Entanglement Detection Research Articles

Few‐Copy Entanglement Detection in the Presence of Noise

AbstractAlthough 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 standard 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 number of measurements are 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.

Optimized search for complex protocols based on entanglement detection

Optimized search for complex protocols based on entanglement detection

Monochorionic-Diamniotic Twin Pregnancy Complicated by Spontaneous Septostomy and Cord Entanglement: A Systematic Review, Evaluation of Complication Rates and Presentation of an Additional Case

Background: Our purpose is to describe the ultrasound findings, both with bi-dimensional and three-dimensional imaging, suggestive of spontaneous septostomy in monochorionic-diamniotic twin pregnancies. Methods: PubMed, Medline and reference lists were searched using “Spontaneous septostomy and twin pregnancy” as keywords. Seventeen articles reporting a total of 25 cases, adding our own, were included in the systematic review. Only English full text articles, the main purpose of which was to describe spontaneous septostomy in twin pregnancies, were included. Results: In our sample the major ultrasound sign arousing suspicion of spontaneous septostomy was found to be an absent or disrupted inter-twin membrane (79% of cases). Twins close to each-other were described in 33% of cases, while cord entanglement was suspected only in 27% of cases. We reported a lower antenatal detection of entanglement when compared with intrapartum evaluation (27% vs 59%). Adverse fetal outcomes occurred in 12% of cases, while 88% of cases were born alive. Conclusions: Spontaneous septostomy represents a diagnostic and clinical challenge for obstetrics providers. Clinicians must focus on ultrasound findings to close surveil fetal wellness and reduce both fetal and neonatal impairment.

Detecting and quantifying entanglement on near-term quantum devices

Quantum entanglement is a key resource in quantum technology, and its quantification is a vital task in the current noisy intermediate-scale quantum (NISQ) era. This paper combines hybrid quantum-classical computation and quasi-probability decomposition to propose two variational quantum algorithms, called variational entanglement detection (VED) and variational logarithmic negativity estimation (VLNE), for detecting and quantifying entanglement on near-term quantum devices, respectively. VED makes use of the positive map criterion and works as follows. Firstly, it decomposes a positive map into a combination of quantum operations implementable on near-term quantum devices. It then variationally estimates the minimal eigenvalue of the final state, obtained by executing these implementable operations on the target state and averaging the output states. Deterministic and probabilistic methods are proposed to compute the average. At last, it asserts that the target state is entangled if the optimized minimal eigenvalue is negative. VLNE builds upon a linear decomposition of the transpose map into Pauli terms and the recently proposed trace distance estimation algorithm. It variationally estimates the well-known logarithmic negativity entanglement measure and could be applied to quantify entanglement on near-term quantum devices. Experimental and numerical results on the Bell state, isotropic states, and Breuer states show the validity of the proposed entanglement detection and quantification methods.

All classes of informationally complete symmetric measurements in finite dimensions

A broad class of informationally complete symmetric measurements is introduced. It can be understood as a common generalization of symmetric, informationally complete POVMs and mutually unbiased bases. Additionally, it provides a natural way to define two new families of mutually unbiased symmetric measurement operators in any finite dimension. We show a general method of their construction, together with an example of an optimal measurement. Finally, we analyze the properties of symmetric measurements and provide applications in entropic relations and entanglement detection.

Demonstrating Shareability of Multipartite Einstein-Podolsky-Rosen Steering.

Einstein-Podolsky-Rosen (EPR) steering, a category of quantum nonlocal correlations describing the ability of one observer to influence another party's state via local measurements, is different from both entanglement and Bell nonlocality by possessing an asymmetric property. For multipartite EPR steering, the monogamous situation, where two observers cannot simultaneously steer the state of the third party, has been investigated rigorously both in theory and experiment. In contrast to the monogamous situation, the shareability of EPR steering in reduced subsystems allows the state of one party to be steered by two or more observers and thus reveals more configurations of multipartite EPR steering. However, the experimental implementation of such a kind of shareability has still been absent until now. Here, in an optical experiment, we provide a proof-of-principle demonstration of the shareability of EPR steering without the constraint of monogamy in a three-qubit system. Moreover, based on the reduced bipartite EPR steering detection results, we verify the genuine three-qubit entanglement results. This work provides a complementary viewpoint for understanding multipartite EPR steering and has potential applications in many quantum information protocols, such as multipartite entanglement detection, quantum cryptography, and the construction of quantum networks.

