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Detecting three or more partite entanglement of pure states with bipartite correlations

Marcin Markiewicz, Wiesław Laskowski, Tomasz Paterek, Marek Żukowski

Published Oct 19, 2012• 0 citations
OpenAlex

Abstract

We show that monogamy of bipartite correlations leads to experimentally friendly conditions for detection of multipartite entanglement of pure states. The conditions make no additional assumptions about tested states and we illustrate their application with Dicke states. Finally, we compare this criterion with quantum marginal problem and criteria based on spin operators.

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We show that monogamy of bipartite correlations leads to experimentally friendly conditions for detection of multipartite entanglement of pure states. The conditions make no additional assumptions about tested states and we illustrate their application with Dicke states. Finally, we compare this criterion with quantum marginal problem and criteria based on spin operators.
Monogamy of bipartite correlations leads, for arbitrary pure multiqubit states, to simple conditions able to indicate various types of multipartite entanglement by being capable of excluding the possibility of kkk separability.
I present methods for detecting entanglement around symmetric Dicke states. In particular, I consider N-qubit symmetric Dicke states with N/2 excitations. I show that for large N these states have the smallest overlap possible with states without genuine multipartite entanglement. Thus these states are particularly well suited for the experimental examination of multipartite entanglement. I present fidelity-based entanglement witness operators for detecting multipartite entanglement around these states. I then consider entanglement criteria, somewhat similar to the spin squeezing criterion, based on the moments or variances of the collective spin operators. Surprisingly, these criteria are based on an upper bound for variances for separable states. I present criteria detecting entanglement in general and criteria detecting only genuine multipartite entanglement. The collective operator measured for this criteria is an important physical quantity: Its expectation value essentially gives the intensity of the radiation when a coherent atomic cloud emits light.
Dicke states represent a class of multipartite entangled states that can be generated experimentally with many applications in quantum information. We propose a method to experimentally detect genuine multipartite entanglement in the vicinity of arbitrary Dicke states. The detection scheme can be used to experimentally quantify the entanglement depth of many-body systems and is easy to implement as it requires measurement of only three collective spin operators. The detection criterion is strong as it heralds multipartite entanglement even in cases where the state fidelity goes down exponentially with the number of qubits.
We present methods for detecting entanglement around N-qubit Dicke states with N/2 excitations. In the first part of the paper we show that for large N these states have the smallest overlap possible with states without multi-partite entanglement. Thus these states are particulary well suited for experiments aimed to create and detect genuine multi-partite entanglement. We present fidelity-based entanglement witness operators for detecting multipartite entanglement around these states. In the second part of the paper we consider entanglement criteria, somewhat similar to spin squeezing, based on the moments or variances of the collective spin operators. We present both criteria detecting entanglement in general and criteria detecting only genuine multi-partite entanglement.
We construct a set of criteria detecting genuine multipartite entanglement in arbitrary dimensional multipartite systems. These criteria are optimally suited for detecting multipartite entanglement in nnn-qubit Dicke states with mmm excitations, as shown in exemplary cases. Furthermore, they can be employed to detect multipartite entanglement in different states related to quantum cloning, decoherence-free communication, and quantum secret sharing. In a detailed analysis, we show that the criteria are also more robust to noise than any other criterion known so far, especially with increasing system size. Furthermore, it is shown that the number of required local observables scales only polynomially with size, thus making the criteria experimentally feasible.
We formulate an entanglement criterion using Peres-Horodecki positive partial transpose operations combined with the Schr\"odinger-Robertson uncertainty relation. We show that any pure entangled bipartite and tripartite state can be detected by experimentally measuring mean values and variances of specific observables. Those observables must satisfy a specific condition in order to be used, and we show their general form in the $2\ifmmode\times\else\texttimes\fi{}2$ (two qubits) dimension case. The criterion is applied on a variety of physical systems including bipartite and multipartite mixed states and reveals itself to be stronger than the Bell inequalities and other criteria. The criterion also work on continuous variable cat states and angular momentum states of the radiation field.