We propose a more general method for detecting a set of entanglement measures, i.e. negativities, in an \emph{arbitrary} tripartite quantum state by local operations and classical communication. To accomplish the detection task using this method, three observers, Alice, Bob and Charlie, do not need to perform the partial transposition maps by the structural physical approximation; instead, they are only required to collectively measure some functions via three local networks supplemented by a classical communication. With these functions, they are able to determine the set of negativities related to the tripartite quantum state.
Einstein-Podolsky-Rosen steering is a kind of powerful nonlocal quantum resource in quantum information processing such as quantum cryptography and quantum communication. Many criteria have been proposed in the past few years to detect steerability, both analytically and numerically, for bipartite quantum systems. We propose effective criteria for tripartite steerability and genuine tripartite steerability of three-qubit quantum states by establishing connections between the tripartite steerability (resp. genuine tripartite steerability) and the tripartite entanglement (resp. genuine tripartit…
Genuine multipartite entanglement plays important roles in quantum information processing. The detection of genuine multipartite entanglement has been long time a challenging problem in the theory of quantum entanglement. We propose a criterion for detecting genuine tripartite entanglement of arbitrary dimensional tripartite states based on quantum Fisher information. We show that this criterion is more effective for some states in detecting genuine tripartite entanglement by detailed example.
Based on the S-R indeterminacy relations in conjugation with the partial transposition, we derive a class of inequalities for detecting entanglement in several tripartite systems, including bosonic, SU(2), and SU(1,1) systems. These inequalities are in general stronger than those based on the usual Heisenberg relations for detecting entanglement. We also discuss the reduction from SU(2) and SU(1,1) to bosonic systems and the generalization to multipartite case.
It is challenging task to detect and measure genuine multipartite entanglement. We investigate the problem by considering the average based positive partial transposition(PPT) criterion and the realignment criterion. Sufficient conditions for detecting genuine tripartite entanglement are presented. We also derive lower bounds for the genuine tripartite entanglement concurrence with respect to the conditions. While the PPT criterion and the realignment criterion are powerful for detecting bipartite entanglement and for providing lower bounds of bipartite concurrences, our results give an effect…
In a recent paper, Bancal et al. put forward the concept of device-independent witnesses of genuine multipartite entanglement. These witnesses are capable of verifying genuine multipartite entanglement produced in a lab without resorting to any knowledge of the dimension of the state space or of the specific form of the measurement operators. As a by-product they found a three-party three-setting Bell inequality which enables to detect genuine tripartite entanglement in a noisy 3-qubit Greenberger-Horne-Zeilinger (GHZ) state for visibilities as low as 2/3 in a device-independent way. In this p…
It is an interesting problem to construct genuine tripartite entangled states based on the collective use of two bipartite entangled states. We consider the case that the states are two-qubit Werner states, we construct the interval of parameter of Werner states such that the tripartite state is genuine entangled. Further, we present the way of detecting the tripartite genuine entanglement using current techniques in experiments. We also investigate the lower bound of genuine multipartite entanglement concurrence.
The probability of successfully controlled teleportating an unknown qubit using a general three-particle state is investigated. We give the analytic expressions of maximal probabilities of successfully controlled teleportating an unknown qubit via several kinds of tripartite states including a tripartite GHZ state and a tripartite W-state.