Local and scalable detection of genuine multipartite single-photon path entanglement

How can a multipartite single-photon path-entangled state be certified efficiently by means of local measurements? We address this question by constructing an entanglement witness based on local photon detections preceded by displacement operations to reveal genuine multipartite entanglement. Our witness is defined as a sum of three observables that can be measured locally and assessed with two measurement settings for any number of parties N. For any bipartition, the maximum mean value of the witness observable over biseparable states is bounded by the maximum eigenvalue of an N×N matrix, which can be computed efficiently. We demonstrate the applicability of our scheme by experimentally testing the witness for heralded 4- and 8-partite single-photon path-entangled states. Our implementation shows the scalability of our witness and opens the door for distributing photonic multipartite entanglement in quantum networks at high rates.

Quantum Verification and Estimation with Few Copies

AbstractAs quantum technologies advance, the ability to generate increasingly large quantum states has experienced rapid development. In this context, the verification and estimation of large entangled systems represent one of the main challenges in the employment of such systems for reliable quantum information processing. Though the most complete technique is undoubtedly full tomography, the inherent exponential increase of experimental and post‐processing resources with system size makes this approach infeasible even at moderate scales. For this reason, there is currently an urgent need to develop novel methods that surpass these limitations. This review article presents novel techniques focusing on a fixed number of resources (sampling complexity), and thus prove suitable for systems of arbitrary dimension. Specifically, a probabilistic framework requiring at best only a single copy for entanglement detection is reviewed, together with the concept of selective quantum state tomography, which enables the estimation of arbitrary elements of an unknown state with a number of copies that is low and independent of the system's size. These hyper‐efficient techniques define a dimensional demarcation for partial tomography and open a path for novel applications.

Unveiling Quantum Entanglement in Many-Body Systems from Partial Information

Quantum entanglement is commonly assumed to be a central resource for quantum computing and quantum simulation. Nonetheless, the capability to detect it in many-body systems is severely limited by the absence of sufficiently scalable and flexible certification tools. This issue is particularly critical in situations where the structure of entanglement is a priori unknown, and where one cannot rely on existing entanglement witnesses. Here, we implement a scheme in which the knowledge of the mean value of arbitrary observables can be used to probe multipartite entanglement in a scalable, certified, and systematic manner. Specifically, we rely on positive semidefinite conditions, independent of partial-transposition-based criteria, necessarily obeyed if the data can be reproduced by a separable state. The violation of any of these conditions yields a specific entanglement witness, tailored to the data of interest, revealing the salient features of the data which are impossible to reproduce without entanglement. We validate this approach by probing theoretical many-body states of several hundreds of qubits relevant to existing experiments: a single-particle quench in a one-dimensional XX chain; a many-body quench in a two-dimensional XX model with 1/r3 interactions; and thermal equilibrium states of Heisenberg and transverse-field Ising chains. In all cases, these investigations have led us to discover new entanglement witnesses, some of which could be characterized analytically, generalizing existing results in the literature. In summary, our paper introduces a flexible data-driven entanglement detection technique for uncharacterized quantum many-body states, of immediate relevance to experiments in a quantum advantage regime.Received 11 August 2021Revised 2 December 2021Accepted 22 February 2022DOI:https://doi.org/10.1103/PRXQuantum.3.010342Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasEntanglement detectionQuantum entanglementPhysical SystemsQuantum spin modelsTechniquesData analysisSemiclassical methodsQuantum InformationAtomic, Molecular & OpticalStatistical Physics

Efficient Bipartite Entanglement Detection Scheme with a Quantum Adversarial Solver.

