Ultrafine Entanglement Witnessing

Abstract

Entanglement witnesses are invaluable for efficient quantum entanglement certification without the need for expensive quantum state tomography. Yet, standard entanglement witnessing requires multiple measurements and its bounds can be elusive as a result of experimental imperfections. Here, we introduce and demonstrate a novel procedure for entanglement detection which simply and seamlessly improves any standard witnessing procedure by using additional available information to tighten the witnessing bounds. Moreover, by relaxing the requirements on the witness operators, our method removes the general need for the difficult task of witness decomposition into local observables. We experimentally demonstrate entanglement detection with our approach using a separable test operator and a simple fixed measurement device for each agent. Finally, we show that the method can be generalized to higher-dimensional and multipartite cases with a complexity that scales linearly with the number of parties. DOI: 10.1103/PhysRevLett.118.110502 Quantum entanglement provides many advantages beyond classical limits, including quantum communication, computation, and information processing [1,2]. Yet, determining whether a given quantum state is entangled or not is a theoretically and experimentally challenging task [3,4]. In particular, the ideal approach of reconstructing the full quantum state via quantum tomography is practically infeasible for all but the smallest systems.An elegant solution to this problem, known as entanglement witnessing, relies on the geometry of the set of nonentangled (separable) quantum states [2,[5][6][7]. Since these states form a convex set, it is always possible to find a hyperplane such that a given entangled state lies on one side of the hyperplane, while all separable states are on the other side, see Fig. 1. This hyperplane is a so-called entanglement witness (EW) and corresponds to a joint observable that has a bounded expectation value over all separable quantum states. Any quantum state that produces a value beyond the bound must be entangled. This simplification, however, comes at a cost: first, different entangled states in general require different EWs to be detected; second, not every EW can be practically realized, i.e., can be decomposed into operators corresponding to available local measurement devices (See also Refs. [7][8][9] for examples of the reverse procedure: constructing EWs from local observables); third, when such a decomposition is possible, it might require multiple measurement devices (with multiple settings) to be implemented; and fourth, witnessing bounds can be elusive in the presence of experimental imperfections. Consequently, the goal is to construct EWs that have a simple decomposition and, at the same time, detect a large set of entangled states.There are three main techniques to improve EWs. First, adding nonlinear terms to the original witness operator [10]; second, using collective measurements of EWs on multiple copies of the quantum state [11]; and third, op...

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