Entanglement is perhaps the most important new feature of the quantum world. It is expressed in quantum theory by the joint measurement formula. We prove the formula for self-adjoint observables from a plausible assumption, which for spacelike separated measurements is an expression of relativistic causality. State reduction is simply a way to express the JMF after one measurement has been made, and its result known.
We propose an entanglement swapping scheme in cavity QED. In the scheme, the previously used joint measurement is not needed. The entanglement swapping in our proposal is a non-post-selection one, i.e., after the swapping is done, the swapped entanglement is still there.
By using of a special reduction way of density matrices, in this Letter we find the entanglement between two bunches of particles, its measure can be represented by the entanglement of formation.
Twenty-five years after the invention of quantum teleportation, the concept of entanglement gained enormous popularity. This is especially nice to those who remember that entanglement was not even taught at universities until the 1990's. Today, entanglement is often presented as a resource, the resource of quantum information science and technology. However, entanglement is exploited twice in quantum teleportation. First, entanglement is the `quantum teleportation channel', i.e. entanglement between distant systems. Second, entanglement appears in the eigenvectors of the joint measurement that…
Operator entanglement of two-qubit joint unitary operations is revisited. Schmidt number is an important attribute of a two-qubit unitary operation, and may have connection with the entanglement measure of the unitary operator. We found the entanglement measure of two-qubit unitary operators is classified by the Schmidt number of the unitary operators. The exact relation between the operator entanglement and the parameters of the unitary operator is clarified too.
We study the entanglement creation between two flux qubits interacting with electromagnetic field modes. No direct interaction between the qubits exists. Entanglement is reached using entanglement swapping method by an interference measurement performed on photons. We discuss the influence of off-resonance and multi-photon initial states on the qubit-qubit entanglement. The presented scheme is able to drive an initially separable state of two qubits into an highly entangled state suitable for quantum information processing.
For a number of basic experiments on two-photon intensity correlations it is pointed out that the results, which are usually explained in terms of the formalism of canonical field quantization, can also be explained in terms of quantum wave packets, where reduction and entanglement are taken into account.
We show that the amount of entanglement needed as an initial resource to set up a certain final amount of entanglement between two ends of a noisy channel can be reduced in certain cases by using quantum repeaters. Our investigation (for various channels) considers cases when a large number of entangled pairs are transmitted through the channel using known asymptotic results and conjectured bounds on distillable entanglement.
Joint measurements of two observables reveal that every state is nonclassical, with the only trivial exception of the state with density matrix proportional to the identity. This naturally includes states considered universally as classical-like, such as SU(2) and Glauber coherent states. We show that this holds because we can always find a joint measurement whose statistics is not separable.
We use hyper-entanglement to experimentally realize deterministic entanglement swapping based on quantum Elegant Joint Measurements. These are joint projections of two qubits onto highly symmetric, iso-entangled, bases. We report measurement fidelities no smaller than $97.4\%$. We showcase the applications of these measurements by using the entanglement swapping procedure to demonstrate quantum correlations in the form of proof-of-principle violations of both bilocal Bell inequalities and more stringent correlation criteria corresponding to full network nonlocality. Our results are a foray int…
Simple joint measurements of pairs of observables reveal that states considered universally as classical-like, such as SU(2) spin coherent states, Glauber coherent states, and thermal states are actually nonclassical. We show that this holds because we can find a joint measurement the statistics of which is not separable. Eventually this may be extended to all states different from the maximally mixed state.
Two auto-ionization systems in a stationary optical field mutually interacting via the dipole-dipole interaction are considered. Their evolution is analytically found. Joint spectra of two ionized electrons are analyzed in detail in the long-time limit for comparable strengths of direct and indirect ionization paths as well as the dominating indirect ionization path. Entanglement in the state of two ionized electrons is quantified using the density of quadratic negativity. Suitable conditions for obtaining highly entangled states are discussed.
