Partial separability and entanglement criteria for multiqubit quantum states

Seevinck, Michael; Uffink, Jos

doi:10.1103/physreva.78.032101

Cited by 103 publications

(194 citation statements)

References 54 publications

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“…It is thus important to make both classifications of entangled states: into admitting and not admitting local realistic models, and into violating and not violating a given Bell inequality. Entanglement and Bell violation of different noisy states has already been studied by several authors [20][21][22][23][24]. All this indicates that entanglement and impossibility of a local hidden variable model are not only different concepts, but also truly different resources [25].…”

Section: Introductionmentioning

confidence: 99%

Entanglement and communication-reducing properties of noisyN-qubit states

et al. 2010

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We consider properties of states of many qubits, which arise after sending certain entangled states via various noisy channels (white noise, coloured noise, local depolarization, dephasing and amplitude damping). Entanglement of these states is studied and their ability to violate certain classes of Bell inequalities. States which violate them allow for higher than classical efficiency of solving related distributed computational tasks with constrained communication. This is a direct property of such states -not requiring their further modification via stochastic local operations and classical communication such as entanglement purification or distillation procedures. We identify novel families of multi-particle states which are entangled but nevertheless allow local realistic description of specific Bell experiments. For some of them, the "gap" between the critical values for entanglement and violation of Bell inequality remains finite even in the limit of infinitely many qubits.

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Section: Introductionmentioning

confidence: 99%

Entanglement and communication-reducing properties of noisyN-qubit states

et al. 2010

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“…It is worth noting that genuine many-body entanglement is known to be essential, e.g., in achieving extreme spin squeezing [39], and also high sensitivity in some general metrology tasks [42]. For well-calibrated or trusted [43] measurement devices, there exist few criteria [39][40][41][42][44][45][46][47][48]] to certify such many-body entanglement. For example, an entanglement depth larger than 28 was recently demonstrated [48] using such a witness.…”

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confidence: 99%

Family of Bell-like Inequalities as Device-Independent Witnesses for Entanglement Depth

et al. 2015

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We present a simple family of Bell inequalities applicable to a scenario involving arbitrarily many parties, each of which performs two binary-outcome measurements. We show that these inequalities are members of the complete set of full-correlation Bell inequalities discovered by Werner-WolfZukowski-Brukner. For scenarios involving a small number of parties, we further verify that these inequalities are facet-defining for the convex set of Bell-local correlations. Moreover, we show that the amount of quantum violation of these inequalities naturally manifests the extent to which the underlying system is genuinely many-body entangled. In other words, our Bell inequalities, when supplemented with the appropriate quantum bounds, naturally serve as device-independent witnesses for entanglement depth, allowing one to certify genuine k-partite entanglement in an arbitrary n ≥ k-partite scenario without relying on any assumption about the measurements being performed, nor the dimension of the underlying physical system. A brief comparison is made between our witnesses and those based on some other Bell inequalities, as well as the quantum Fisher information. A family of witnesses for genuine k-partite nonlocality applicable to an arbitrary n ≥ k-partite scenario based on our Bell inequalities is also presented. One of the most important no-go theorems in physics concerns the impossibility to reproduce all quantum mechanical predictions using any locally-causal theory [1] -a fact commonly referred to as Bell's theorem [2]. An important observation leading to this celebrated result is that measurement statistics allowed by such theories must satisfy constraints in the form of an inequality, a Bell inequality. Since these inequalities only involve experimentally accessible quantities, their violation -a manifestation of Bell-nonlocality [3] -can be, and has been (modulo some arguably implausible loopholes [4]) empirically demonstrated (see, e.g., [3][4][5] and references therein).Clearly, Bell inequalities played an instrumental role in the aforementioned discovery. Remarkably, they also find applications in numerous quantum information and communication tasks, e.g., in quantum key distribution involving untrusted devices [6][7][8], in the reduction of communication complexity [9], in the expansion of trusted random numbers [10,11], in certifying the Hilbert space dimension of physical systems [12,13], in self-testing [14-18] of quantum devices, in witnessing [19][20][21] and quantifying [22-25] (multipartite) quantum entanglement using untrusted devices etc. For a recent review on these and other applications, see [3].Identifying interesting or useful Bell inequalities is nonetheless by no means obvious. For instance, the approach of solving for the complete set of optimal, i.e., facet-defining Bell inequalities for a given experimental scenario -though potentially useful for the identification of non-Bell-local (hereafter nonlocal) correlationstypically produces a large number of inequalities with no * yliang@phys.ethz....

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“…However, they can be easily determined from the expectation values of local observables [31,[33][34][35], as we see below. To determine the off-diagonal and diagonal elements that appear in the expression (5) we present local observables in terms of Pauli operators [17].…”

Section: Experimental Feasibilitymentioning

confidence: 99%

“…The separability condition which is given in terms of density matrix elements is found useful in detecting genuine multipartite entanglement and nonseparability of multipartite states [27,28,31]. Inspired by this, we derive our k-separability condition by using the density matrix elements.…”

Section: Counts On Partitions Of K-separable N -Partite Statesmentioning

confidence: 99%

On the Non-k-Separability of Dicke Class of States and N-Qudit W States

Ananth

Senthilvelan

2015

Int J Theor Phys

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In this paper, we present the separability criteria to identify non-k-separability and genuine multipartite entanglement in mixed multipartite states using elements of density matrices. Our criteria can detect the non-k-separability of Dicke class of states, anti W states and mixtures thereof and higher dimensional W class of states. We then investigate the performance of our criteria by considering N -qubit Dicke states with arbitrary excitations added with white noise and mixture of N -qudit W state with white noise. We also study the robustness of our criteria against white noise. Further, we demonstrate that our criteria are experimentally implementable by means of local observables such as Pauli matrices and generalized Gell-Mann matrices.

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Partial separability and entanglement criteria for multiqubit quantum states

Cited by 103 publications

References 54 publications

Entanglement and communication-reducing properties of noisyN-qubit states

Entanglement and communication-reducing properties of noisyN-qubit states

Family of Bell-like Inequalities as Device-Independent Witnesses for Entanglement Depth

On the Non-k-Separability of Dicke Class of States and N-Qudit W States

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