Joonwoo Bae, Markus Tiersch, Simeon Sauer, Fernando de Melo, Florian Mintert, Beatrix Hiesmayr, Andreas Buchleitner
We derive an explicit analytic estimate for the entanglement of a large class of bipartite quantum states which extends into bound entanglement regions. This is done by using an efficiently computable concurrence lower bound, which is further employed to numerically construct a volume of $3 \times 3$ bound entangled states.
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It is well known that random bipartite pure states are typically maximally entangled within an arbitrarily small error. Showing that the marginals of random bipartite pure states are typically extremely close to the maximally mixed state, is a way to prove the above. However, a more direct way to prove the above is to estimate the distance of random bipartite pure states from the set of maximally entangled states. Here, we find the average distance between a random bipartite pure state and the set of maximally entanglement states as quantified by three different quantifiers of the distance and…
Entangling power, gate typicality, and measurement-induced phase transitions
本研究聚焦含两量子比特幺正门的混合量子电路中的测量诱导相变，发现纠缠能力与门典型性可解释全局二分纠缠行为、实现幺正算符的普适类分类，且恒等门场景下的解析纠缠熵结果与数值模拟高度吻合。
In this contribution we relate two different key concepts: mutually unbiased bases (MUBs) and entanglement; in particular we focus on bound entanglement, i.e. highly mixed states which cannot be distilled by local operations and classical communications. For a certain class of states --for which the state-space forms a "magic" simplex-- we analyze the set of bound entangled states detected by the MUB criterion for different dimensions d and number of particles n. We find that the geometry is similar for different d and n, consequently, the MUB criterion opens possibilities to investigate the t…
Group symmetric LOCC measurement for detecting maximally entangled state is considered. Usually, this type measurement has continuous-valued outcomes. However, any realizable measurement has finite-valued outcomes. This paper proposes discrete realizations of such a group symmetric LOCC measurement.
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.
Quantum error detection has always been a fundamental challenge in a fault-tolerant quantum computer. Hence, it is of immense importance to detect and deal with arbitrary errors to efficiently perform quantum computation. Several error detection codes have been proposed and realized for lower number of qubit systems. Here we present an error detection code for a (2n+1)-qubit entangled state using two syndrome qubits and simulate it on IBM's 16-qubit quantum computer for a 13-qubit entangled system. The code is able to detect an arbitrary quantum error in any one of the first 2n qubits of the (…
We construct a family of map which is shown to be positive when imposing certain condition on the parameters. Then we show that the constructed map can never be completely positive. After tuning the parameters, we found that the map still remain positive but it is not completely positive. We then use the positive but not completely positive map in the detection of bound entangled state and negative partial transpose entangled states.
In the asymptotic setting, the optimal test for hypotheses testing of the maximally entangled state is derived under several locality conditions for measurements. The optimal test is obtained in several cases with the asymptotic framework as well as the finite-sample framework. In addition, the experimental scheme for the optimal test is presented.
Quantum steering inequalities allow to demonstrate the presence of entanglement between two parties when one of the two measurement device is not trusted. In this paper we show that quantum steering can be demonstrated for arbitrary low detection efficiency by using two-qubit non-maximally entangled states. Our result can have important applications in one-sided device-independent quantum key distribution.