Einstein-Podolsky-Rosen (EPR) steering is a form of quantum nonlocality which is intermediate between entanglement and Bell nonlocality. EPR steering is a resource for quantum key distribution that is device independent on only one side in that it certifies bipartite entanglement when one party's device is not characterized while the other party's device is fully characterized. In this work, we introduce two types of genuine tripartite EPR-steering, and derive two steering inequalities to detect them. In a semi-device-independent scenario where only the dimensions of two parties are assumed, t…
Due to the difficulties present in experimentally preparing genuine tripartite entanglement, it is important to explore the possibility of multiple usage of a single genuine entangled state. In the present paper, we present one such possibility by considering a scenario consisting of three spin-$\frac{1}{2}$ particles shared between Alice, Bob and multiple Charlies. Alice performs measurements on the first particle, Bob performs measurements on the second particle and multiple Charlies perform measurements on the third particle sequentially and independently. In this scenario, we investigate w…
Detecting genuine multipartite entanglement using moments of positive maps
S. N. Bose National Centre for Basic Sciences（S. N. 玻色基础科学国家中心）；Networked Quantum Devices Unit, Okinawa Institute of Science and Technology Graduate University（冲绳科学技术大学院大学网络化量子器件单元）；School of Physical Sciences, Indian Institute of Technology Goa（印度果阿理工学院物理科学学院）
The possibility to explain quantum correlations via (possibly) unknown causal influences propagating gradually and continuously at a finite speed v > c has attracted a lot of attention recently. In particular, it could be shown that this assumption leads to correlations that can be exploited for superluminal communication. This was achieved studying the set of possible correlations that are allowed within such a model and comparing them to correlations produced by local measurements on a four-party entangled quantum state. Here, we report on a quantum state that allows for the same conclusion …
The existence and nature of tripartite entanglement of a noninteracting Fermi gas (NIFG) is investigated. Three new classes of parameterized entanglement witnesses (EWs) are introduced with the aim of detecting genuine tripartite entanglement in the three-body reduced density matrix and discriminating between the presence of the two types of genuine tripartite entanglement, W\B and GHZ\W. By choosing appropriate EW operators, the problem of finding GHZ and W EWs is reduced to linear programming. Specifically, we devise new W EWs based on a spin-chain model with periodic boundary conditions, an…
Local distinguishability of five orthogonal product states on bipartite and tripartite quantum systems
College of Computer Science and Engineering, Shandong University of Science and Technology（山东科技大学计算机科学与工程学院）；Faculty of Information Technology, Beijing University of Technology（北京工业大学信息学部）；College of Mathematics and Systems Science, Shandong University of Science and Technology（山东科技大学数学与系统科学学院）
We present a supervised secure entanglement sharing protocol via tripartite W states for faithful quantum teleportation. By guaranteeing a secure entanglement distribution in the charge of a third believed supervisor, quantum information of an unknown state of a 2-level particle can be faithfully teleported from the sender to the remote receiver via the Bell states distilled from the tripartite W states. We emphasize that reliable teleportation after our protocol between two communication parties depends on the agreement of the supervisor to cooperate via taking the W states as both the quantu…
Channels composed by Einstein-Podolsky-Rosen (EPR) pairs are capable of teleporting arbitrary multipartite states. The question arises whether EPR channels are also optimal against imperfections. In particular, the teleportation of Greenberger-Horne-Zeilinger states (GHZ) requires three EPR states as the channel and full measurements in the Bell basis. We show that, by using two GHZ states as the channel, it is possible to transport any unknown three-qubit state of the form $c_0|000\rangle+c_1|111\rangle$. The teleportation is made through measurements in the GHZ basis, and, to obtain determin…
We show how the presence of entanglement in a bipartite Gaussian state can be detected by the amount of work extracted by a continuos variable Szilard-like device, where the bipartite state serves as the working medium of the engine. We provide an expression for the work extracted in such a process and specialize it to the case of Gaussian states. The extractable work provides a sufficient condition to witness entanglement in generic two-mode states, becoming also necessary for squeezed thermal states. We extend the protocol to tripartite Gaussian states, and show that the full structure of in…
The emergence of a diverging length scale in many-body systems at a quantum phase transition implies that total entanglement has to reach its maximum there. In order to fully characterize this, one has to consider multipartite entanglement as, for instance, bipartite entanglement between individual particles fails to signal this effect. However, quantification of multipartite entanglement is very hard and detecting it may not be possible due to the lack of accessibility to all individual particles. For these reasons it will be more sensible to partition the system into relevant subsystems, eac…
Tripartite quantum correlations obtained by post-selection from twin beams
Institute of Physics of the Czech Academy of Sciences（捷克科学院物理研究所）；Joint Laboratory of Optics of Palacky University and Institute of Physics of CAS（帕拉茨基大学与捷克科学院物理研究所光学联合实验室）；Faculty of Science, Palacký University（帕拉茨基大学理学院）
While the detection of entanglement has been proved already to be quite a difficult task, experimental quantification of entanglement is even more challenging. In this work, we derive an analytical lower bound for the concurrence of a bipartite mix quantum state in arbitrary dimension. The lower bound is experimentally implementable in a feasible way, which enabling quantification of entanglement in a broad variety of cases
We explore the possibility of entanglement detection in continuous variable systems by entanglement witnesses based on covariance matrices, constructible from random homodyne measurements. We propose new linear constraints characterizing the entanglement witnesses based on second moments, and use them in a semidefinite program providing the optimal entanglement test for given random measurements. We test the method on the class of squeezed vacuum states and study the efficiency of entanglement detection in general unknown covariance matrices.
