We give an overview of different types of entanglement that can be generated in experiments, as well as of various protocols that can be used to verify or quantify entanglement. We propose several criteria that, we argue, should be applied to experimental entanglement verification procedures. Explicit examples demonstrate that not following these criteria will tend to result in overestimating the amount of entanglement generated in an experiment or in infering entanglement when there is none. We distinguish protocols meant to refute or eliminate hidden-variable models from those meant to verify entanglement.
We report on experimental studies on entanglement quantification and verification based on uncertainty relations for systems consisting of two qubits. The new proposed measure is shown to be invariant under local unitary transformations, by which entanglement quantification is implemented for two-qubit pure states. The nonlocal uncertainty relations for two-qubit pure states are also used for entanglement verification which serves as a basic proposition and promise to be a good choice for verification of multipartite entanglement.
We report on the quantification of entanglement by means of entanglement measures on a four- and a six- qubit cluster state realized by using photons entangled both in polarization and linear momentum. This paper also addresss the question of the scaling of entanglement bounds from incomplete tomographic information on the density matrix under realistic experimental conditions.
We propose a protocol how to generate and verify bipartite Gaussian entanglement between two mechanical modes coupled to a single optical cavity, by means of short optical pulses and measurement. Our protocol requires neither the resolved sideband regime, nor low thermal phonon occupancy, and allows the generation and verification of quantum entanglement in less than a mechanical period of motion. Entanglement is generated via effective two-mode mechanical squeezing through conditioning position measurements. We study the robustness of entanglement to experimental deviations in mechanical freq…
Local unitary stabilizer subgroups constitute powerful invariants for distinguishing various types of multipartite entanglement. In this paper, we show how stabilizers can be used as a basis for entanglement verification protocols on distributed quantum networks using minimal resources. As an example, we develop and analyze the performance of a protocol to verify membership in the space of Werner states, that is, multi-qubit states that are invariant under the action of any 1-qubit unitary applied to all the qubits.
Entanglement and quantum interference are key ingredients in a variety of quantum information processing tasks. Harnessing the generation and characterization of entanglement in high-dimensional state spaces is a necessary prerequisite towards practical quantum protocols. Here, we use quantum interference on a beam splitter to engineer hyperentanglement in polarization and discrete frequency degrees of freedom (DOF). We show how independent measurements of polarization and frequency DOF allow for the verification of high-dimensional entanglement in the combined state space. These results may i…
The security analysis of quantum key distribution is difficult to perform when there is efficiency mismatch between various threshold detectors involved in an experimental setup. Even the verification that the device actually performs in the quantum domain, referred to as the task of entanglement verification, is hard to perform. In this article we provide such an entanglement-verification method for characterized detection-efficiency mismatch. Our method does not rely on a cut-off of photon numbers in the optical signal. It can be applied independently of the degrees of freedom involved, thus…
We experimentally investigate the properties of hyperentangled states displaying simultaneous entanglement in multiple degrees of freedom, and find that Bell tests beyond the standard Clauser, Horne, Shimony, Holt inequality can reveal a higher-dimensional nature in a device-independent way. Specifically, we show that hyperentangled states possess more than just simultaneous entanglement in separate degrees of freedom but also entanglement in a higher dimensional Hilbert space. We also verify the steerability of hyperentangled quantum states by steering different photonic degrees of freedom.
Bell inequalities were meant to test quantum mechanics vs local hidden variable models, but can also be used to verify entanglement. For entanglement verification purposes one assumes the validity of quantum mechanics as well as quantum descriptions of one's measurements. With the help of these assumptions it is possible to derive a strengthened Bell inequality whose violation implies entanglement. We generalize known examples of such inequalities by relating the expectation value of the Bell operator to a particular quantitative measure of entanglement, namely the negativity. Moreover, we obt…
In continuous-variable quantum information processing detectors are necessarily coarse grained and of finite range. We discuss how especially the latter feature is a bug and may easily lead to overoptimistic estimates of entanglement and of security, when missed data outside the detector range are ignored. We show that entropic separability or security criteria are much superior to variance-based criteria for mitigating the negative effects of this bug.