The recognition of entanglement states is a notoriously difficult problem when no prior information is available. Here, we propose an efficient quantum adversarial bipartite entanglement detection scheme to address this issue. Our proposal reformulates the bipartite entanglement detection as a two-player zero-sum game completed by parameterized quantum circuits, where a two-outcome measurement can be used to query a classical binary result about whether the input state is bipartite entangled or not. In principle, for an N-qubit quantum state, the runtime complexity of our proposal is O(poly(N)T) with T being the number of iterations. We experimentally implement our protocol on a linear optical network and exhibit its effectiveness to accomplish the bipartite entanglement detection for 5-qubit quantum pure states and 2-qubit quantum mixed states. Our work paves the way for using near-term quantum machines to tackle entanglement detection on multipartite entangled quantum systems.

Detection of genuine tripartite entanglement based on Bloch representation of density matrices

We study the genuine multipartite entanglement in tripartite quantum systems. By using the Schmidt decomposition and local unitary transformation, we convert the general states to simpler forms and consider certain matrices from correlation tensors in the Bloch representation of the simplified density matrices. Using these special matrices, we obtain new criteria for genuine multipartite entanglement. Detail examples show that our criteria are able to detect more tripartite entangled and genuine tripartite entangled states than some existing criteria.

Optimal fidelity witnesses for gravitational entanglement

Optomechanical systems open new possibilities in fundamental research at the interface between quantum information and gravity. Recently, an ambitious experimental proposal was suggested by Bose et al. to measure the entanglement between two optomechanical systems generated by their gravitational interaction. The scheme relies on witnessing entanglement between the two systems. Here we develop a general framework to study the quality of bipartite entanglement witnesses using fidelity witnesses. We then apply this framework to the gravitational entanglement proposal, optimizing for the detection of entanglement. We construct a witness consisting of only 5 non-trivial spin measurements, which we compare with other proposed witnesses. With post-processing our witness can detect entanglement for any choice of phases in the setup, up to a set of measure zero.

Nonlocal operation enhanced entanglement detection and classification

Based on the nature that nonlocal operation will change the fixed quantum statistical speed limited by the local operation, we study the performance of Ising-type nonlocal operation in multipartite entanglement detection and classification. We first present the formula of quantum statistical speed for general quantum state under the two-body nonlocal operation, and then investigate several important and experimentally relevant states, including N-qubit W state, Twin-Fock state, Q state and N-qubit GHZ state. The results show that the optimal nonlocal operation can be used to address some intractable problems encountered under the local operation, such as the classification of N-qubit W state and entanglement detection of Q state at the edges. Meanwhile, some defects are presented and discussed. Interestingly, the N-qubit GHZ state is found to be stable when it is probed by weaker nonlocal operation (γ≤N−1) and it maybe helpful to the experimental research. Our work provides an alternative route to investigate entanglement detection and classification, especially for the novel and complex quantum system.

Operational Detection of Entanglement via Quantum Designs

AbstractFrom an operational point of view, several new entanglement detection criteria are proposed using quantum designs. These criteria are constructed by considering the correlations defined with quantum designs. Counter‐intuitively, the criteria with more settings are exactly equivalent to the corresponding ones with the minimal number of settings, namely the symmetric informationally complete positive operator‐valued measures (SIC POVMs). Fundamentally, this observation highlights the potentially unique role played by SIC POVMs in quantum information processing. Experimentally, this provides the minimal number of settings that one should choose for detecting entanglement. Furthermore, it is found that nonlinear criteria are not always better than linear ones for the task of entanglement detection.

