Uncertainty Inequalities as Entanglement Criteria for Negative Partial-Transpose States

Nha, Hyunchul; Zubairy, M. Suhail

doi:10.1103/physrevlett.101.130402

Cited by 59 publications

(67 citation statements)

References 31 publications

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“…Bell reached a striking conclusion: quantum states with positive Wigner functions should allow for local realistic descriptions, since in this case the Wigner function itself serves as a classical probability distribution of the x and p variables [223]. A surprising example is the EPR state (128), with Wigner function given by [223] …”

Section: Bell Non-localitymentioning

confidence: 99%

“…To evaluate this criterion, it is necessary to reconstruct the covariance matrix [120,121]. Violation of the Simon, MGVT or DGCZ criteria are sufficient for identifying quantum states with negative partial transpose (NPT) [126,127,128]. In the general case, violation of these criteria is not a necessary condition for entanglement even in the case of Gaussian states, due to the existence of bound entangled states which have a positive partial transpose.…”

Section: Continuous Variable Entanglement Criteriamentioning

confidence: 99%

“…That is, the EPR state (128) is an eigenstate of operators of the type F α F 2π−α , F α F 4π−α , etc. When α + β = π (mod2π), the correlated EPR state (128) evolves to an anticorrelated EPR state…”

Section: Correlations At Intermediate Planesmentioning

confidence: 99%

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Spatial correlations in parametric down-conversion

et al. 2010

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The transverse spatial effects observed in photon pairs produced by parametric down-conversion provide a robust and fertile testing ground for studies of quantum mechanics, non-classical states of light, correlated imaging and quantum information. Over the last 20 years there has been much progress in this area, ranging from technical advances and applications such as quantum imaging to investigations of fundamental aspects of quantum physics such as complementarity relations, Bell's inequality violation and entanglement. The field has grown immensely: a quick search shows that there are hundreds of papers published in this field, some with hundreds of citations. The objective of this article is to review the building blocks and major theoretical and experimental advances in the field, along with some possible technical applications and connections to other research areas.

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Section: Bell Non-localitymentioning

confidence: 99%

Section: Continuous Variable Entanglement Criteriamentioning

confidence: 99%

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Spatial correlations in parametric down-conversion

et al. 2010

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“…An interesting study of SR for entangled systems has been worked out in Ref. 3. The interplay between entanglement and the uncertainty relation has been explored in a number of interesting papers.…”

Section: Introductionmentioning

confidence: 99%

Minimum Uncertainty and Entanglement

Dass

Qureshi

Sheel

2013

Int. J. Mod. Phys. B

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We address the question, does a system A being entangled with another system B, put any constraints on the Heisenberg uncertainty relation (or the Schrödinger-Robertson inequality)? We find that the equality of the uncertainty relation cannot be reached for any two noncommuting observables, for finite dimensional Hilbert spaces if the Schmidt rank of the entangled state is maximal. One consequence is that the lower bound of the uncertainty relation can never be attained for any two observables for qubits, if the state is entangled. For infinite-dimensional Hilbert space too, we show that there is a class of physically interesting entangled states for which no two noncommuting observables can attain the minimum uncertainty equality.

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“…In [14] the quantum nonlocality of some four-qubit states, the GHZ state, W state, cluster state and the state proposed in [15], has been investigated, towards the optimal violations of the Bell inequality for these states. The classification of entanglement has been also studied in such as [16][17][18][19] with linear inequalities for qubit systems and [20] with non-linear inequalities for detecting bi-separable states in arbitrary dimensional quantum systems.…”

mentioning

confidence: 99%

Characterization of four-qubit states via Bell inequalities

2013

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A set of Bell inequalities classifying the quantum entanglement of four-qubit states is presented. These inequalities involve only two measurement settings per observer and can characterize fully separable, bi-separable and tri-separable quantum states. In addition, a quadratic inequality of the Bell operators for four-qubit systems is derived. Bell inequalities, separability, Bell operatorsCitation: Zhao H, Zhang X H, Fei S M, et al. Characterization of four-qubit states via Bell inequalities. Chin Sci Bull, 2013Bull, , 58: 2334Bull, -2339Bull, , doi: 10.1007 The Bell inequality [1] provided the first possibility to distinguish experimentally between quantum-mechanical predictions and those of local realistic models. Derivations of new and stronger Bell inequalities are one of the most important and challenging subjects in quantum information processing. Since Bell's work, there were many important generalizations such as [2-11] and references therein. The Bell inequalities presented in [12] involve only two measurement settings per observer and can detect perfectly the quantum entanglement of the generalized GHZ states. By using the idea in constructing Bell operators [12], a set of new Bell inequalities are given in [13], which gives rise to a finer classification of the entanglement for three-qubit systems.The entanglement of four-qubit systems has been treated in terms of Bell inequalities of Mermin-Klyshko type. In [14] the quantum nonlocality of some four-qubit states, the GHZ state, W state, cluster state and the state proposed in [15], has been investigated, towards the optimal violations of the Bell inequality for these states. The classification of entanglement has been also studied in such as [16][17][18][19] with linear inequalities for qubit systems and [20] with non-linear inequalities for detecting bi-separable states in arbitrary dimensional quantum systems.In this work, we study the quantum entanglement of four-*Corresponding author (email: zhaohui@bjut.edu.cn) qubit systems by using the idea in constructing Bell operators in [12]. We generalize the results of three-qubit systems in [13] to four-qubit systems. It has been shown that the standard Werner-Wolf-Żukowski-Brukner (WWZB) inequalities cannot detect the entanglement of the generalized Greenberger-Horne-Zeilinger (GHZ) states given by |ψ = cos α|0, ..., 0 + sin α|1, ..., 1 with 0 α π/4 [21, 22]. However, the Bell operators constructed in the way provided in [12] can detect the entanglement of the generalized GHZ state wholly. Our Bell operators are constructed by using the idea in [12]. The resulted Bell inequalities can distinguish fully separable, bi-separable and tri-separable states of a four-qubit system. Moreover, these linear Bell inequalities involve only two measurement settings per observer. Analytical formulas of the average values of the Bell operators for four-qubit systems are also derived. And a quadratic inequality of the Bell operators for all four-qubit systems has been presented. Explicit geometrical pictures show t...

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Uncertainty Inequalities as Entanglement Criteria for Negative Partial-Transpose States

Cited by 59 publications

References 31 publications

Spatial correlations in parametric down-conversion

Spatial correlations in parametric down-conversion

Minimum Uncertainty and Entanglement

Characterization of four-qubit states via Bell inequalities

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