An optical procedure in the context of continuous variables to verify bipartite entanglement without destroying both systems and their entanglement is proposed. To perform the nondestructive verification of entanglement, the method relies on beam-splitter and quantum nondemolition (QND) interactions of the signal modes with two ancillary probe modes. The probe modes are measured by homodyne detections, and the obtained information is used to feed forward modulation of signal modes, concluding the procedure. Characterizing the method by figures of merit used in QND processes, we can establish t…
We present a method to test quantum behavior of quantum information processing devices, such as quantum memories, teleportation devices, channels and quantum key distribution protocols. The test of quantum behavior can be phrased as the verification of effective entanglement. Necessary separability criteria are formulated in terms of a matrix of expectation values in conjunction with the partial transposition map. Our method is designed to reduce the resources for entanglement verification. A particular protocol based on coherent states and homodyne detection is used to illustrate the method. …
The controlled generation of entangled states and their subsequent detection are integral aspects of quantum information science. In this work, we analyse the application of nonlinear witnesses to the verification of entanglement, and we demonstrate experimentally that nonlinear witnesses perform significantly better than linear witnesses. Specifically, we demonstrate that a single non- linear entanglement witness is able to determine to a high degree of certainty that a mixed state containing orbital angular momentum (OAM) entanglement of specific forms is entangled for any relative phase and…
Suppose an experimentalist wishes to verify that his apparatus produces entangled quantum states. A finite amount of data cannot conclusively demonstrate entanglement, so drawing conclusions from real-world data requires statistical reasoning. We propose a reliable method to quantify the weight of evidence for (or against) entanglement, based on a likelihood ratio test. Our method is universal in that it can be applied to any sort of measurements. We demonstrate the method by applying it to two simulated experiments on two qubits. The first measures a single entanglement witness, while the sec…
Any experiment attempting to verify the presence of entanglement in a physical system can only generate a finite amount of data. The statement that entanglement was present in the system can thus never be issued with certainty, requiring instead a statistical analysis of the data. Because entanglement plays a central role in the performance of quantum devices, it is crucial to make statistical claims in entanglement verification experiments that are reliable and have a clear interpretation. In this work, we apply recent results by M. Christandl and R. Renner to construct a reliable entanglemen…
We consider entanglement detection for quantum key distribution systems that use two signal states and continuous variable measurements. This problem can be formulated as a separability problem in a qubit-mode system. To verify entanglement, we introduce an object that combines the covariance matrix of the mode with the density matrix of the qubit. We derive necessary separability criteria for this scenario. These criteria can be readily evaluated using semidefinite programming and we apply them to the specific quantum key distribution protocol.
The quantification of quantum entanglement is a central issue in quantum information theory. Recently, Gao \emph{et al}. ( \href{http://dx.doi.org/10.1103/PhysRevLett.112.180501}{Phys. Rev. Lett. \textbf{112}, 180501 (2014)}) pointed out that the maximum of entanglement measure of the permutational invariant part of $ρ$ ought to be a lower bound on entanglement measure of the original state $ρ$, and proposed that this argument can be used as an additional requirement for (multipartite) entanglement measures. Whether any individual proposed entanglement measure satisfies the requirement still h…
In this paper, we consider the problem of entanglement verification across the quantum memories of any two nodes of a quantum network. Its solution can be a means for detecting (albeit not preventing) the presence of intruders that have taken full control of a node, either to make a denial-of-service attack or to reprogram the node. Looking for strategies that only require local operations and classical communication (LOCC), we propose two entanglement verification protocols characterized by increasing robustness and efficiency.
