Surface acoustic waves (SAWs) can create moving quantum dots in piezoelectric materials. Here we show how electron-spin qubits located on dynamic quantum dots can be entangled. Previous theoretical and numerical models of quantum-dot entanglement generation have been insufficient to study quantum dynamics in realistic experimental devices. We utilize state-of-the-art graphics processing units to simulate the wave function dynamics of two electrons carried by a SAW through a 2D semiconductor heterostructure. We build a methodology to implement a power-of-SWAP gate via the Coulomb interaction. A benefit of the SAW architecture is that it provides a coherent way of transporting the qubits through an electrostatic potential. This architecture allows us to avoid problems associated with fast control pulses and guarantees operation consistency, providing an advantage over static qubits. For inter-dot barrier heights where the double occupation energy is sufficiently greater than the double-dot hopping energy, we find that parameters based on experiments in GaAs/AlGaAs heterostructures can produce a high-fidelity root-of-SWAP operation. Our results provide a methodology for a crucial component of dynamic-qubit quantum computing.
Entanglement swapping is gaining widespread attention due to its application in entanglement distribution among different parts of quantum appliances. We investigate the entanglement swapping for pure and noisy systems, and argue different entanglement quantifiers for quantum states. We explore the relationship between the entanglement of initial states and the average entanglement of final states in terms of concurrence and negativity. We find that if initial quantum states are maximally entangled and we make measurements in the Bell basis, then average concurrence and average negativity of f…
We consider entanglement swapping, a key component of quantum network operations and entanglement distribution. Pure entangled states, which are the desired input to the swapping protocol, are typically mixed by environmental interactions causing a reduction in their degree of entanglement. Thus an understanding of entanglement swapping with partially mixed states is of importance. Here we present a general analytical solution for entanglement swapping of arbitrary two-qubit states. Our result provides a comprehensive method for analyzing entanglement swapping in quantum networks. First, we sh…
We present a multiparty simultaneous quantum identity authentication protocol based on entanglement swapping. In our protocol, the multi-user can be authenticated by a trusted third party simultaneously.
In this paper we study the swap operation in a two-qubit anisotropic XXZ model in the presence of an inhomogeneous magnetic field. We establish the range of anisotropic parameter within which the swap operation is feasible. The swap errors caused by the inhomogeneous field are evaluated.
Two qubits in pure entangled states going through separate paths and interacting with their own individual environments will gradually lose their entanglement. Here we show that the entanglement change of a two-qubit state due to amplitude damping noises can be recovered by entanglement swapping. Some initial states can be asymptotically purified into maximally entangled states by iteratively using our protocol.
We proposed a scheme on secret sharing of quantum information based on entanglement swapping in cavity QED. In our scheme, the effects of cavity decay and thermal field are all eliminated.
We introduce a class of two-level multi-particle Greenberger-Horne-Zeilinger (GHZ) states, and study entanglement swapping between two systems for Bell states and the class of GHZ states in qubit systems, respectively. We give the formulas for the entanglement swapping of Bell states and GHZ states in any number of qubit systems. We further consider entanglement swapping between any number of Bell states and between any number of the introduced GHZ states, and propose a series of entanglement swapping schemes in a detailed way. We illustrate the applications of such schemes in quantum informat…
An unconditionally secure quantum cion tossing protocol for two remote participants via entangled swapping is presented. The security of this protocol is guaranteed by the nonlocal property of quantum entanglement and the classical complexity.
