Entangled States and Local Measurements

Device-independent certification of entangled measurements

We present a device-independent protocol to test if a given black-box measurement device is entangled, that is, has entangled eigenstates. Our scheme involves three parties and is inspired by entanglement swapping; the test uses the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality, checked between each pair of parties. Also, focusing on the case where all particles are qubits, we characterize quantitatively the deviation of the measurement device from a perfect Bell state measurement.

Self-testing entangled measurements in quantum networks

Self-testing refers to the possibility of characterizing an unknown quantum device based only on the observed statistics. Here we develop methods for self-testing entangled quantum measurements, a key element for quantum networks. Our approach is based on the natural assumption that separated physical sources in a network should be considered independent. This provides a natural formulation of the problem of certifying entangled measurements. Considering the setup of entanglement swapping, we derive a robust self-test for the Bell-state measurement, tolerating noise levels up to 5%. We also di…

Analysis of Quantum Correlation in Successive Spin Measurements, Classical Communication of Spin $S$ Singlet States and Quantum Nonlocality of two Qubit Entangled States

In this thesis, we study about three subjects 1- Classical simulation of two spin-$s$ singlet correlations for all $s$ involving spin measurements, 2- Quantum correlations in successive single spin measurements, 3- Non locality without inequality for almost all two-qubit entangled states based on Cabello's non locality argument.

Generating entangled fermions by accelerated measurements on the vacuum

It is shown that accelerated projective measurements on the vacuum of a free Dirac spinor field results in an entangled state for an inertial observer. The physical mechanism at work is the Davies-Unruh effect. The produced state is always entangled and its entanglement increases as a function of the acceleration, reaching maximal entanglement in the asymptotic limit of infinite acceleration where Bell states are produced.

Quantum dense coding in multiparticle entangled states via local measurements

In this paper, we study quantum dense coding between two arbitrarily fixed particles in a (N+2)-particle maximally-entangled states through introducing an auxiliary qubit and carrying out local measurements. It is shown that the transmitted classical information amount through such an entangled quantum channel usually is less than two classical bits. However, the information amount may reach two classical bits of information, and the classical information capacity is independent of the number of the entangled particles in the initial entangled state under certain conditions. The results offer …

Scheme for measurement-based quantum computation on projected entangled-pair states

Recently it has been shown that projected entangled-pair states can be considered as a (physically motivated) resource state for measurement-based quantum computation. Here we elaborate on how to construct a deterministic measurement-based quantum computation model on projected entangled-pair states. In particular, we use this scheme to build a 4-level many-body model for universal quantum computation on qubits. We also derive a 3-local parent Hamiltonian for this model, whose ground state is non-degenerate.

Sub-Shot-Noise Quantum Optical Interferometry: A Comparison of Entangled State Performance within a Unified Measurement Scheme

Phase measurement using a lossless Mach-Zehnder interferometer with certain entangled $N$-photon states can lead to a phase sensitivity of the order of 1/N, the Heisenberg limit. However, previously considered output measurement schemes are different for different input states to achieve this limit. We show that it is possible to achieve this limit just by the parity measurement for all the commonly proposed entangled states. Based on the parity measurement scheme, the reductions of the phase sensitivity in the presence of photon loss are examined for the various input states.

Precision frequency measurements with entangled states

We demonstrate how quantum entanglement can be used for precision frequency measurements with trapped ions. In particular, we show how to suppress linear Zeeman shifts in optical frequency measurements by using maximally entangled states of two ions even if the individual ions do not have any field-independent transition. In addition, this technique allows for an accurate measurement of small external field frequency shifts such as the electric quadrupole shift which are important for ion clock experiments.

Super-resolving phase measurements with a multi-photon entangled state

Using a linear optical elements and post-selection, we construct an entangled polarization state of three photons in the same spatial mode. This state is analogous to a ``photon-number path entangled state'' and can be used for super-resolving interferometry. Measuring a birefringent phase shift, we demonstrate two- and three-fold improvements in phase resolution.