This Letter verifies the potential of several classes of entangled coherent state in well known quantum metrology which includes detection of classical external force, and shows that there is a class of entangled coherent state for the external force detection system without the quantum limit in the detection of the light. In the case of the precision measurement of continuos parameter like phase measurement, the entangled coherent state with perfect entanglement does not provide remarkable benefit, but we provide a concrete example that certain class of entangled coherent state gives a remark…
Postselected Entangled States by Photon Detection
本研究针对弱激发系统常用后选择纠缠机制的适用局限，提出通过光子探测使高激发二能级发射体系综产生纠缠的方法，验证连续光子探测可抵消退相干影响恢复自旋压缩，为开放量子系统生成后选择纠缠提供新路径。
One of us has recently elaborated a theory for modelling concepts that uses the state context property (SCoP) formalism, i.e. a generalization of the quantum formalism. This formalism incorporates context into the mathematical structure used to represent a concept, and thereby models how context influences the typicality of a single exemplar and the applicability of a single property of a concept, which provides a solution of the 'Pet-Fish problem' and other difficulties occurring in concept theory. Then, a quantum model has been worked out which reproduces the membership weights of several ex…
Ultra-high-rate detection of entangled photon pairs
研究纠缠光子对高速探测问题，采用16像素超导纳米线单光子探测器减轻探测器死时间影响，在相关实验中实现每秒超300万次计数的符合率，为高速纠缠光子量子信息处理奠定基础。
Single spin detection is one of the important tasks in the field of quantum metrology. Many experiments about the single spin detection has been performed. However, due to the weak magnetic fields from the single spin, a long measurement time is required to achieve a reasonably high signal-to-noise ratio. Here, we propose an alternative way to realize rapid and accurate single spin detection with entangled states. While it is known that entanglement can improve the sensitivity to measure globally applied magnetic fields, we investigate a strategy to use the entanglement for detecting spatially…
We investigate the detection of entanglement in $n$-partite quantum states. We obtain practical separability criteria to identify genuinely entangled and non-separable mixed quantum states. No numerical optimization or eigenvalue evaluation is needed, and our criteria can be evaluated by simple computations involving components of the density matrix. We provide examples in which our criteria perform better than all known separability criteria. Specifically, we are able to detect genuine $n$-partite entanglement which has previously not been identified. In addition, our criteria can be used in …
Towards robust detection of entangled two-photon absorption
本研究针对低通量下纠缠双光子吸收（ETPA）检测存争议的问题，通过构建纠缠光子对横向空间关联，在室温低通量下于有机和无机发色团中观测到ETPA迹象，方案抗常见伪影且信号与关联面积、吸收截面正相关，推进了ETPA验证与纠缠光物质相互作用研究。
We study how well answer to the question ``Is the given quantum state equal to a certain maximally entangled state?'' using LOCC, in the context of hypothesis testing. Under several locality and invariance conditions, optimal tests will be derived for several special cases by using basic theory of group representations. Some optimal tests are realized by performing quantum teleportation and checking whether the state is teleported. We will also give a finite process for realizing some optimal tests. The performance of the tests will be numerically compared.
Currently available separability criteria for continuous-variable states are generally based on the covariance matrix of quadrature operators. The well-known separability criterion of Duan et al. [Phys. Rev. Lett. 84, 2722 (2000)] and Simon [Phys. Rev. Lett. 84, 2726 (2000)] , for example, gives a necessary and sufficient condition for a two-mode Gaussian state to be separable, but leaves many entangled non-Gaussian states undetected. Here, we introduce an improvement of this criterion that enables a stronger entanglement detection. The improved condition is based on the knowledge of an additi…
We address binary optical communication in single-mode and entangled quantum noisy channels. For single-mode we present a systematic comparison between direct photodetection and homodyne detection in realistic conditions, i.e. taking into account the noise that occurs both during the propagation and the detection of the signals. We then consider entangled channels based on twin-beam state of radiation, and show that with realistic heterodyne detection the error probability at fixed channel energy is reduced in comparison to the single-mode cases for a large range of values of quantum efficienc…
We examine the violation of the majorization relations between the eigenvalues of the full and reduced density operators of entangled states of composite systems and its detection using generalized entropic forms based on arbitrary concave functions. It is shown that the violation of these relations may not always be detected by the conditional von Neumann and Tsallis entropies (for any $q>0$). Families of smooth entropic forms which are always able to detect such violations are, however, provided. These features are then examined for particular sets of mixed states in a two-qudit system, whic…
Detection and Classification of Bipartite and Multipartite Entangled States
本文基于SPA-PT方法系统研究二分与多分量子纠缠态的检测、分类与量化，提出三量子比特SLOCC不等价类分类判据，并定义新纠缠度量“结构化负度”，且方法具备实验可实现性。
