Complementarity of one-particle and two-particle interference

Jaeger, Gregg; Horne, Maria; Shimony, Abner

doi:10.1103/physreva.48.1023

Cited by 149 publications

(179 citation statements)

References 11 publications

(11 reference statements)

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“…One can show that for pure states, P 1 is always equal to P 2 . We note here that there exists a complementarity relationship between P 12 and P j , namely, P 2 12 P 2 j 1; j 1; 2 [14]. Since 0 6 P 1 ; P 2 6 1, one may then conclude that 0 6 P 12 6 1.…”

Section: Degree Of Two-photon Polarizationmentioning

confidence: 77%

Quantum entanglement and the two-photon Stokes parameters

Abouraddy

Sergienko

Saleh

et al. 2002

Optics Communications

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A formalism for two-photon Stokes parameters is introduced to describe the polarization entanglement of photon pairs. This leads to the de®nition of a degree of two-photon polarization, which describes the extent to which the two photons act as a pair and not as two independent photons. This pair-wise polarization is complementary to the degree of polarization of the individual photons. The approach provided here has a number of advantages over the density matrix formalism: it allows the one-and two-photon features of the state to be separated and o ers a visualization of the mixedness of the state of polarization. Ó

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Section: Degree Of Two-photon Polarizationmentioning

confidence: 77%

Quantum entanglement and the two-photon Stokes parameters

Abouraddy

Sergienko

Saleh

et al. 2002

Optics Communications

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“…In our example below, only 3 settings suffice to detect entanglement if we have certain knowledge about ρ and we optimize the local decomposition of the corresponding witness. Our approach has similar advantages with respect to the detection of entanglement visibility [12], which in principle requires a continuous family of devices' settings.Another way of detecting entanglement by local mea-1 …”

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confidence: 99%

Detection of entanglement with few local measurements

et al. 2002

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We introduce a general method for the experimental detection of entanglement by performing only few local measurements, assuming some prior knowledge of the density matrix. The idea is based on the minimal decomposition of witness operators into a pseudo-mixture of local operators. We discuss an experimentally relevant case of two qubits, and show an example how bound entanglement can be detected with few local measurements. 03.67.Dd, 03.67.Hk, A central aim in the physics of quantum information is to create and detect entanglement -the resource that allows to realize various quantum protocols. Recently, much progress has been achieved experimentally in creating entangled states [1]. In every real experiment noise and imperfections are present so that the generated states, although intended to be entangled, may in fact be separable. Therefore, it is important to find efficient experimental methods to test whether a given imperfect state ρ is indeed entangled.Obviously, the ultimate goal of entanglement detection is to characterize entanglement quantitatively, and identify regions in the parameter space which allow to maximize entanglement for a particular quantum information processing task. The first step towards this ambitious goal is to detect whether a given state is entangled or not.The question of direct detection of quantum entanglement has been recently addressed in Refs. [2][3][4]. In [3,4] the authors study the case of mixed states and find efficient ways to estimate the entanglement of an unknown state. Their method is based on structural approximations of some linear maps followed by a spectrum estimation. Although experimentally viable the method is not very easy to implement and it requires further modifications in order to be performed by local measurements [5]. Here, we approach the same problem from a different perspective. We use special observables, the so-called witness operators [6,7] and their optimal decomposition into a sum of local projectors. Note that in this way we answer an open question posed recently in [8], where non-local measurements of entanglement witnesses were studied.The construction of a witness for a given arbitrary state is, in general, a formidable task. It can, however, be accomplished in typical experimental situations where one has some a priori information about the density matrix. This is always the case when the experiment is aimed at producing a certain state, rather than checking properties of an a priori unknown state. We discuss two experimentally relevant situations in this paper, namely the generation of a definite pure entangled state of two parties, and the generation of a specific bound entangled edge state. In both cases our method can be applied in arbitrary dimensions.Having constructed a witness, its measurement can be performed locally, since every observable can be decomposed in terms of a product basis in the operator space. Here we propose two ways of optimizing such local measurements. The first one consists in looking for the optimal number of l...