Experimental semi-device-independent certification of entangled measurements

Certifying the entanglement of quantum states with Bell inequalities allows one to guarantee the security of quantum information protocols independently of imperfections in the measuring devices. Here we present a similar procedure for witnessing entangled measurements, which play a central role in many quantum information tasks. Our procedure is termed semi-device-independent, as it uses uncharacterized quantum preparations of fixed Hilbert space dimension. Using a photonic setup, we experimentally certify an entangled measurement using measurement statistics only. We also apply our technique…

Weak Measurements with Entangled Probes

Encoding the imaginary part of a weak value onto an initially entangled probe can modify its entanglement content - provided the probe observable can distinguish between states of different entropies. Apart from fundamental interest, this result illustrates the utility of the imaginary weak value as a calculational tool in certain entanglement concentration protocols.

Distillation of free entanglement from bound entangled states using weak measurements

We propose a scheme for distillation of free bipartite entanglement from bipartite bound-entangled states. The crucial element of our scheme is an ancillary system that is coupled to the initial bound-entangled state via appropriate weak measurements. We show that in this protocol free entanglement can be always generated with nonzero probability by using a single copy of the bound-entangled state. We also derive a lower bound on the entanglement cost of the protocol, and conclude that, on average, applying weaker measurements results in relatively higher values of free entanglement as well as…

Non-Bilocal Measurement via Entangled State

Two observers, who share a pair of particles in an entangled mixed state, can use it to perform some non-bilocal measurement over another bipartite system. In particular, one can construct a specific game played by the observers against a coordinator, in which they can score better than a pair of observers who only share a classical communication channel.

等纠缠基与联合测量

Iso-entangled bases and joint measurements

针对纠缠测量研究不足的问题，系统研究纠缠测量并给出2量子比特投影联合测量等纠缠基等价类的完整分类，应用于三角网络得出相关测量结论，还讨论了高维部分结果。

Performing Quantum Measurement in Suitably Entangled States Originates the Quantum Computation Speed Up

We provide a justification of the quantum speed-up based on the complementary roles played by the reversible preparation of an entangled state before measurement and by the final measurement action.

Remote preparation of three-photon entangled states via single-photon measurement

Remote state preparation (RSP) provides an indirect way of manipulating quantum information based on the nonlocal effect of quantum measurement. Although RSP has been demonstrated in recent years to remotely prepare multi-photon states, quantum measurement on the same number of photons was required, i.e., to prepare N-photon states via RSP, quantum measurement on the other N-photons was required, hence significantly limiting practicality and applicability of RSP. Here we report the first experimental demonstration of remote preparation of three-photon entangled states by measuring only a singl…

Production of Information and Entropy in measurement of entangled states

Problem of classification of all the set of entangled states is considered. Invariance of entangled states relative to transformations from a group of symmetry of qubit space leads to classification of all states of the system through irreducible representations from that group. Excess of entropy of a subsystem over entropy of the whole system indicates the presence of entaglement in the system.

Bell-state measurement and quantum teleportation using linear optics: two-photon pairs, entangled coherent states, and hybrid entanglement

We review and compare Bell-state measurement and quantum teleportation schemes using linear optics with three different types of resources, i.e., two-photon pairs, entangled coherent states and hybrid entangled states. Remarkably, perfect teleportation with linear optics is possible in principle based on a hybrid approach that combines two-photon pairs and entangled coherent states. It turns out that hybrid approach allows to perform Bell-state measurement and local Pauli operations in a deterministic way, while it requires photon number resolving measurements.

Experimental Entangled Entanglement

All previous tests of local realism have studied correlations between single-particle measurements. In the present experiment, we have performed a Bell experiment on three particles in which one of the measurements corresponds to a projection onto a maximally-entangled state. We show theoretically and experimentally, that correlations between these entangled measurements and single-particle measurements are too strong for any local-realistic theory and are experimentally exploited to violate a CHSH-Bell inequality by more than 5 standard deviations. We refer to this possibility as "entangled e…