This thesis is an attempt to enhance understanding of the following questions A- Given a multipartite quantum state (possibly mixed), how to find out whether it is entangled or separable? (Detection of entanglement.) B- Given an entangled state, how to decide how much entangled it is? (Measure of entanglement.), in the context of multipartite quantum states. We have explored two approaches. In the first approach, we assign a weighted graph with multipartite quantum state and address the question of separability in terms of these graphs and various operations involving them. In the second appro…
Entangled photons are a crucial resource for quantum communication and linear optical quantum computation. Unfortunately, the applicability of many photon-based schemes is limited due to the stochastic character of the photon sources. Therefore, a worldwide effort has focused in overcoming the limitation of probabilistic emission by generating two-photon entangled states conditioned on the detection of auxiliary photons. Here we present the first heralded generation of photon states that are maximally entangled in polarization with linear optics and standard photon detection from spontaneous p…
Entanglement, describing the inseparability of a quantum multiparty system, is one of the most intriguing features of quantum mechanics. Violation of Bell inequality, for ruling out the possibility of local hidden variable theories, is commonly used as a strong witness for quantum entanglement. In previous Bell test experiments with photonic entanglement based on two-photon coincidence measurement, the photon temporal wave packets are absorbed completely by the detectors. That is, the photon coherence time is much shorter than the detection time window. Here we demonstrate generation of freque…
In [J. C. Howell and J. A. Yeazell, Phys. Rev. A 62, 012102 (2000)], a proposal is made to generate entangled macroscopically distinguishable states of two spatially separated traveling optical modes. We model the decoherence due to light scattering during the propagation along an optical transmission line and propose a setup allowing an entanglement purification from a number of preparations which are partially decohered due to transmission. A purification is achieved even without any manual intervention. We consider a nondemolition configuration to measure the purity of the state as contrast…
We study effects of phase fluctuations on phase sensitivity and visibility of a class of robust path-entangled photon Fock states (known as mm' states) as compared to the maximally path-entangled N00N states in presence of realistic phase fluctuations such as turbulence noise. Our results demonstrate that the mm' states, which are more robust than the N00N state against photon loss, perform equally well when subject to such fluctuations. We show that the phase sensitivity with parity detection for both of the above states saturates the quantum Cramer-Rao bound in presence of such noise, sugges…
Quantum coherence and quantum entanglement are two strong pillars in quantum information theory. We study here for the possibility of any connection between these two important aspects of quantum mechanics while studying the entanglement detection problem for the detection of bipartite higher dimensional entangled states and multipartite entangled states. To achieve our goal, we derive the lower bound $L$ of $l_{1}$ norm of coherence of bipartite qubit-qudit system using the criterion that detect entanglement. Furthermore, we deduce the upper bound $U$ of $l_{1}$ norm of coherence of separable…
Energy-time entangled photon pairs remain tightly correlated in time when the photons are passed through equal magnitude, but opposite in sign, dispersion. A recent experimental demonstration has observed this effect on ultrafast time-scales using second-harmonic generation of the photon pairs. However, the experimental signature of this effect does not require energy-time entanglement. Here, we demonstrate a directly analogue to this effect in narrow-band second harmonic generation of a pair of classical laser pulses under similar conditions. Perfect cancellation is observed for fs pulses wit…
Detection of mixed bipartite entangled state in arbitrary dimension via structural physical approximation of partial transposition
本研究基于部分转置的结构物理近似方法，提出三种任意维混合两体负部分转置纠缠态的实验可实现检测判据，给出纠缠度新的实验可测上下界，并在两量子比特、三量子比特-量子比特系统中验证了判据。
Quantum illumination using polarization-entangled photon pairs for enhanced object detection
本文实验证明偏振纠缠光子对量子照明可检测反射率低至0.05、信噪比0.003的目标，CHSH类关联度量对损耗噪声鲁棒，并能估计反射率。
We have theoretically investigated the possibility of using any of several continuous-variable Bell-type inequalities - for which the dichotomic measurements are achieved with coarse-grained quadrature (homodyne) measurements - in a multi-party configuration where each participant is given a section, in the frequency domain, of the output of an optical parametric oscillator which has been synchronously-pumped with a frequency comb. Such light sources are undergoing intense study due to their novel properties, including the potential for production of light entangled in many hundreds of physica…
We present several entanglement conditions in order to detect bound entangled states in continuous variable systems. Specifically, Werner and Wolf [Phys. Rev. Lett. 86, 3658 (2001)] and Horodecki and Lewenstein [Phys. Rev. Lett. 85, 2657 (2000)] have proposed examples of bound entangled Gaussian state and bound entangled non-Gaussian state, respectively, of which entanglement can be detected by using our entanglement conditions.
