Entangled particles exhibit quantum correlations over arbitrary long distances in time and space which cannot be mimicked by local realistic models. In order to detect and utilize these correlations for quantum information tasks, measurements in different bases are necessary. A variety of schemes for experimentally characterizing quantum states have been devised. However, these are often experimentally demanding in terms of stability and insensitivity against noise. Standard methods such as state tomography and Bell tests will fail to reliably detect quantum correlations in the presence of unknown local perturbations to the measuring apparatus, as consecutive measurements must be co-ordinated via a shared choice of measurement basis (a shared reference frame). So called reference frame independent schemes overcome this difficulty, however, even these schemes fail when the choice of local measurement setting is not repeatable, i.e. when there is drift.
Entangled particles exhibit quantum correlations over arbitrary long distances in time and space which cannot be mimicked by local realistic models. In order to detect and utilize these correlations for quantum information tasks, measurements in different bases are necessary. A variety of schemes for experimentally characterizing quantum states have been devised. However, these are often experimentally demanding in terms of stability and insensitivity against noise. Standard methods such as state tomography and Bell tests will fail to reliably detect quantum correlations in the presence of unknown local perturbations to the measuring apparatus, as consecutive measurements must be co-ordinated via a shared choice of measurement basis (a shared reference frame). So called reference frame independent schemes overcome this difficulty, however, even these schemes fail when the choice of local measurement setting is not repeatable, i.e. when there is drift.
The fact that quantum mechanics predicts stronger correlations than classical physics is an essential cornerstone of quantum information processing. Indeed, these quantum correlations are a valuable resource for various tasks, such as quantum key distribution or quantum teleportation, but characterizing these correlations in an experimental setting is a formidable task, especially in scenarios where no shared reference frames are available. By definition, quantum correlations are reference-frame independent, i.e., invariant under local transformations; this physically motivated invariance implies, however, a dedicated mathematical structure and, therefore, constitutes a roadblock for an efficient analysis of these correlations in experiments. Here we provide a method to directly measure any locally invariant property of quantum states using locally randomized measurements, and we present a detailed toolbox to analyze these correlations for two quantum bits. We implement these methods experimentally using pairs of entangled photons, characterizing their usefulness for quantum teleportation and their potential to display quantum nonlocality in its simplest form. Our results can be applied to various quantum computing platforms, allowing simple analysis of correlations between arbitrary distant qubits in the architecture.
We show that the expectation value of squared correlations measured along random local directions is an identifier of quantum entanglement in pure states, which can be directly experimentally assessed if two copies of the state are available. Entanglement can therefore be detected by parties who do not share a common reference frame and whose local reference frames, such as polarizers or Stern-Gerlach magnets, remain unknown. Furthermore, we also show that in every experimental run, access to only one qubit from the macroscopic reference is sufficient to identify entanglement, violate a Bell inequality, and, in fact, observe all phenomena observable with macroscopic references. Finally, we provide a state-independent entanglement witness solely in terms of random correlations and emphasize how data gathered for a single random measurement setting per party reliably detects entanglement. This is only possible due to utilized randomness and should find practical applications in experimental confirmation of multiphoton entanglement or space experiments.
Quantum entanglement is one of the core features of quantum theory. While it is typically revealed by measurements along carefully chosen directions, here we review different methods based on so-called random or randomized measurements. Although this approach might seem inefficient at first, sampling correlations in various random directions is a powerful tool to study properties which are invariant under local-unitary transformations. Based on random measurements, entanglement can be detected and characterized without a shared reference frame between the observers or even if local reference frames cannot be defined. This overview article discusses different methods using random measurements to detect genuine multipartite entanglement and to distinguish SLOCC classes. Furthermore, it reviews how measurement directions can efficiently be obtained based on spherical designs.
We report on the first experimental verification of mode-independent entanglement. Commonly, the entanglement of a state is firmly based on pre-defined parties that are correlated, and the state might be disentangled when the definition of the parties is changed. Exceeding this party-dependent concept, we realize a type of quantum entanglement that persists even if the parties, in our case modes, are transformed. This safeguards the performance of entanglement in real-world applications, such as quantum communication settings involving noise and untrusted parties. For the state generation, we present an experimental scheme based on a fully reconfigurable temporally multiplexed interferometer with measurement-induced nonlinearities, which generates heralded two-photon states in two modes that are entangled for all choices of orthonormal mode basis. For the certification process, we utilize a tailored quantum-state tomography, achieving fidelities that validate the presence of mode-independent entanglement as a resilient and operationally advantageous quantum correlation.
Quantum entanglement, has been acknowledged as a precious resource due to its inherent nonclassical correlations between subsystems. These quantum correlations have the potential for many quantum processes, including canonical ones: quantum cryptography, quantum teleportation, and dense coding. To exploit the advantages of quantum entanglement, two essential premises are required, i.e., to prepare high-quality entanglement and characterize quality level of prepared entanglement. Thus far, quantum entanglement can be produced in various quantum systems; however, it appears that this new resource is complex and difficult to characterize. The standard methods to characterize multipartite entanglement, e.g., entanglement witness, state tomography, or quantum state verification, require full knowledge of the Hilbert space dimension and precise calibration of measurement devices, which are usually difficult to acquire in experiment. The most radical way to overcome these problems is to detect entanglement solely based on the Bell-like correlations of measurement outcomes collected in the experiment, namely, device-independent characterization of entanglement. This article reviews the recently developed device-independent methods to characterize entanglement, including self-testing and device-independent certification of entanglement. These approaches can be widely applied in kinds of quantum information processing, especially for those with security demands.
The experimental detection of multipartite entanglement usually requires a number of appropriately chosen local quantum measurements that are aligned with respect to a previously shared common reference frame. The latter, however, can be a challenging prerequisite, e.g., for satellite-based photonic quantum communication, making the development of alternative detection strategies desirable. One possibility for avoiding the distribution of classical reference frames is to perform a number of local measurements with settings distributed uniformly at random. In this Letter, we follow such a treatment and show that an improved detection and characterization of multipartite entanglement is possible by combining statistical moments of different order. To do so, we make use of designs that are pseudorandom processes allowing us to link the present entanglement criteria to ordinary reference frame independent ones. The strengths of our methods are illustrated in various cases, starting with two qubits and followed by more involved multipartite scenarios.