Efficient evaluation of quantum observables using entangled measurements

The advent of cloud quantum computing has led to the rapid development of quantum algorithms. In particular, it is necessary to study variational quantum-classical hybrid algorithms, which are executable on noisy intermediate-scale quantum (NISQ) computers. Evaluations of observables appear frequently in the variational quantum-classical hybrid algorithms for NISQ computers. By speeding up the evaluation of observables, it is possible to realize a faster algorithm and save resources of quantum computers. Grouping of observables with separable measurements has been conventionally used, and the …

Teleportation for atomic entangled state by entanglement swapping with separate measurements in cavity QED

Experimentally feasible scheme for teleportation of atomic entangled state via entanglement swapping is proposed in cavity quantum electrodynamics (QED) without joint Bell-state measurement (BSM). In the teleportation processes the interaction between atoms and a single-mode nonresonant cavity with the assistance of a strong classical driving field substitute the joint measurements. The discussion of the scheme indicates that it can be realized by current technologies.

New kind of asymmetric integration projection operators constructed by entangled state representations and parity measurement

By means of the technique of integration within an ordered product of operators and Dirac notation, we introduce a new kind of asymmetric integration projection operators in entangled state representations. These asymmetric projection operators are proved to be the Hermitian operator. Then, we rigorously demonstrate that they correspond to a parity measurement combined with a beam splitter when any two-mode quantum state passes through such device. Therefore we obtain a new relation between a Hermitian operator and the entangled state representation. As applications, we recover the previous re…

Measurement-Device-Independent Entanglement Witnesses for All Entangled Quantum States

The problem of demonstrating entanglement is central to quantum information processing applications. Resorting to standard entanglement witnesses requires one to perfectly trust the implementation of the measurements to be performed on the entangled state, which may be an unjustified assumption. Inspired by the recent work of F. Buscemi [Phys. Rev. Lett. 108, 200401 (2012)], we introduce the concept of Measurement-Device-Independent Entanglement Witnesses (MDI-EWs), which allow one to demonstrate entanglement of all entangled quantum states with untrusted measurement apparatuses. We show how t…

Feasible Linear-optics Generation of Polarization-entangled Photons Assisted with Single-photon Quantum Non-demolition Measurement

We propose a feasible scheme to create $n$-party ($n\geq 2$) polarization-entangled photon states in a controllable way. The scheme requires only single-photon sources, single-photon quantum non-demolition measurement (SP-QNDM) and simple linear optical elements, usually with high perfections. The SP-QNDM acts as a non-destructive projection measurement onto the wanted entangled states and filters out the unwanted terms. Our scheme in fact realizes entanglement of non-interacting photons; the interaction occurs only implicitly in the optical elements and SP-QNDM. We also briefly consider purif…

Direct Measurement Methods of Density Matrix of an Entangled Quantum State

In general, the state of a quantum system represented by density operator and its determination is a fundamental problem in quantum mechanics. A method of direct measurement of matrix element of density operator of a single two dimensional quantum system using weak measurement was theoretically proposed[Phys. Rev. Lett. 134, 070402(2012)] and experimentally demonstrated[Phys. Rev. Lett. 117, 120401(2016)] by Lundeen et al. Furthermore, recently the Guo-Guang Can et al.[Phys. Rev. Lett. 123, 150402(2019)] investigated the method of direct measurement of a nonlocal entangled quantum state. Howev…

One-step direct measurement of the entangled W states with cross-Kerr nonlinearity

We propose a scheme to directly measure the entangled W states with cross-Kerr nonlinearity mediums. This scheme can measure three-photon, four-photon, and even N-photon W states in one step. Only PBSs and cross-Kerr nonlinearity mediums are used in this scheme, which is feasible for experiments. We describe the three-photon W states measurement process and extend it to four-photon and N-photon W states.

Modulation and Measurement of Time-Energy Entangled Photons

We describe a proof-of-principal experiment demonstrating a Fourier technique for measuring the shape of biphoton wavepackets. The technique is based on the use of synchronously driven fast modulators and slow (integrating) detectors.