Analytical performance evaluation of quantum radar architectures: From single-photon to entangled-noise radars
本文全面分析了两类量子雷达（直接探测和纠缠噪声雷达），推导了最大探测距离的解析表达式，并引入参数范围增强因子量化纠缠噪声雷达相对于经典对应物的优势。
Most states in the Hilbert space are maximally entangled. This fact has proven useful to investigate - among other things - the foundations of statistical mechanics. Unfortunately, most states in the Hilbert space of a quantum many body system are not physically accessible. We define physical ensembles of states by acting on random factorized states by a circuit of length k of random and independent unitaries with local support. We study the typicality of entanglement by means of the purity of the reduced state. We find that for a time k=O(1) the typical purity obeys the area law. Thus, the up…
Homodyne detection is optimal for quantum interferometry with path-entangled coherent states
针对纠缠相干态和量子比特哪条路径态的差分相位估计，本文证明无需光子数分辨探测器的零差检测可饱和量子Cramér-Rao界，并在光子损失下保持相位无关的稳健性能。
Photon modes have an important role in characterizing the quantum sources of light. Proper coupling of various photon modes obtained in spontaneous parametric down conversion (SPDC) process in optical fibers is essential to generate an effective source of entangled photons. The two main pre-detection factors affecting the biphoton mode coupling in SPDC are the pump beam focusing parameter and the crystal thickness. We present the numerical and experimental results on the effect of pump focusing on conditional down-converted photon modes for a Type-I BBO crystal. We experimentally verify that b…
Quantum state transfer between microwave and optical frequencies is essential for connecting superconducting quantum circuits to coherent optical systems and extending microwave quantum networks over long distances. To build such a hybrid `quantum Internet,' an important experiment in the quantum regime is to entangle microwave and optical modes. Based on the model of a generic cavity electro-optomechanical system, we present a heralded scheme to generate entangled microwave--optical photon pairs, which can bypass the efficiency threshold for quantum channel capacity in direct transfer protoco…
We inspect different quantum optical setups from the viewpoint of entanglement generation and detection. As a first step we consider a planar semiconductor microcavity and optimize the Bell-type correlations and their robustness against dephasing to create strong bipartite entanglement between polariton branches, which subsequently can be transfered to the emitted photons. In a second step, in order to create multipartite entangled light, we place the microcavity in an optical resonator driven by pump pulses with a frequency comb spectrum. For this system we show how phase matching of all comb…
In this work we analyse the structure of highly-entangled multimode squeezed states, such as those generated by broadband pulses undergoing type-II parametric down-conversion (PDC). Such down-conversion has previously been touted as a natural and efficient means of cluster-state generation, and therefore a viable future pathway to quantum computation. We first detail how broadband PDC processes lead directly to a series of orthogonal supermodes that are linear combinations of the original frequency modes. We then calculate the total squeezing of the multimode entangled states when they are ass…
We investigate performances of pure continuous variable states in discriminating thermal and identity channels by comparing their M-copy error probability bounds. This offers us a simplified mathematical analysis for quantum target detection with slightly modified features: the object -- if it is present -- perfectly reflects the signal beam irradiating it, while thermal noise photons are returned to the receiver in its absence. This model facilitates us to obtain analytic results on error-probability bounds i.e., the quantum Chernoff bound and the lower bound constructed from the Bhattacharya…
We report on the first experimental realization of the entanglement witness for polarization entangled photons. It represents a recently discovered significant quantum information protocol which is based on few local measurements. The present demonstration has been applied to the so-called Werner states, a family of ''mixed'' quantum states that include both entangled and non entangled states. These states have been generated by a novel high brilliance source of entanglement which allows to continuously tune the degree of mixedness.