Entanglement and symmetrization lead to non-separable states that can modify physical properties. Using the example of atomic absorption we compare both types of effects when they are relevant at once. The presence of multi-particle superpositions largely alters the absorption rates of identical atoms, even inhibiting the dependence on overlapping for fermions. We also identify a set of non-standard excluded states related to multi-fermion superposition that naturally emerge in this context. We propose an arrangement based on the dissociation of molecules to test these ideas.
Phenomena induced by the existence of entanglement, such as nonlocal correlations, exhibit characteristic properties of quantum mechanics distinguishing from classical theories. When entanglement is accompanied by classical communication, it enhances the power of quantum operations jointly performed by two spatially separated parties. Such a power has been analyzed by the gap between the performances of joint quantum operations implementable by local operations at each party connected by classical communication with and without the assistance of entanglement. In this work, we present a new for…
The scheme for entanglement teleportation is proposed to incorporate multipartite entanglement of four qubits as a quantum channel. Based on the invariance of entanglement teleportation under arbitrary two-qubit unitary transformation, we derive relations of separabilities for joint measurements at a sending station and for unitary operations at a receiving station. From the relations of separabilities it is found that an inseparable quantum channel always leads to a total teleportation of entanglement with an inseparable joint measurement and/or a nonlocal unitary operation.
We consider a variant of the entanglement of assistance, as independently introduced by D.P. DiVincenzo {\em et al.} ({\tt quant-ph/9803033}) and O. Cohen (Phys. Rev. Lett. {\bf 80}, 2493 (1998)). Instead of considering three-party states in which one of the parties, the assistant, performs a measurement such that the remaining two parties are left with on average as much entanglement as possible, we consider four-party states where two parties play the role of assistants. We answer several questions that arise naturally in this scenario, such as (i) how much more entanglement can be produced …
Linear-optical systems can implement photonic quantum walks that simulate systems with nontrivial topological properties. Here, such photonic walks are used to jointly entangle polarization and winding number. This joint entanglement allows information processing tasks to be performed with interactive access to a wide variety of topological features. Topological considerations are used to suppress errors, with polarization allowing easy measurement and manipulation of qubits. We provide three examples of this approach: production of two-photon systems with entangled winding number (including t…
The problem of inferring the outcome of a simultaneous measurement of two non-commuting observables is addressed. We show that for certain pairs with dense spectra, precise inferences of the measurement outcomes are possible in pre-and post-selected ensembles, and if the selections involve entangled states with some other system. We show that the problem is related to the problem of assigning weak values to a continuous family of operators, and give explicit examples where this problem is solvable. Some foundational implications are briefly discussed.
In this work, we show that while all measures of mixedness may be used to witness entanglement, all such entangled states must have a negative partial transpose (NPT). Though computing the negativity of the partial transpose scales well at high dimension, it relies on knowing the complete quantum state, which does not. To address this, we compare different measures of mixedness over uniform ensembles of joint quantum states at varying dimension to gauge their relative success in witnessing entanglement. In doing so, we find that comparing joint and marginal purities is overwhelmingly more succ…
We propose, analyze, and evaluate a technique for the joint measurement of time-frequency entanglement between two photons. In particular, we show that the frequency sum and time difference of two photons could be simultaneously measured through the sum-frequency generation process, without measuring the time or frequency of each individual photon. We demonstrate the usefulness of this technique by using it to design a time-frequency entanglement based continuous variable superdense coding and a quantum illumination protocol. Performance analysis of these two protocols suggests that the joint …
In this paper we analyze the existence of joint probabilities for the Bell-type and GHZ entangled states. We then propose the usage of nonmonotonic upper probabilities as a tool to derive consistent joint upper probabilities for the contextual hidden variables. Finally, we show that for the extreme example of no error, the GHZ state allows for the definition of a joint upper probability that is consistent with the strong correlations.