Loss-Induced Limits to Phase Measurement Precision with Maximally Entangled States

The presence of loss limits the precision of an approach to phase measurement using maximally entangled states, also referred to as NOON states. A calculation using a simple beam-splitter model of loss shows that, for all nonzero values L of the loss, phase measurement precision degrades with increasing number N of entangled photons for N sufficiently large. For L above a critical value of approximately 0.785, phase measurement precision degrades with increasing N for all values of N. For L near zero, phase measurement precision improves with increasing N down to a limiting precision of approx…

Effects of multiple pairs on visibility measurements of entangled photons generated by spontaneous parametric processes

Entangled photon-pair sources based on spontaneous parametric processes are widely used in photonic quantum information experiments. In this paper, we clarify the relationship between average photon-pair number and the visibility of two-photon interference (TPI) using those entanglement sources. We consider sources that generate distinguishable and indistinguishable entangled photon pairs, assuming coincidence measurements that use threshold detectors. We present formulas for the TPI visibility of a polarization entanglement that take account of all the high-order multi-pair emission events. M…

Semi-device-independent characterisation of multipartite entangled states and measurements

The semi-device-independent framework allows one to draw conclusions about properties of an unknown quantum system under weak assumptions. Here we present a semi-device-independent scheme for the characterisation of multipartite entanglement based around a game played by several isolated parties whose devices are uncharacterised beyond an assumption about the dimension of their Hilbert spaces. Our scheme can certify that an $n$-partite high-dimensional quantum state features genuine multipartite entanglement. Moreover, the scheme can certify that a joint measurement on $n$ subsystems is entang…

Experimental evaluation of the non-classical relation between measurement errors using entangled photon pairs as a probe

We have experimentally evaluated the non-classical relation between measurement errors in a joint measurement of two non-commuting polarizations by using entangled photon pairs as a probe. The joint measurement was realized by filtering polarization directions that are sensitive to both of the two target polarizations and the same filtering procedures were applied independently to the two photons of an entangled pair. Since the statistically independent measurement errors of two identical measurements performed on entangled pairs will reduce an overall visibility of the correlation by the squa…

Nonsequential positive-operator-valued measurements on entangled mixed states do not always violate a Bell inequality

We present a local-hidden-variable model for positive-operator-valued measurements (an LHVPOV model) on a class of entangled generalized Werner states, thus demonstrating that such measurements do not always violate a Bell-type inequality. We also show that, in general, if the state $ρ'$ can be obtained from $ρ$ with certainty by local quantum operations without classical communication then an LHVPOV model for the state $ρ$ implies the existence of such a model for $ρ'$.

三重测量不确定性与可分离态与纠缠态的区分

Triple measurements uncertainty and the distinguishment between the separable and entangled states

本文通过三重测量不确定性常数的推导，揭示了其与可分离态和纠缠态区分的深刻联系。

Long distance measurement-device-independent quantum key distribution with entangled photon sources

We present a practical method that can make quantum key distribution (QKD), for the first time, both ultra-long-distance and immune to all attacks in the detection system. This method is an important extension of the measurement-device-independent QKD (MDI-QKD) - MDI-QKD with entangled photon sources in the middle. By proposing a general model and simulating an entanglement based QKD experiment, we find that MDI-QKD with one entangled photon source in the middle can practically tolerate 77 dB combined loss (367km standard telecom fiber) in the asymptotic limit, and it can still tolerate 60 dB …

Efficient verification of entangled continuous-variable quantum states with local measurements

Continuous-variable quantum states are of particular importance in various quantum information processing tasks including quantum communication and quantum sensing. However, a bottleneck has emerged with the fast increasing in size of the quantum systems which severely hinders their efficient characterization. In this work, we establish a systematic framework for verifying entangled continuous-variable quantum states by employing local measurements only. Our protocol is able to achieve the unconditionally high verification efficiency which is quadratically better than quantum tomography as wel…

Perfect discrimination of quantum measurements using entangled systems

Distinguishing physical processes is one of the fundamental problems in quantum physics. Although distinguishability of quantum preparations and quantum channels have been studied considerably, distinguishability of quantum measurements remains largely unexplored. We investigate the problem of single-shot discrimination of quantum measurements using two strategies, one based on single quantum systems and the other one based on entangled quantum systems. First, we formally define both scenarios. We then construct sets of measurements (including non-projective) in arbitrary finite dimensions tha…

