaussian states are a topic of active current research [1,6]. For non-Gaussian states there is some progress in finding criteria for entanglement [7], but much less in quantifying it.In this letter we present a new approach to this problem, allowing entanglement to be quantified locally in arbitrary (including non-Gaussian) continuous-variable states. We concentrate on entanglement localized near particular regions in configuration space, which we analyse via a thought experiment in which the entangled state is first measured to localise it. This corresponds to a particular type of projective filtering, used to identify the distribution of entanglement in a state which has a preexisting bipartite structure. This contrasts with previous studies [8,9,10] of the entanglement of a finite region of space with the rest of the system. We show that in the limit where the sizes of the measured regions become very small the description of each mode in the system becomes isomorphic to a single qubit. In two-mode systems simple expressions result for entanglement monotones (concurrence and negativity), yielding natural definitions for corresponding densities in configuration space.The filtering process. Let Alice and Bob share a state of two distinguishable one-dimensional particles (or two modes). Alice can measure only the position of her particle or mode (coordinate q A ), Bob the position of his (coordinate q B ). They filter their state by determining whether or not the particles are found in particular regions of configuration space, and discard instances in which they are not. We refer to the resulting subensemble as the 'discarding ensemble'. For example, if Alice measures whether her coordinate is in a sub-region a, the corresponding projector iŝwhere...

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Entanglement transfer from continuous variables to qubits

Cited by 78 publications

References 24 publications

Entanglement, purity, and energy: Two qubits versus two modes

Entanglement, purity, and energy: Two qubits versus two modes

Entanglement Reciprocation between Qubits and Continuous Variables

Entanglement in general two-mode continuous-variable states: Local approach and mapping to a two-qubit system

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