In quantum information theory, the reliable and effective detection of entanglement is of paramount importance. However, given an unknown state, assessing its entanglement is a challenging task. To attack this problem, we investigate the use of random local measurements, from which entanglement witnesses are then constructed via semidefinite programming methods. We propose a scheme of successively increasing the number of measurements until the presence of entanglement can be unambiguously concluded, and investigate its performance in various examples.
We propose a single observable to witness the nonzero quantum discord of an unknown quantum state provided that we have four copies of the state. The expectation value of this observable provides a necessary and sufficient condition for nonzero quantum discord in $2\times N$ systems and a necessary condition in higher finite-dimensional bipartite systems. Furthermore, a nontrivial lower bound of quantum discord can be obtained from this expectation value. The proposed observable can be experimentally measured in exactly the same easy manner as that of the entanglement witness, moreover a quant…
There are at least a number of ways to formally define complexity. Most of them relate to some kind of minimal description of the studied object. Being this one in form of minimal resources of minimal effort needed to generate the object itself. This is usually achieved by detecting and taking advantage of regularities within the object. Regularities can commonly be described in an information-theoretic approach by quantifying the amount of correlation playing a role in the system, this being spatial, temporal or both. This is the approach closely related to the extent that the whole cannot be…
We consider implementations of a bipartite unitary on many pairs of unknown input states by local operation and classical communication assisted by shared entanglement. We investigate to what extent the entanglement cost and the classical communication cost can be compressed by allowing nonzero but vanishing error in the asymptotic limit of infinite pairs. We show that a lower bound on the minimal entanglement cost, the forward classical communication cost, and the backward classical communication cost per pair is given by the Schmidt strength of the unitary. We also prove that an upper bound …
We construct a single observable measurement of which mean value on four copies of an {\it unknown} two-qubit state is sufficient for unambiguous decision whether the state is separable or entangled. In other words, there exists a universal collective entanglement witness detecting all two-qubit entanglement. The test is directly linked to a function which characterizes to some extent the entanglement quantitatively. This function is an entanglement monotone under so--called local pure operations and classical communication (pLOCC) which preserve local dimensions. Moreover it provides tight up…
Whereas in standard quantum state tomography one estimates an unknown state by performing various measurements with known devices, and whereas in detector tomography one estimates the POVM elements of a measurement device by subjecting to it various known states, we consider here the case of SPAM (state preparation and measurement) tomography where neither the states nor the measurement device are assumed known. For $d$-dimensional systems measured by $d$-outcome detectors, we find there are at most $d^2(d^2-1)$ "gauge" parameters that can never be determined by any such experiment, irrespecti…
We present a quantum circuit that transforms an unknown three-qubit state into its canonical form, up to relative phases, given many copies of the original state. The circuit is made of three single-qubit parametrized quantum gates, and the optimal values for the parameters are learned in a variational fashion. Once this transformation is achieved, direct measurement of outcome probabilities in the computational basis provides an estimate of the tangle, which quantifies genuine tripartite entanglement. We perform simulations on a set of random states under different noise conditions to asses t…
We present the general scheme for construction of noiseless networks detecting entanglement with the help of linear, hermiticity-preserving maps. We show how to apply the method to detect entanglement of unknown state without its prior reconstruction. In particular, we prove there always exists noiseless network detecting entanglement with the help of positive, but not completely positive maps. Then the generalization of the method to the case of entanglement detection with arbitrary, not necessarily hermiticity-preserving, linear contractions on product states is presented.