Simultaneous Certification of Entangled States and Measurements in Bounded Dimensional Semi-Quantum Games

Certification of quantum systems and operations is a central task in quantum information processing. Most current schemes rely on a tomography with fully characterised devices, while this may not be met in real experiments. Device characterisations can be removed with device-independent tests, it is technically challenging at the moment, though. In this letter, we investigate the problem of certifying entangled states and measurements via semi-quantum games, a type of non-local quantum games with well characterised quantum inputs, balancing practicality and device-independence. We first design…

Device-independent certification of maximal randomness from pure entangled two-qutrit states using non-projective measurements

While it has recently been demonstrated how to certify the maximal amount of randomness from any pure two-qubit entangled state in a device-independent way [E. Woodhead et al., Phys. Rev. Research 2, 042028(R)(2020)], the problem of optimal randomness certification from entangled states of higher local dimension remains open. Here we introduce a method for device-independent certification of the maximal possible amount of $2\log_23$ random bits using pure bipartite entangled two-qutrit states and extremal nine-outcome general non-projective measurements. To this aim, we exploit the extended Be…

大型纠缠系统上弱测量的测量时间

Measurement time of weak measurements on large entangled systems

本文证明仅用弱测量即可重现多体非局域纠缠波函数的坍缩，并发现单激发在N个量子比特间纠缠态的坍缩时间按N的双对数标度，支持自发弱测量作为一切物理测量基础的自洽假设。

Measurements of semi-local and non-maximally entangled states

Consistency with relativistic causality narrows down dramatically the class of measurable observables. We argue that by weakening the preparation role of ideal measurements, many of these observables become measurable. Particularly, we show by applying entanglement assisted remote operations, that all Hermitian observable of a $2\times2$-dimensional bipartite system are measurable.

纠缠态分离子系统的测量

Measurements on the separated subsystems of an entangled state

本文针对复合量子系统纠缠态分离子系统的测量问题，提出通过自由矢量空间的（陪集）态获取测量投影的方法，消除了随机坍缩的需求，揭示了非定域性的产生机制。

纠缠光子对红外光谱中的测量不确定性

Measurement Uncertainty in Infrared Spectroscopy with Entangled Photon Pairs

该研究针对红外波段纠缠多参数光谱测量机制不明的问题，发现了约束纠缠光子对红外光谱多参数测量精度的不确定关系，揭示了折射率与吸收系数测量精度的权衡规律，为纠缠辅助光谱的实验设计与应用提供指导。

Multiple Observers Can Share the Nonlocality of Half of an Entangled Pair by Using Optimal Weak Measurements

We investigate the trade-off between information gain and disturbance for a class of weak von Neumann measurements on spin-$\frac{1}{2}$ particles, and derive the unusual measurement pointer state that saturates this trade-off. We then consider the fundamental question of sharing the non-locality of a single particle of an entangled pair among multiple observers, and demonstrate that by exploiting the information gain disturbance trade-off, one can obtain an arbitrarily long sequence of consecutive and independent violations of the CHSH-Bell inequality.

Demonstrating the power of quantum computers, certification of highly entangled measurements and scalable quantum nonlocality

Increasingly sophisticated quantum computers motivate the exploration of their abilities in certifying genuine quantum phenomena. Here, we demonstrate the power of state-of-the-art IBM quantum computers in correlation experiments inspired by quantum networks. Our experiments feature up to 12 qubits and require the implementation of paradigmatic Bell-State Measurements for scalable entanglement-swapping. First, we demonstrate quantum correlations that defy classical models in up to nine-qubit systems while only assuming that the quantum computer operates on qubits. Harvesting these quantum adva…

Teleportation of entangled states without Bell-state measurement

In a recent paper [Phys. Rev. A 70, 025803 (2004)] we presented a scheme to teleport an entanglement of zero- and one-photon states from a bimodal cavity to another one, with 100% success probability. Here, inspired on recent results in the literature, we have modified our previous proposal to teleport the same entangled state without using Bell-state measurements. For comparison, the time spent, the fidelity, and the success probability for this teleportation are considered.