Instantaneous nonlocal quantum computation (INQC) evades apparent quantum and relativistic constraints and allows to attack generic quantum position verification (QPV) protocols (aiming at securely certifying the location of a distant prover) at an exponential entanglement cost. We consider adversaries sharing maximally entangled pairs of qudits and find low-dimensional INQC attacks against the simple practical family of QPV protocols based on single photons polarized at an angle $θ$. We find exact attacks against some rational angles, including some sitting outside of the Clifford hierarchy (…
Multipartite entanglement has been widely regarded as key resources in distributed quantum computing, for instance, multi-party cryptography, measurement based quantum computing, quantum algorithms. It also plays a fundamental role in quantum phase transitions, even responsible for transport efficiency in biological systems. Certifying multipartite entanglement is generally a fundamental task. Since an $N$ qubit state is parameterized by $4^N-1$ real numbers, one is interested to design a measurement setup that reveals multipartite entanglement with as little effort as possible, at least witho…
There exists, in general, a convex set of quantum state estimators that maximize the likelihood for informationally incomplete data. We propose an estimation scheme, catered to measurement data of this kind, to search for the exact maximum-likelihood-maximum-entropy estimator using semidefinite programming and a standard multi-dimensional function optimization routine. This scheme can be used to infer the expectation values of a set of entanglement witnesses that can be used to verify the entanglement of the unknown quantum state for composite systems. Next, we establish an alternative numeric…
Many protocols and experiments in quantum information science are described in terms of simple measurements on qubits. However, in a real implementation, the exact description is more difficult, and more complicated observables are used. The question arises whether a claim of entanglement in the simplified description still holds, if the difference between the realistic and simplified models is taken into account. We show that a positive entanglement statement remains valid if a certain positive linear map connecting the two descriptions--a so-called squashing operation--exists; then lower bou…
The ability to unconditionally verify the location of a communication receiver would lead to a wide range of new security paradigms. However, it is known that unconditional location verification in classical communication systems is impossible. In this work we show how unconditional location verification can be achieved with the use of quantum communication channels. Our verification remains unconditional irrespective of the number of receivers, computational capacity, or any other physical resource held by an adversary. Quantum location verification represents a new application of quantum ent…
Entangled quantum states, such as N00N states, are of major importance for quantum technologies due to their quantum-enhanced performance. At the same time, their quantum correlations are relatively vulnerable when they are subjected to imperfections. Therefore, it is crucial to determine under which circumstances their distinct quantum features can be exploited. In this paper, we study the entanglement property of noisy N00N states. This class of states is a generalization of N00N states including various attenuation effects, such as mixing, constant or fluctuating losses, and dephasing. To v…
We use the entanglement sampling techniques developed by Dupuis, Fawzi and Wehner to find a lower bound on the entanglement needed by a coalition of cheater attacking the quantum position verification protocol using the four BB84 states in the scenario where the cheaters have no access to a quantum channel but share a (possibly mixed) entangled state $\tildeΦ$. For a protocol using n qubits, a necessary condition for cheating is that the max- relative entropy of entanglement $E_{\max}(\tildeΦ)\ge n-O(\log n)$. This improves previously known best lower bound by a factor $\sim4$, and it is essen…
Various protocols exist by which a referee can be convinced that two observers share an entangled resource. Such protocols typically specify the types of communication allowed, and the degrees of trust required, between the referee and each observer. Here it is shown that the need for any degree of trust of the observers by the referee can be completely removed via the referee using classical and quantum communication channels appropriately. In particular, trust-free verification of Bell nonlocality, EPR-steering, and entanglement, respectively, requires two classical channels, one classical a…
Multipartite entangled states are a fundamental resource for a wide range of quantum information processing tasks. In particular, in quantum networks it is essential for the parties involved to be able to verify if entanglement is present before they carry out a given distributed task. Here we design and experimentally demonstrate a protocol that allows any party in a network to check if a source is distributing a genuinely multipartite entangled state, even in the presence of untrusted parties. The protocol remains secure against dishonest behaviour of the source and other parties, including …
Verification of entanglement is an important tool to characterize sources and devices for use in quantum computing and communication applications. In a vast majority of experiments entanglement witnesses (EW) are used in order to prove the presence of entanglement in a quantum state. EWs can be constructed from available measurement results and do not require a reconstruction of the whole density matrix (full tomography), which is especially valuable for high-dimensional systems. We provide a method to construct {\it accessible nonlinear EWs}, which incorporate two important properties. First,…
We establish conditions under which the experimental verification of quantum error-correcting behavior against a linear set of error operators $\ce$ suffices for the verification of noiseless subsystems of an error algebra $\ca$ contained in $\ce$. From a practical standpoint, our results imply that the verification of a noiseless subsystem need not require the explicit verification of noiseless behavior for all possible initial states of the syndrome subsystem.