We analyse the problem of distillation of entanglement of mixed states in higher dimensional compound systems. Employing the positive maps method [M. Horodecki et al., Phys. Lett. A 223 1 (1996)] we introduce and analyse a criterion of separability which relates the structures of the total density matrix and its reductions. We show that any state violating the criterion can be distilled by suitable generalization of the two-qubit protocol which distills any inseparable two-qubit state. Conversely, all the states which can be distilled by such a protocol must violate the criterion. The proof in…
Qutrit entanglement and joint multi-parameter estimation in an optical clock platform
Max-Planck-Institut für Quantenoptik（马克斯·普朗克量子光学研究所）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Peking University（北京大学）；Vienna Center for Quantum Science and Technology（维也纳量子科学与技术中心）；Atominstitut, TU Wien（维也纳工业大学原子研究所）；Fakultät für Physik, Ludwig-Maximilians-Universität（慕尼黑大学物理学院）；Collaborative Innovation Center of Extreme Optics, Shanxi University（山西大学极端光学协同创新中心）；Hefei National Laboratory（合肥国家实验室）
Polarization-entangled photon pairs can be efficiently prepared into pure Bell states with a high fidelity via type-II spontaneous parametric down-conversion (SPDC) of narrow-band pump light. However, the use of femtosecond pump pulses to generate multi-photon states with precise timing often requires spectral filtering to maintain a high quality of polarization entanglement. This typically reduces the efficiency of photon pair collection. We experimentally map the polarization correlations of photon pairs from such a source over a range of down-converted wavelengths with a high spectral resol…
Suppose Alice and Bob jointly possess a pure state, $|ψ\ra$. Using local operations on their respective systems and classical communication it may be possible for Alice and Bob to transform $|ψ\ra$ into another joint state $|ϕ\ra$. This Letter gives necessary and sufficient conditions for this process of entanglement transformation to be possible. These conditions reveal a partial ordering on the entangled states, and connect quantum entanglement to the algebraic theory of majorization. As a consequence, we find that there exist essentially different types of entanglement for bipartite quantum…
In 2017 an idea considering a pair of Hermitian operators of product form was published, which is called ultrafine entanglement witnessing. In 2018 some rigorous results were given. Here we improve their work. First we point this idea can be directly derived from an earlier concept named joint separable numerical range and explain how it works as a series of witnesses. Second by a simple method we present a sufficient condition for an effective pair. Finally we prove this condition is necessary for optimization.
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.
We study theoretically the teleportation of controlled-phase (CZ) gate through measurement-based quantum information processing for continuous-variable systems. We examine the degree of entanglement in the output modes of the teleported CZ-gate for two classes of resource states: the canonical cluster states that are constructed via direct implementations of two-mode squeezing operations, and the linear-optical version of cluster states which are built from linear-optical networks of beam splitters and phase shifters. In order to reduce the excess noise arising from finite-squeezed resource st…
We investigate multipartite entanglement for composite quantum systems in a pure state. Using the generalized Bloch representation for n-qubit states, we express the condition that all k-qubit reductions of the whole system are maximally mixed, reflecting maximum bipartite entanglement across all k vs. n-k bipartitions. As a special case, we examine the class of balanced pure states, which are constructed from a subset of the Pauli group P_n that is isomorphic to Z_2^n. This makes a connection with the theory of quantum error-correcting codes and provides bounds on the largest allowed k for fi…
We provide a generalization of the reduction and Robertson positive maps in matrix algebras. They give rise to a new class of optimal entanglement witnesses. Their structural physical approximation is analyzed. As a byproduct we provide a new examples of PPT (Positive Partial Transpose) entangled states.
Entanglement appears under two different forms in quantum theory, namely as a property of states of joint systems and as a property of measurement eigenstates in joint measurements. By combining these two aspects of entanglement, it is possible to generate nonlocality between particles that never interacted, using the protocol of entanglement swapping. We show that even in the more constraining bilocal scenario where distant sources of particles are assumed to be independent, i.e. to share no prior randomness, this process can be simulated classically with bounded communication, using only 9 b…
A method for reconstructing joint photon-number distributions of twin beams from the experimental photocount histograms is suggested and experimentally implemented. Contrary to the standard reconstruction methods, it incorporates spatial noise reduction based on spatial pairing of photons. Superior performance of the method above the usual one for the maximum-likelihood approach is demonstrated.