纠缠测量保真度估计的局部态方法

Fidelity Estimation of Entangled Measurements with Local States

提出仅需局部态制备与经典后处理的协议，通过按重要性选择泡利本征态测量，高效估计n比特纠缠测量保真度，样本复杂度由非零期望泡利算符数决定，并以稳定子Rényi熵度量估计难度。

使用非投影测量对最大纠缠态进行认证

Certification of the maximally entangled state using non-projective measurements

针对单边设备无关情形，本文提出利用三个三输出极值 POVM 非投影测量自测试两量子比特最大纠缠态，并验证其对白噪声的鲁棒性。

The entangled measurement state is not a paradoxical superposition of the detector

The entangled state that results when a detector measures a superposed quantum system has spawned decades of concern about the problem of definite outcomes or "Schrodinger's cat." This state seems to describe a detector in an indefinite or "smeared" situation of indicating two macroscopic configurations simultaneously. This would be paradoxical. Since all entangled states are known to have nonlocal properties, and since measurements have obvious nonlocal characteristics, it's natural to turn to nonlocality experiments for insight into this question. Unlike the measurement situation where the p…

Direct observation of Hardy's paradox by joint weak measurement with an entangled photon pair

We implemented a joint weak measurement of the trajectories of two photons in a photonic version of Hardy's experiment. The joint weak measurement has been performed via an entangled meter state in polarization degrees of freedom of the two photons. Unlike Hardy's original argument in which the contradiction is inferred by retrodiction, our experiment reveals its paradoxical nature as preposterous values actually read out from the meter. Such a direct observation of a paradox will give us a new insight into the spooky action of quantum mechanics.

Non-local polarization alignment and control in fiber using feedback from correlated measurements of entangled photons

Quantum measurements that use the entangled photons' polarization to encode quantum information require calibration and alignment of the measurement bases between spatially separate observers. Because of the changing birefringence in optical fibers arising from temperature fluctuations or external mechanical vibrations, the polarization state at the end of a fiber channel is unpredictable and time-varying. Polarization tracking and stabilization methods originally developed for classical optical communications cannot be applied to polarization-entangled photons, where the separately detected p…

Proposed Experimental Test for Proving Quantum Contextuality with Non-entangled Photons

We present a new and feasible test proving quantum contextuality in four-dimensional Hiltbert space. In our scheme, a contradiction between quantum mechanics and noncontextual hidden variables is revealed through the measurement statistics of two joint measurements of an ensemble of non-entangled qubits. The origin of nonclassicality is fully attributed to the measurement process. Quantum optical realization using photon pairs and linear optics are presented.

Geometric discord and Measurement-induced nonlocality for well known bound entangled states

We employ geometric discord and measurement induced nonlocality to quantify non classical correlations of some well-known bipartite bound entangled states, namely the two families of Horodecki's ($2\otimes 4$, $3\otimes 3$ and $4\otimes 4$ dimensional) bound entangled states and that of Bennett etal's in $3\otimes 3$ dimension. In most of the cases our results are analytic and both the measures attain relatively small value. The amount of quantumness in the $4\otimes 4$ bound entangled state of Benatti etal and the $2\otimes 8$ state having the same matrix representation (in computational basi…

Observation of Nonlocality Sharing among Three Observers with One Entangled Pair via Optimal Weak Measurement

Bell nonlocality plays a fundamental role in quantum theory. Numerous tests of the Bell inequality have been reported since the ground-breaking discovery of the Bell theorem.Up to now, however, most discussions of the Bell scenario have focused on a single pair of entangled particles distributed to only two separated observers. Recently, it has been shown surprisingly that multiple observers can share the nonlocality present in a single particle from an entangled pair using the method of weak measurements [Phys. Rev. Lett. {\bf 114}, 250401 (2015)]. Here we report an observation of double CHSH…

Remote spectral measurement using entangled photons

By utilizing the frequency anticorrelation of two-photon states produced via spontaneous parametric down conversion (SPDC), the working principle of a novel remote spectrometer is demonstrated. With the help of a local scanning monochromator, the spectral transmission function of an optical element (or atmosphere) at remote locations can be characterized for wide range of wavelengths with expected high resolution.