High-dimensional entanglement is significant for the fundamental studies of quantum physics and offers unique advantages in various quantum information processing (QIP) tasks. Integrated quantum devices have recently emerged as a promising platform for creating, processing, and detecting complex high-dimensional entangled states. A crucial step towards practical quantum technologies is to verify that these devices work reliably with an optimal strategy. In this work, we experimentally implement an optimal quantum verification strategy on a three-dimensional maximally entangled state using loca…
Future quantum information networks will likely consist of quantum and classical agents, who have the ability to communicate in a variety of ways with trusted and untrusted parties and securely delegate computational tasks to untrusted large-scale quantum computing servers. Multipartite quantum entanglement is a fundamental resource for such a network and hence it is imperative to study the possibility of verifying a multipartite entanglement source in a way that is efficient and provides strong guarantees even in the presence of multiple dishonest parties. In this work, we show how an agent o…
The verification of quantum entanglement under the influence of realistic noise and decoherence is crucial for the development of quantum technologies. Unfortunately, a full entanglement characterization is generally not possible with most entanglement criteria such as entanglement witnesses or the partial transposition criterion. In particular, so called bound entanglement cannot be certified via the partial transposition criterion. Here we present the full entanglement verification of dephased qubit and qutrit Werner states via entanglement quasiprobabilities. Remarkably, we are able to reve…
I raise some doubts concerning a protocol recently applied in an experiment (Walborn et al, Nature) to measure entanglement. The protocol is much simpler than other known entanglement-verification methods, but, I argue, needs assumptions (namely that the state generated is known and pure) that are too strong to be allowed and that are not justified in most experiments. An extension of the protocol suggested in quant-ph/0605250 is much harder to implement and still relies on assumptions not justified in entanglement-verification protocols, as demonstrated by an explicit example.
A core process in many quantum tasks is the generation of entanglement. It is being actively studied in a variety of physical settings - from simple bipartite systems to complex multipartite systems. In this work we experimentally study the generation of bipartite entanglement in a nanophotonic system. Entanglement is generated via the quantum interference of two surface plasmon polaritons in a beamsplitter structure, i.e. utilising the Hong-Ou-Mandel (HOM) effect, and its presence is verified using quantum state tomography. The amount of entanglement is quantified by the concurrence and we fi…
The verification and quantification of experimentally created entanglement by simple measurements, especially between distant particles, is an important basic task in quantum processing. When composite systems are subjected to local measurements the measurement data will exhibit correlations, whether these systems are classical or quantum. Therefore, the observation of correlations in the classical measurement record does not automatically imply the presence of quantum correlations in the system under investigation. In this work we explore the question of when correlations, or other measuremen…
A key ingredient in emerging quantum-enhanced technologies is the ability to coherently manipulate and detect superpositions of basis states. In integrated optics implementations, transverse spatial modes supported by multimode structures offer an attractive carrier of quantum superpositions. Here we propose an integrated dynamic mode converter based on the electro-optic effect in nonlinear channel waveguides for deterministic transformations between mutually non-orthogonal bases of spatial modes. We theoretically show its capability to demonstrate a violation of a Bell-type Clauser-Horne-Shim…
Many experiments in quantum information aim at creating multi-partite entangled states. Quantifying the amount of entanglement that was actually generated can, in principle, be accomplished using full-state tomography. This method requires the determination of a parameter set that is growing exponentially with the number of qubits and becomes infeasible even for moderate numbers of particles. Non-trivial bounds on experimentally prepared entanglement can however be obtained from partial information on the density matrix. The fundamental question that needs to be addressed in this context is th…