Not All Entangled States are Useful for Ancilla‐Assisted Quantum Process Tomography

AbstractIt is well known that one can extract all the information of an unknown quantum channel by means of quantum process tomography, such as standard quantum‐process tomography and ancilla‐assisted quantum process tomography (AAQPT). Furthermore, it is shown that entanglement is not necessary for AAQPT; there exist separable states that are also useful for it. Surprisingly, in this work we find that not all entangled states are useful for AAQPT; there also exist some entangled states that are useless. The realignment operation used in entanglement detection can be related to the question whether a bipartite state is useful for AAQPT. The relationship between them is derived and the process of extracting the complete information of an unknown channel by the realignment operation shown. Based on this relationship, examples of a two‐qutrit entangled state and a two‐qutrit bound entangled state are presented. Both of these two examples are entangled but they cannot be used for AAQPT. Last but not the least, experimental verification is been performed on the IBM platform.

Estimating Non-Gaussianity of a Quantum State by Measuring Orthogonal Quadratures.

We derive the lower bounds for a non-Gaussianity measure based on quantum relative entropy (QRE). Our approach draws on the observation that the QRE-based non-Gaussianity measure of a single-mode quantum state is lower bounded by a function of the negentropies for quadrature distributions with maximum and minimum variances. We demonstrate that the lower bound can outperform the previously proposed bound by the negentropy of a quadrature distribution. Furthermore, we extend our method to establish lower bounds for the QRE-based non-Gaussianity measure of a multimode quantum state that can be measured by homodyne detection, with or without leveraging a Gaussian unitary operation. Finally, we explore how our lower bound finds application in non-Gaussian entanglement detection.

Detection of genuine multipartite entanglement based on principal basis matrix representations

We study the genuine multipartite entanglement in tripartite quantum systems by using the principal basis matrix representations of density matrices. Using the Schmidt decomposition and local unitary transformation, we first convert the general states to simpler forms and then construct some special matrices from the correlation tensors of the simplified density matrices. Based on the different linear combinations of these matrices, necessary conditions are presented to detect genuine multipartite entanglement of tripartite states. Detailed examples show that our method can detect more entangled states than previous ones.

Quantum Radars and Lidars: Concepts, realizations, and perspectives

Quantum radars and lidars are a novel, much-discussed, and rapidly evolving field of quantum science and technology, promising remarkable advantages in such basic tasks as target detection, ranging, and recognition. Quantum radars and lidars have already moved from the realm of theoretical considerations toward experiments, green, and as is the case for lidars, toward practical applications. Here we review the underlying concepts and present the basic configurations of quantum radars and lidars based on photonic entanglement and single-photon detection. We also briefly discuss the methods of producing entangled photons, such as spontaneous parametric down conversion (SPDC), spontaneous four-wave mixing, Josephson parametric amplifiers (JPAs), and quantum antennas. We show that quantum technologies open promising avenues toward the enhancement of signal-to-noise ratio (SNR) and overcoming the Rayleigh limit in radar and lidar systems.

A perspective on quantum entanglement in optomechanical systems

Quantum entanglement in optomechanical systems plays an important role in the progress of quantum science and technology, such as the exploration of fundamental physics and quantum information processing. Although the physical law of quantum mechanics does not specifically limit the size of objects that carry the entangled states, the experimental preparation and detection of quantum entanglement in the macro world still face great challenges. Fortunately, with the experimental advances in recent years, several pioneering works have demonstrated non-local correlation and entanglement among mechanical oscillators or between oscillators and electromagnetic fields. In this perspective, we summarize the theoretical and experimental progress related to the macro entanglement states in optomechanical systems and outlook its future direction and potential applications.

Detecting Entanglement Structure in Continuous Many-Body Quantum Systems.

A prerequisite for the comprehensive understanding of many-body quantum systems is a characterization in terms of their entanglement structure. The experimental detection of entanglement in spatially extended many-body systems describable by quantum fields still presents a major challenge. We develop a general scheme for certifying entanglement and demonstrate it by revealing entanglement between distinct subsystems of a spinor Bose-Einstein condensate. Our scheme builds on the spatially resolved simultaneous detection of the quantum field in two conjugate observables which allows the experimental confirmation of quantum correlations between local as well as nonlocal partitions of the system. The detection of squeezing in Bogoliubov modes in a multimode setting illustrates its potential to boost the capabilities of quantum simulations to study entanglement in spatially extended many-body systems.