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“…Following the previous investigations [19,20,25] we consider the corrected joint probability P e1e2 defined as…”

Section: (4)mentioning

confidence: 99%

“…The scheme works for any arbitrary pure state of a two-qubit cavity system even when no prior knowledge about the state is given. The scheme derives from the realization that the concurrence coincides with the two-particle visibility under suitable interferometric setups, which in turn derives from previous theoretical investigations [19,20,24,25,26,27,28,29,30] that revealed complementarity between one-particle and twoparticle interferences and consequently intimate relations between two-particle interference and the concurrence.The scheme for single-particle interference. A twolevel atom prepared in its ground state passes successively through cavity A, a dispersive interaction region and cavity B.…”

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confidence: 97%

“…The question naturally arises whether entanglement can be estimated without having to fully reconstruct the unknown state. It has been shown that the answer to this question is yes at least for the case of pure two-qubit states [7,8], although, even in this case, more than one observable need to be measured.In recent years, several methods [9,10,11,12,13] have been proposed for detecting and measuring entanglement without a full reconstruction of the state; e.g., the method [9] based on the technique of minimal and optimal tomography [14,15] performed on one of the entangled pair, the method [10] based on entanglement witness [16,17] which was realized experimentally [18], the method [11,12] based on PPT criterion [1,2], and the method [13] based on two-particle interferometry [19,20]. These methods, although much simpler than the full state reconstruction, are not completely free of experimental difficulties, as they require either controlled unitary operations or some prior knowledge about the quantum state in question, or they can detect entanglement but not measure its amount.…”

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confidence: 99%

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Proposal for direct measurement of concurrence via visibility in a cavity QED system

Lee

et al. 2008

Phys. Rev. A

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An experimental scheme is proposed that allows direct measurement of the concurrence of a twoqubit cavity system. It is based on the cavity-QED technology using atoms as flying qubits and relies on the identity of the two-particle visibility of the atomic probability with the concurrence of the cavity system. The scheme works for any arbitrary pure initial state of the two-qubit cavity system.The question of how to detect the presence and amount of entanglement is one of the central issues in quantum information science. There exist theoretical criteria and measures such as the positive partial transpose (PPT) criterion [1,2], entanglement of formation [3] and concurrence [4] that, in principle, allow one to determine the presence and amount of entanglement. It is, however, difficult to observe such criteria and measures experimentally. The PPT criterion involves a nonphysical operation of partial transposition (complex conjugation) of the density matrix elements, while the entanglement of formation and the concurrence are complicated nonlinear functions of the system state. One is thus led to think that one may have to rely on the technique of a full tomographic reconstruction of the quantum state to measure the entanglement of an unknown quantum state. This technique, although successfully implemented for small systems [5,6], is highly inefficient and difficult especially for large systems, as a large number of observables need to be measured. The question naturally arises whether entanglement can be estimated without having to fully reconstruct the unknown state. It has been shown that the answer to this question is yes at least for the case of pure two-qubit states [7,8], although, even in this case, more than one observable need to be measured.In recent years, several methods [9,10,11,12,13] have been proposed for detecting and measuring entanglement without a full reconstruction of the state; e.g., the method [9] based on the technique of minimal and optimal tomography [14,15] performed on one of the entangled pair, the method [10] based on entanglement witness [16,17] which was realized experimentally [18], the method [11,12] based on PPT criterion [1,2], and the method [13] based on two-particle interferometry [19,20]. These methods, although much simpler than the full state reconstruction, are not completely free of experimental difficulties, as they require either controlled unitary operations or some prior knowledge about the quantum state in question, or they can detect entanglement but not measure its amount.Very recently, direct measurement of the concurrence of a two-photon pure entangled state was demonstrated experimentally using linear optical means [21]. The experiment is based on the realization [22] that entanglement properties are well captured by the expectation value of a certain Hermitian operator with respect to two copies of a pure state. As such, this method requires measurements on two copies of a state. It also requires CNOT operations. Application of this method to matter qubits (a...

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Complementarity of one-particle and two-particle interference

Cited by 149 publications

References 11 publications

Quantum entanglement and the two-photon Stokes parameters

Quantum entanglement and the two-photon Stokes parameters

Detection of entanglement with few local measurements

Proposal for direct measurement of concurrence via visibility in a cavity QED system

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