Entanglement is an essential resource in quantum information science [1] and its presence in any quantum system can be experimentally detected through entanglement witness operators [2]. In particular, measuring a negative expectation value of a witness with high statistical confidence provides a necessary and sufficient condition to confirm the generation of a genuine multipartite [3] and/or d-level entangled state [4]. In recent years, the experimental generation of complex quantum states has intensified the need for witnesses that are capable of detecting such systems and are experimentally optimal at the same time. This means that the witness should require the least measurement effort (in terms of number and complexity of the measurement settings), include only projections on single qudits, while at the same time possessing a high noise tolerance (Fig. 1a). However, "experimentally-friendly" witnesses capable of accomplishing these tasks have not been derived yet.
Entanglement is an essential resource in quantum information science [1] and its presence in any quantum system can be experimentally detected through entanglement witness operators [2]. In particular, measuring a negative expectation value of a witness with high statistical confidence provides a necessary and sufficient condition to confirm the generation of a genuine multipartite [3] and/or d-level entangled state [4]. In recent years, the experimental generation of complex quantum states has intensified the need for witnesses that are capable of detecting such systems and are experimentally optimal at the same time. This means that the witness should require the least measurement effort (in terms of number and complexity of the measurement settings), include only projections on single qudits, while at the same time possessing a high noise tolerance (Fig. 1a). However, "experimentally-friendly" witnesses capable of accomplishing these tasks have not been derived yet.
Entanglement witnesses are operators that are crucial for confirming the generation of specific quantum systems, such as multipartite and high-dimensional states. For this reason, many witnesses have been theoretically derived which commonly focus on establishing tight bounds and exhibit mathematical compactness as well as symmetry properties similar to that of the quantum state. However, for increasingly complex quantum systems, established witnesses have lacked experimental achievability, as it has become progressively more challenging to design the corresponding experiments. Here, we present a universal approach to derive entanglement witnesses that are capable of detecting the presence of any targeted complex pure quantum system and that can be customized towards experimental restrictions or accessible measurement settings. Using this technique, we derive experimentally optimized witnesses that are able to detect multipartite d-level cluster states, and that require only two measurement settings. We present explicit examples for customizing the witness operators given different realistic experimental restrictions, including witnesses for high-dimensional entanglement that use only two-dimensional projection measurements. Our work enables us to confirm the presence of probed quantum states using methods that are compatible with practical experimental realizations in different quantum platforms.
Although the realization of useful quantum computers poses significant challenges, swift progress in emerging quantum technologies is making this goal realistically approachable. In this context, one of the essential resources is quantum entanglement, which allows for quantum computations outperforming their classical counterparts. However, the task of entanglement detection is not always straightforward for several reasons. One of the main challenges is that standardly-used methods rapidly become unfeasible when dealing with quantum states containing more than a few qubits. Typically, this is due to the fact that a vast amount of measurements is needed on many copies of the state. Generally, it is not unusual to deal with a very limited number of state copies in experimental settings - in fact, this may be the case for many large quantum systems. In this article, an overview is provided of a probabilistic approach that enables high-confidence genuine multipartite entanglement detection using an exceptionally low number of state copies. Additionally, a study is presented that shows that this protocol remains efficient also in the presence of noise, thus confirming the practicality of the method for near-term quantum devices and its suitability for complex experimental settings.
Entanglement witnesses are essential for certifying entanglement, yet constructing ones that are both noise-robust and economical in measurement settings remains challenging - particularly beyond qubits and for non-stabilizer ("magic") states. We present a machine-learning method that, given a target state and a user-specified number of measurement settings, generates an entanglement witness optimized for noise tolerance in the neighborhood of that state, requiring only local measurements. The approach is fully general, applying to multipartite qubit and qudit systems alike, including non-stabilizer states. For N qudits of dimension d, we train on the fully-separable eigenstates of each qudit's SU(d) generators to find a prototype witness, then tune the witness's bias term via gradient descent to maximize noise tolerance. Adversarial training further strengthens the witnesses, delivering greater noise tolerance with even fewer settings; critically, under this scheme the required training-set size becomes independent of system size. We package the entire pipeline as an automated script that, in every case we tested, produces witnesses surpassing all existing methods in noise tolerance and/or number of measurement settings. We demonstrate the method on Bell, GHZ, W, and hypergraph states, along with a range of qudit states, spanning 2-6 qubits, bipartite qudits up to d=10, and tripartite qutrits. Our witnesses achieve perfect accuracy across both physical experimental test states and large numerical sets of separable mixed states-including 30 million test states for a 3-qubit W-state witness and 10 million for a 4-qubit hypergraph-state witness-and we experimentally confirm the noise tolerance of Bell- and hypergraph state witnesses on both photonic and superconducting platforms, respectively.
Certifying entanglement of a multipartite state is generally considered a demanding task. Since an N qubit state is parametrized by 4^{N}-1 real numbers, one might naively expect that the measurement effort of generic entanglement detection also scales exponentially with N. Here, we introduce a general scheme to construct efficient witnesses requiring a constant number of measurements independent of the number of qubits for states like, e.g., Greenberger-Horne-Zeilinger states, cluster states, and Dicke states. For four qubits, we apply this novel method to experimental realizations of the aforementioned states and prove genuine four-partite entanglement with two measurement settings only.
The design of detection strategies for multipartite entanglement stands as a central importance on our understanding of fundamental quantum mechanics and has had a substantial impact on quantum information applications. However, accurate and robust detection approaches are severely hindered, particularly when the number of nodes grows rapidly like in a quantum network. Here we present a general and operational framework that generates alternative entanglement witness for an arbitrary targeted state. The framework enjoys a systematic and high-efficient character and allows to substantiate genuine multipartite entanglement for a variety of states that arise naturally in practical situations and to dramatically outperform currently standard methods. With excellent noise tolerance, our framework should be broadly applicable to witness genuine multipartite entanglement in various practically scenarios and to facilitate the best use of entangled resources in the emerging area of quantum network.
Experimental detection of entanglement of an arbitrary state of a given bipartite system is crucial for exploring many areas of quantum information processing. But such a detection should be made in a device-independent way if the preparation process of the state is considered to be faithful, in order to avoid detection of a separable state as an entangled one. The recently developed scheme of detecting bipartite entanglement in a measurement-device-independent way [Phys. Rev. Lett. 110, 060405 (2013)] does require information about the state. Here, by using Auguisiak et al.'s universal entanglement witness scheme for two-qubit states [Phys. Rev. A 77, 030301 (2008)], we provide a universal entanglement detection scheme for two-qubit states in a measurement-device-independent way. We also provide a set of universal witness operators for detecting NPT-ness (negative under partial transpose) of two-qudit states in a measurement-device-independent way. We conjecture that no such universal entanglement witness scheme exists for PPT (positive under partial transpose) entangled states. We also analyze the robustness of some of the experimental schemes---for detecting entanglement in a measurement-device-independent way---under the influence of noise in the inputs (from the referee) as well as in the measurement operator.