In this paper, we investigate the critical efficiency of detectors to observe Bell nonlocality using multiple copies of the maximally entangled two-qubit state carried by a single pair of particles, such as hyperentangled states, and the product of Pauli measurements. It is known that in a Clauser-Horne-Shimony-Holt (CHSH) Bell test the symmetric detection efficiency of $82.84\%$ can be tolerated for the two-qubit maximally entangled state. We beat this enigmatic threshold by entangling two particles with multiple degrees of freedom. The obtained upper bounds of the symmetric detection efficie…
Rank-based entanglement detection for bound entangled states
本文提出基于秩的纠缠检测方法，通过分析矩阵的秩-1生成性质，发现新的PPT纠缠态并构造边缘态。
We suggest an improved version of Robertson-Schrödinger uncertainty relation for canonically conjugate variables by taking into account a pair of characteristics of states: non-Gaussianity and mixedness quantified by using fidelity and entropy, respectively. This relation is saturated by both Gaussian and Fock states, and provides strictly improved bound for any non-Gaussian states or mixed states. For the case of Gaussian states, it is reduced to the entropy-bounded uncertainty relation derived by Dodonov. Furthermore, we consider readily computable measures of both characteristics, and find …
In this work, we experimentally created and characterized a class of qubit-ququart PPT (positive under partial transpose) entangled states using three nuclear spins on an nuclear magnetic resonance (NMR) quantum information processor. Entanglement detection and characterization for systems with a Hilbert space dimension $\ge 2 \otimes 3$ is nontrivial since there are states in such systems which are both PPT as well as entangled. The experimental detection scheme that we devised for the detection of qubit-ququart PPT entanglement was based on the measurement of three Pauli operators with high …
Single photon avalanche diode arrays can provide both the spatial and temporal information of each detected photon. We present here the characterization of entangled light with a sensor specifically designed for quantum imaging applications. The sensors is time-tagging each detection events at the pixel level with sub-nanosecond accuracy, within frames of 50 ns. The spatial correlations between any number of detections in a defined temporal window can thus be directly extracted from the data. We show the ability of the sensor to characterize space-momentum entangled photon pairs emitted by spo…
We propose a versatile and efficient method to generate a broad class of complex entangled states of many atoms via the detection of a single photon. For an atomic ensemble contained in a strongly coupled optical cavity illuminated by weak single- or multi-frequency light, the atom-light interaction entangles the frequency spectrum of a transmitted photon with the collective spin of the atomic ensemble. Simple time-resolved detection of the transmitted photon then projects the atomic ensemble into a desired pure entangled state. This method can be implemented with existing technology, yields h…
Weak-value amplification (WVA) provides a way for amplified detection of a tiny physical signal at the expense of a lower detection probability. Despite this trade-off, due to its robustness against certain types of noise, WVA has advantages over conventional measurements in precision metrology. Moreover, it has been shown that WVA-based metrology can reach the Heisenberg-limit using entangled resources, but preparing macroscopic entangled resources remains challenging. Here we demonstrate a novel WVA scheme based on iterative interactions, achieving the Heisenberg-limited precision scaling wi…
We derive a class of inequalities, from the uncertainty relations of the SU(1,1) and the SU(2) algebra in conjunction with partial transposition, that must be satisfied by any separable two-mode states. These inequalities are presented in terms of the su(2) operators J_x, J_y, and the total photon number N_a+N_b. They include as special cases the inequality derived by Hillery and Zubairy [Phys. Rev. Lett. 96, 050503 (2006)], and the one by Agarwal and Biswas [New J. Phys. 7, 211 (2005)]. In particular, optimization over the whole inequalities leads to the criterion obtained by Agarwal and Bisw…
We propose a simple quantum network to detect multipartite entangled states of bosons, and show how to implement this network for neutral atoms stored in an optical lattice. We investigate the special properties of cluster states, multipartite entangled states and superpositions of distinct macroscopic quantum states that can be identified by the network.