So-called direct measurements of entanglement are collective measurements on multiple copies of a (bipartite or multipartite) quantum system that directly provide one a value for some entanglement measure, such as the concurrence for bipartite states. Multiple copies are needed since the entanglement of a mixed state is not a linear function of the density matrix. Unfortunately, so far all experimental implementations of direct measurements made unverified assumptions about the form of the states, and, therefore, do not qualify as entanglement verification tests. I discuss how a direct measure…
The effect of a number of mechanisms designed to suppress decoherence in open quantum systems are studied with respect to their effectiveness at slowing down the loss of entanglement. The effect of photonic band-gap materials and frequency modulation of the system-bath coupling are along expected lines in this regard. However, other control schemes, like resonance fluorescence, achieve quite the contrary: increasing the strength of the control kills entanglement off faster. The effect of dynamic decoupling schemes on two qualitatively different system-bath interactions are studied in depth. Dy…
We give a scheme for interpreting shaded tangles as quantum circuits, with the property that if two shaded tangles are ambient isotopic, their corresponding computational effects are identical. We analyze 11 known quantum procedures in this way -- including entanglement manipulation, error correction and teleportation -- and in each case present a fully-topological formal verification, yielding generalized procedures in some cases. We also use our methods to identify 2 new procedures, for topological state transfer and quantum error correction. Our formalism yields in some cases significant ne…
Quantum networks are promising tools for the implementation of long-range quantum communication. The characterization of quantum correlations in networks and their usefulness for information processing is therefore central for the progress of the field, but so far only results for small basic network structures or pure quantum states are known. Here we show that symmetries provide a versatile tool for the analysis of correlations in quantum networks. We provide an analytical approach to characterize correlations in large network structures with arbitrary topologies. As examples, we show that e…
Mutually unbiased bases (MUBs) provide a standard tool in the verification of quantum states, especially when harnessing a complete set for optimal quantum state tomography. In this work, we investigate the detection of entanglement via inequivalent sets of MUBs, with a particular focus on unextendible MUBs. These are bases for which an additional unbiased basis cannot be constructed and, consequently, are unsuitable for quantum state verification. Here, we show that unextendible MUBs, as well as other inequivalent sets in higher dimensions, can be more effective in the verification of entangl…
We present a composably secure protocol allowing $n$ parties to test an entanglement generation resource controlled by a possibly dishonest party. The test consists only in local quantum operations and authenticated classical communication once a state is shared among them and provides composable security, namely it can be used as a secure subroutine by $n$ honest parties within larger communication protocols to test if a source is sharing quantum states that are at least $ε$-close to the GHZ state. This claim comes on top of previous results on multipartite entanglement verification where the…
We generalize previously proposed conditions each measure of entanglement has to satisfy. We present a class of entanglement measures that satisfy these conditions and show that the Quantum Relative Entropy and Bures Metric generate two measures of this class. We calculate the measures of entanglement for a number of mixed two spin 1/2 systems using the Quantum Relative Entropy, and provide an efficient numerical method to obtain the measures of entanglement in this case. In addition, we prove a number of properties of our entanglement measure which have important physical implications. We bri…
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 develop a novel method by formulating 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 entangle…
Faking entanglement with imperceptible measurement deviations
Tampere University（坦佩雷大学）；Lund University（隆德大学）；TU Wien（维也纳工业大学）；Quantum Technology Laboratories GmbH（量子技术实验室有限公司）；VTT Technical Research Centre of Finland（芬兰国家技术研究中心）
We present a general strategy to derive entanglement criteria which consists in performing a mapping from qudits to qubits that preserves the separability of the parties and SU(2) rotational invariance. Consequently, it is possible to apply the well known positive partial transpose criterion to reveal the existence of quantum correlations between qudits. We discuss some examples of entangled states that are detected using the proposed strategy. Finally, we demonstrate, using our scheme, how some variance-based entanglement witnesses can be generalized from qubits to higher dimensional spin sys…