We study the entanglement properties of a pair of two-level atoms going through a cavity one after another. The initial joint state of two successive atoms that enter the cavity is unentangled. Interactions mediated by the cavity photon field result in the final two-atom state being of a mixed entangled type. We consider the field statistics of the Fock state field, and the thermal field, respectively, inside the cavity. The entanglement of formation of the joint two-atom state is calculated for both these cases as a function of the Rabi-angle $gt$. We present a comparitive study of two-atom e…
We investigate the properties of three entanglement measures that quantify the statistical distinguishability of a given state with the closest disentangled state that has the same reductions as the primary state. In particular, we concentrate on the relative entropy of entanglement with reversed entries. We show that this quantity is an entanglement monotone which is strongly additive, thereby demonstrating that monotonicity under local quantum operations and strong additivity are compatible in principle. In accordance with the presented statistical interpretation which is provided, this enta…
We introduce the theory of operator monotone functions and employ it to derive a new inequality relating the quantum relative entropy and the quantum conditional entropy. We present applications of this new inequality and in particular we prove a new lower bound on the relative entropy of entanglement and other properties of entanglement measures.
The inevitable interaction between quantum systems and environment induces effects of decoherence which may be so strong as to destroy any initial entanglement between the systems, a phenomenon known as "entanglement breaking". Here we show the simplest examples where the combination of two entanglement-breaking channels into a joint correlated-noise environment reactivates the distribution of entanglement, with classes of entangled states which are perfectly transmitted from a middle station (Charlie) to two remote stations (Alice and Bob). Surprisingly, this reactivation is induced by the pr…
The stabiliser formalism allows the efficient description of a sizeable class of pure as well as mixed quantum states of N-qubit systems. That same formalism has important applications in the field of quantum error correcting codes, where mixed stabiliser states correspond to projectors on subspaces associated with stabiliser codes. Here, we derive efficient reduction procedures to obtain various useful normal forms for stabiliser states. We explicitly prove that these procedures will always converge to the correct result and that these procedures are efficient in that they only require a poly…
An experimentally realizable model based on the interaction between an excited two-level atom and a radiation field inside two quantum electrodynamics cavities is proposed. It consists of sending an excited two-level atom through two serial cavities which contain the radiation field. Hence, the Lindblad master equation described the reduced density matrix of the joint-joint field system inside the cavities is exactly solved in Markovian and non-Markovian regimes. However, the rate of entanglement inherent in the total field-field system are evaluated using various witnesses of entanglement suc…
We propose a linear optical scheme for the teleportation of unknown ionic states, the entanglement concentration for nonmaximally entangled states for ions via entanglement swapping and the remote preparation for ionic entangled states. The unique advantage of the scheme is that the joint Bell-state measurement needed in the previous schemes is not needed in the current scheme, i.e. the joint Bell-state measurement has been converted into the product of separate measurements on single ions and photons. In addition, the current scheme can realize the quantum information processes for ions by us…
We show that combining randomized measurement protocols with importance sampling allows for characterizing entanglement in significantly larger quantum systems and in a more efficient way than in previous work. A drastic reduction of statistical errors is obtained using classical techniques of machine-learning and tensor networks using partial information on the quantum state. In present experimental settings of engineered many-body quantum systems this effectively doubles the (sub-)system sizes for which entanglement can be measured. In particular, we show an exponential reduction of the requ…
Broadband quantum noise reduction can be achieved in gravitational wave detectors by injecting frequency dependent squeezed light into the the dark port of the interferometer. This frequency dependent squeezing can be generated by combining squeezed light with external filter cavities. However, in future long baseline interferometers (LBIs), the filter cavity required to achieve the broadband squeezing has a low bandwidth -- necessitating a very long cavity to mitigate the issue from optical loss. It has been shown recently that by taking advantage of Einstein-Podolsky-Rosen (EPR) entanglement…