Entanglement of high-dimensional and multipartite quantum systems offer promising perspectives in quantum information processing. However, the characterization and measure of such kind of entanglement is of great challenge. Here we consider the overlaps between the maximal quantum mean values and the classical bound of the CHSH inequalities for pairwise-qubit states in two-dimensional subspaces. We show that the concurrence of a pure state in any high-dimensional multipartite system can be equivalently represented by these overlaps. Here we consider the projections of an arbitrary high-dimensi…
We investigate the practicality of the method proposed by Maciel et al. [Phys. Rev. A. 80, 032325(2009)] for detecting the entanglement of two spatial qutrits (3-dimensional quantum systems), which are encoded in the discrete transverse momentum of single photons transmitted through a multi-slit aperture. The method is based on the acquisition of partial information of the quantum state through projective measurements, and a data processing analysis done with semi-definite programs. This analysis relies on generating gradually an optimal entanglement witness operator, and numerical investigati…
We undertake experimental detection of the entanglement present in arbitrary three-qubit pure quantum states on an NMR quantum information processor. Measurements of only four observables suffice to experimentally differentiate between the six classes of states which are inequivalent under stochastic local operation and classical communication (SLOCC). The experimental realization is achieved by mapping the desired observables onto Pauli $z$-operators of a single qubit, which is directly amenable to measurement. The detection scheme is applied to known entangled states as well as to states ran…
Entanglement witness is an effective method to detect entanglement in unknown states without doing full tomography. One of the most widespread schemes of witnessing entanglement is measuring its fidelity with respect to a pure entangled state. Recently, a large class of states whose entanglement can not be detected with the fidelity witness has been discovered in Phys.Rev.Lett \textbf{124},200502(2020). They are called unfaithful states. In this paper we propose a new way to detect entanglement by calculating the lower bound of entanglement using measurement results. Numerical simulation shows…
Assume that two distant parties, Alice and Bob, as well as an adversary, Eve, have access to (quantum) systems prepared jointly according to a tripartite state. In addition, Alice and Bob can use local operations and authenticated public classical communication. Their goal is to establish a key which is unknown to Eve. We initiate the study of this scenario as a unification of two standard scenarios: (i) key distillation (agreement) from classical correlations and (ii) key distillation from pure tripartite quantum states. Firstly, we obtain generalisations of fundamental results related to sce…
Quantum coherence has wide-ranging applications from quantum thermodynamics to quantum metrology, quantum channel discrimination and even quantum biology. Thus, detecting and quantifying coherence are two fundamental problems in quantum resource theory. Here, we introduce feasible methods to detect and estimate the coherence by constructing coherence witnesses for any finite-dimensional states. Our coherence witnesses detect coherent states by testing whether the expectation value of the witness is negative or not. Two typical coherence witnesses are proposed and discussed based on our witness…
Quantum information theory sets the ultimate limits for any information-processing task. In rangefinding and LIDAR, the presence or absence of a target can be tested by detecting different states at the receiver. In this Letter, we use quantum hypothesis testing for an unknown coherent-state return signal in order to derive the limits of symmetric and asymmetric error probabilities of single-shot ranging experiments. We engineer a single measurement independent of the range, which in some cases saturates the quantum bound and for others is presumably the best measurement to approach it. In add…
Quantum metrology uses quantum states with no classical counterpart to measure a physical quantity with extraordinary sensitivity or precision. Most metrology schemes measure a single parameter of a dynamical process by probing it with a specially designed quantum state. The success of such a scheme usually relies on the process belonging to a particular one-parameter family. If this assumption is violated, or if the goal is to measure more than one parameter, a different quantum state may perform better. In the most extreme case, we know nothing about the process and wish to learn everything.…
The entanglement content of high-dimensional random pure states is almost maximal, nevertheless, we show that, due to the complexity of such states, the detection of their entanglement using witness operators is rather difficult. We discuss the case of unknown random states, and the case of known random states for which we can optimize the entanglement witness. Moreover, we show that coarse graining, modeled by considering mixtures of m random states instead of pure ones, leads to a decay in the entanglement detection probability exponential with m. Our results also allow to explain the emerge…