We analyze the diffraction regime of the Kapitza-Dirac effect for particles entangled in momentum. The detection patterns show two-particle interferences. In the single-mode case we identify a discontinuity in the set of joint detection probabilities, associated with the disconnected character of the space of non-separable states. For Gaussian multi-mode states we derive the diffraction patterns, providing an example of the dependence of the light-matter interaction on entanglement. When the particles are identical, we can explore the relation between exchange and entanglement effects. We find…
We present two entanglement concentration protocols (ECPs) for arbitrary three-electron W state based on their charges and spins. Different from other ECPs, in both two ECPs, with the help of the electronic polarization beam splitter (PBS) and charge detection, the less-entangled W state can be concentrated into a maximally entangled state only with some single charge qubits. The second ECP is more optimal than the first one, for by constructing the complete parity check gate, the second ECP can be used repeatedly to further concentrate the less-entangled state and obtain a higher success prob…
Construction of PPT entangled state and its detection by using second-order moment of the partial transposition
本文提出利用部分转置的二阶矩构造PPT纠缠态，并通过实验验证其在量子密码学中的应用价值。
An experimental test of Bell's inequality allows ruling out any local-realistic description of nature by measuring correlations between distant systems. While such tests are conceptually simple, there are strict requirements concerning the detection efficiency of the involved measurements, as well as the enforcement of spacelike separation between the measurement events. Only very recently could both loopholes be closed simultaneously. Here we present a statistically significant, event-ready Bell test based on combining heralded entanglement of atoms separated by $398\,\mathrm{m}$ with fast an…
We propose a thought experiment to detect low-energy Quantum Gravity phenomena using Quantum Optical Information Technologies. Gravitational field perturbations, such as gravitational waves and quantum gravity fluctuations, decohere the entangled photon pairs, revealing the presence of gravitational field fluctuations including those more speculative sources such as compact extra dimensions and the sub-millimetric hypothetical low-energy quantum gravity phenomena and then set a limit for the decoherence of photon bunches and entangled pairs in space detectable with the current astronomical spa…
Entanglement is one of the key resources of quantum information science which makes identification of entangled states essential to a wide range of quantum technologies and phenomena. This problem is however both computationally and experimentally challenging. Here we use autoencoder neural networks to find semi-optimal set of incomplete measurements that are most informative for the detection of entangled states. We show that it is possible to find high-performance entanglement detectors with as few as three measurements. Also, with the complete information of the state, we develop a neural n…
The detection power of real entanglement witnesses under local unitary equivalence
该研究对比实与复纠缠见证的检测能力，给出实纠缠见证可检测纠缠态的充要条件，证明局域等价于实纠缠见证的见证可检测所有NPT态及一类两qutrit PPT纠缠态，并提出反例检验方法与局域投影相关结果。
Experimental tests of Bell's inequality allow to distinguish quantum mechanics from local hidden variable theories. Such tests are performed by measuring correlations of two entangled particles (e.g. polarization of photons or spins of atoms). In order to constitute conclusive evidence, two conditions have to be satisfied. First, strict separation of the measurement events in the sense of special relativity is required ("locality loophole"). Second, almost all entangled pairs have to be detected (for particles in a maximally entangled state the required detector efficiency is 82.8%), which is …
We demonstrate how to map out the phase diagram of a two dimensional quantum many body system with no prior physical knowledge by applying deep \textit{anomaly detection} to ground states from infinite projected entangled pair state simulations. As a benchmark, the phase diagram of the 2D frustrated bilayer Heisenberg model is analyzed, which exhibits a second-order and two first-order quantum phase transitions. We show that in order to get a good qualitative picture of the transition lines, it suffices to use data from the cost-efficient simple update optimization. Results are further improve…
We propose and analyze a probabilistic but heralded scheme to generate pure, entangled, non-Gaussian states of collective spin in large atomic ensembles by means of single-photon detection. One photon announces the preparation of a Dicke state, while two or more photons announce Schrödinger cat states. The method produces pure states even for finite photon detection efficiency and weak atom-photon coupling. The entanglement generation can be made quasi-deterministic by means of repeated trial and feedback, enabling metrology beyond the standard quantum limit.
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