A new class of entanglement witnesses (EWs) called reduction type entanglement witnesses is introduced, which can detect some multi-qudit entangeled states including PPT ones with Hilbert space of dimension $d_{_{1}}\otimes d_{_{2}}\otimes...\otimes d_{_{n}}$. The novelty of this work comes from the fact that the feasible regions turn out to be convex polygons, hence the manipulation of these EWs reduces to linear programming which can be solved \emph{exactly} by using simplex method. The decomposability and non-decomposability of these EWs are studied and it is shown that it has a close conne…
Given a finite number $N$ of copies of a qubit state we compute the maximum fidelity that can be attained using joint-measurement protocols for estimating its purity. We prove that in the asymptotic $N\to\infty$ limit, separable-measurement protocols can be as efficient as the optimal joint-measurement one if classical communication is used. This in turn shows that the optimal estimation of the entanglement of a two-qubit state can also be achieved asymptotically with fully separable measurements. The relationship between our global Bayesian approach and the quantum Cramer-Rao bound is also di…
Quantum teleportation with partially entangled joint measurements induced by coherent errors
Korea Institute of Science and Technology (KIST)（韩国科学技术院）；Kyung Hee University（庆熙大学）；Korea University of Science and Technology (UST)（韩国科学技术院）；Korea Institute for Advanced Study（韩国高等研究院）；Pohang University of Science and Technology (POSTECH)（浦项工科大学）
We consider random bipartite quantum states obtained by tracing out one subsystem from a random, uniformly distributed, tripartite pure quantum state. We compute thresholds for the dimension of the system being traced out, so that the resulting bipartite quantum state satisfies the reduction criterion in different asymptotic regimes. We consider as well the basis-independent version of the reduction criterion (the absolute reduction criterion), computing thresholds for the corresponding eigenvalue sets. We do the same for other sets relevant in the study of absolute separability, using techniq…
In this paper we show how weak joint measurement and local feedback can be used to control entanglement generation between two qubits. To do this, we make use of a decoherence free subspace (DFS). Weak measurement and feedback can be used to drive the system into this subspace rapidly. Once within the subspace, feedback can generate entanglement rapidly, or turn off entanglement generation dynamically. We also consider, in the context of weak measurement, some of differences between purification and generating entanglement.
It is well known that Bell inequality supporting the local realism can be violated in quantum mechanics. Numerous tests of such a violation have been demonstrated with bipartite entanglements. Using spectral jointmeasurements of the qubits, we here propose a scheme to test the tripartite Mermin inequality (a three-qubit Bell-type inequality) with three qubits dispersively-coupled to a driven cavity. First, we show how to generate a three-qubit Greenberger-Horne-Zeilinger (GHZ) state by only one-step quantum operation. Then, spectral joint-measurements are introduced to directly confirm such a …
While the experimental detection of entanglement provides already quite a difficult task, experimental quantification of entanglement is even more challenging, and has not yet been studied thoroughly. In this paper we discuss several issues concerning bounds on concurrence measurable collectively on copies of a given quantum state. Firstly, we concentrate on the recent bound on concurrence by Mintert--Buchleitner [F. Mintert and A. Buchleitner, Phys. Rev. Lett. 98, 140505 (2007)]. Relating it to the reduction criterion for separability we provide yet another proof of the bound and point out so…
Large Scale Entanglement Structure Detection in 100-Qubit Systems via Local Joint Measurements
School of Applied Science, Beijing Information Science and Technology University（北京信息科技大学应用科学学院）；School of Instrument Science and Opto-Electronics Engineering, Beijing Information Science and Technology University（北京信息科技大学仪器科学与光电工程学院）；School of Physics, Beihang University（北京航空航天大学物理学院）；School of Future Technology, Henan University（河南大学未来技术学院）；Shenzhen Institute of Beihang University（北京航空航天大学深圳研究院）；Jiangxi Beidouyun Intelligent Technology Co. Ltd.（江西北斗云智能科技有限公司）；School of Automation (School of Artificial Intelligence), Beijing Information Science and Technology University（北京信息科技大学自动化学院（人工智能学院））；School of Space and Earth Sciences, Beihang University（北京航空航天大学空天科学学院）
