Abstract
Multipartite entanglement is very poorly understood despite all the theoretical and experimental advances of the last decades. Preparation, manipulation and identification of this resource is crucial for both practical and fundamental reasons. However, the difficulty in the practical manipulation and the complexity of the data generated by measurements on these systems increase rapidly with the number of parties. Therefore, we would like to experimentally address the problem of how much information about multipartite entanglement we can access with incomplete measurements. In particular, it was shown that some types of pure multipartite entangled states can be witnessed without measuring the correlations [M. Walter et al., Science 340, 1205 (2013)] between parties, which is strongly demanding experimentally. We explore this method using an optical setup that permits the preparation and the complete tomographic reconstruction of many inequivalent classes of three- and four-partite entangled states, and compare complete versus incomplete information. We show that the method is useful in practice, even for non-pure states or non ideal measurement conditions.
Highlights
According to quantum mechanics, the state of a system can be represented by a linear combination of different eigenstates of an observable
The main idea is to use twin photons, which are entangled in the polarization degree of freedom, and to perform some operations to entangle this degree of freedom with the spatial mode of one or both photons, to produce three- or fourpartite entangled states, respectively
We begin with all the qubits initialized in the state j0 ̄ii, with i 1⁄4 Ap; Bp; As. (This represents a general initial state and not necessarily the usual computational basis employed throughout the text.) In step 1, we implement a Hadamard (H) and a controlled- NOT (CNOT) gate in qubits Ap and Bp producing a global state that is entangled in the ApBp partition and separable with respect to As
Summary
The state of a system can be represented by a linear combination of different eigenstates of an observable. How to theoretically identify and experimentally distinguish such classes is one of the fundamental problems in this field Another issue is related to the fact that the number of measurements, measurement time, and computational effort for processing the tomographic data of a multipartite state scales exponentially with the number of qubits. We test the limits of validity of a witness for multipartite entanglement [6] in a real laboratory scenario, in contrast to the ideal case of pure states We test this requirement experimentally and show that in our data, the criteria remain useful to study the properties of different kinds of entanglement, even under. This improvement is related to the reduced number of measurements and to the reduced sensitivity to imperfections like nonunity detection efficiency
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