Abstract Detecting entanglement in multipartite quantum states is an inherently probabilistic process, typically with a few measured samples. The level of confidence in entanglement detection quantifies the scheme’s validity via the probability that the signal comes from a separable state, offering a meaningful figure of merit for big datasets. Yet, with limited samples, avoiding experimental data misinterpretations requires considering not only the probabilities concerning separable states but also the probability that the signal came from an entangled state, i.e. the detection scheme’s efficiency. We demonstrate this explicitly and apply a general method to optimize both the validity and the efficiency in small data sets providing examples using at most 20 state copies. The method is based on an analytical model of finite statistics effects on correlation functions which takes into account both a Frequentist as well as a Bayesian approach and is applicable to arbitrary entanglement witnesses.
Abstract Detecting entanglement in multipartite quantum states is an inherently probabilistic process, typically with a few measured samples. The level of confidence in entanglement detection quantifies the scheme’s validity via the probability that the signal comes from a separable state, offering a meaningful figure of merit for big datasets. Yet, with limited samples, avoiding experimental data misinterpretations requires considering not only the probabilities concerning separable states but also the probability that the signal came from an entangled state, i.e. the detection scheme’s efficiency. We demonstrate this explicitly and apply a general method to optimize both the validity and the efficiency in small data sets providing examples using at most 20 state copies. The method is based on an analytical model of finite statistics effects on correlation functions which takes into account both a Frequentist as well as a Bayesian approach and is applicable to arbitrary entanglement witnesses.
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.
Abstract One of the main challenges of quantum information is the reliable verification of quantum entanglement. The conventional detection schemes require repeated measurement on a large number of identically prepared systems. This is hard to achieve in practice when dealing with large-scale entangled quantum systems. In this letter we formulate verification as a decision procedure, i.e., entanglement is seen as the ability of quantum system to answer certain “yes-no questions”. We show that for a variety of large quantum states even a single copy suffices to detect entanglement with a high probability by using local measurements. For example, a single copy of a 16-qubit k-producible state or one copy of 24-qubit linear cluster state suffices to verify entanglement with more than 95% confidence. Our method is applicable to many important classes of states, such as cluster states or ground states of local Hamiltonians in general.
Abstract 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 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.
Multipartite entanglement is a key resource allowing quantum devices to outperform their classical counterparts, and entanglement certification is fundamental to assess any quantum advantage. The only scalable certification scheme relies on entanglement witnessing, typically effective only for special entangled states. Here, we focus on finite sets of measurements on quantum states (hereafter called quantum data), and we propose an approach which, given a particular spatial partitioning of the system of interest, can effectively ascertain whether or not the dataset is compatible with a separable state. When compatibility is disproven, the approach produces the optimal entanglement witness for the quantum data at hand. Our approach is based on mapping separable states onto equilibrium classical field theories on a lattice and on mapping the compatibility problem onto an inverse statistical problem, whose solution is reached in polynomial time whenever the classical field theory does not describe a glassy system. Our results pave the way for systematic entanglement certification in quantum devices, optimized with respect to the accessible observables.
Genuine multipartite entanglement represents the strongest type of entanglement, which is an essential resource for quantum information processing. Standard methods to detect genuine multipartite entanglement, e.g., entanglement witnesses, 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 an 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 independently. However, it is difficult to certify genuine entanglement of practical multipartite states in this way, and even more difficult to quantify it, due to the difficulty in identifying optimal multipartite Bell inequalities and protocols tolerant to state impurity. In this Letter, we explore a general and robust device-independent method that can be applied to various realistic multipartite quantum states in arbitrary finite dimension, while merely relying on bipartite Bell inequalities. Our method allows us both to certify the presence of genuine multipartite entanglement and to quantify it. Several important classes of entangled states are tested with this method, leading to the detection of genuinely entangled states. We also certify genuine multipartite entanglement in weakly entangled Greenberger-Horne-Zeilinger states, showing that the method applies equally well to less standard states.
One of the main foci of modern applied quantum information theory\nis the production of large-scale quantum entanglement involving many\nparticles, to achieve the next-generation quantum technologies. Although a full-scale quantum computer is still far away in time, in the next\nfew years we can expect to have quantum devices composed of up to a\nhundred controllable qubits. The primary challenge in moving towards\nsuch devices lies in the development of reliable and resource-efficient\ndetection techniques to prove genuine quantum advantage. The main\nobjective of this thesis is to investigate novel methods to detect the presence of quantum correlations in such systems, in particular, quantum\nentanglement and quantum nonlocality.\nThe first part of this thesis is dedicated to entanglement detection\nin large-scale quantum systems. Our main goal is to develop a novel\nprobabilistic method in which entanglement is seen as an ability of a\nquantum system to accomplish certain information-processing tasks.\nWe show that for certain classes of large (e.g. few tens of qubits) quantum states, even a single copy of a quantum state suffices to detect\nentanglement with a high confidence. Compared to the standard detection methods, this makes our method exceptionally resource-efficient.\nThe developed probabilistic scheme applies to multiple classes of states, vital for quantum computation, such as cluster states or ground\nstates of local Hamiltonians.\nIn the second part of this thesis, we develop a generic framework\nfor translating any entanglement witness into a resource-efficient probabilistic scheme. We show that the confidence level of entanglement\ndetection grows exponentially fast with the number of detection events,\nwhich makes this ansatz very efficient and reliable. Furthermore, we\npresent the first experimental performance of our method by verifying\nthe presence of entanglement in a photonic six-qubit cluster state.\nThe third part of this thesis describes the extension of our entanglement verification method to quantum nonlocality. Concrete examples\nare presented where we convert Bell’s inequalities into the probabilistic\nprocedure and incorporate our method into self-testing schemes. We\nshow that the performance of our method significantly exceeds the ability of the existing methods for detection of quantum nonlocality and\nself-testing.\nThe last part of this thesis is a study of the weak-convergence properties of random variables generated by quantum measurements. Beginning with a sequence of random variables generated by repeated\nunsharp quantum measurements, we study the limit distribution of\nmeasured relative frequency. We provide the de Finetti-type of representation theorem for all separable states, showing that the measured\ndistribution can be well approximated by a mixture of normal distributions. Additionally, we investigate the convergence rates and show\nthat the relative frequency converges to some constant at the rate of\norder 1=pN for all separable inputs. Finally, we provide an example of\na strictly unsharp quantum measurement where we obtain better scaling by using entangled inputs. We find such behaviour of entangled\nstates relevant for quantum information processing.