The usual entanglement swapping protocol can entangle two particles that never interact. Here we demonstrate an all-versus-nothing violation of local realism for a partial entanglement swapping process. A Clauser-Horne-Shimony-Holt-type inequality for two particles entangled by entanglement swapping is proposed for a practical experiment and can be violated quantum mechanically up to 4 beyond Cirel'son's bound 2sqr(2). Our result uncovers the intriguing nonlocal character of entanglement swapping and may lead to a conclusive (loophole-free) test of local realism versus quantum mechanics. The e…
We develop a theory and accompanying mathematical model for quantum communication via any number of intermediate entanglement swapping operations and solve numerically for up to three intermediate entanglement swapping operations. Our model yields two-photon interference visibilities post-selected on photon counts at the intermediate entanglement-swapping stations. Realistic experimental conditions are accommodated through parametric down-conversion rate, photon-counter efficiencies and dark-count rates, and instrument and transmission losses. We calculate achievable quantum communication dist…
A SWAP operation between different types of qubits of single photons is essential for manipulating hyperentangled photons for a variety of applications. We have implemented an efficient SWAP gate for the momentum and polarization degrees of freedom of single photons. The SWAP gate was utilized in a single-photon two-qubit quantum logic circuit to deterministically transfer momentum entanglement between a pair of down-converted photons to polarization entanglement. The polarization entanglement thus obtained violates Bell's inequality by more than 150 standard deviations.
In this paper, we investigate the possibility of entanglement swapping between two distinct qubits coupled to their own (in general) non-Markovian environments. This is done via Bell state measurement performing on the photons leaving the dissipative cavities. In the continuation, we introduce the concept of entangling power to measure the average of swapped entanglement over all possible pure initial states. Then, we present our results in two strong and weak coupling regimes and discuss the role of detuning parameter in each regime on the amount of swapped entanglement. We also determine the…
In a recent interesting article Chris Nagele, Ebubechukwu O. IloOkeke, Peter P. Rohde, Jonathan P. Dowling, and Tim Byrnes discuss an entanglement swapping experiment using a setup where it is possible to switch the time ordering of measurements. I would like to draw your attention to the fact that the very same idea was introduced in two previous papers, and briefly address some important points related to the subject.
Quantum entanglement swapping is one of the most promising ways to realize the quantum connection among local quantum nodes. In this Letter, we present an experimental demonstration of the entanglement swapping between two independent multipartite entangled states, each of which involves a tripartite Greenberger-Horne-Zeilinger (GHZ) entangled state of an optical field. The entanglement swapping is implemented deterministically by means of a joint measurement on two optical modes coming from the two multipartite entangled states respectively and the classical feedforward of the measurement res…
We show that braiding transformation is a natural approach to describe quantum entanglement, by using the unitary braiding operators to realize entanglement swapping and generate the GHZ states as well as the linear cluster states. A Hamiltonian is constructed from the unitary $\check{R}_{i,i+1}(θ,ϕ)$-matrix, where $ϕ=ωt$ is time-dependent while $θ$ is time-independent. This in turn allows us to investigate the Berry phase in the entanglement space.
We report two key distribution schemes achieved by swapping quantum entanglement. Using two Bell states, two bits of secret key can be shared between two distant parties that play symmetric and equal roles. We also address eavesdropping attacks against the schemes.
We analyze theoretically a scheme that produces spin squeezing via the continuous swapping of atom-photon entanglement into atom-atom entanglement, and propose an explicit experimental system where the necessary atom-field coupling can be realized. This scheme is found to be robust against perturbations due to other atom-field coupling channels.
Entanglement is a unique property of quantum systems and an essential resource for many quantum technologies. The ability to transfer or swap entanglement between systems is an important protocol in quantum information science. Entanglement between photons forms the basis of distributed quantum networks and the demonstration of photonic entanglement swapping is essential for their realization. Here an experiment demonstrating entanglement swapping from two independent multimode time-frequency entangled sources is presented, resulting in multiple heralded temporal-mode Bell states. Entanglement…
We recall several cryptographic protocols based on entanglement alone and also on entanglement swapping. We make an exposition in terms of the geometrical aspects of the involved Hilbert spaces, and we concentrate on the formal nature of the used transformations.
A general proof of the security against eavesdropping of a previously introduced protocol for two-party quantum key distribution based on entanglement swapping [Phys. Rev. A {\bf 61}, 052312 (2000)] is provided. In addition, the protocol is extended to permit multiparty quantum key distribution and secret sharing of classical information.
Entanglement swapping generates remote quantum correlations between particles that have not interacted and is the cornerstone of long-distance quantum communication, quantum networks, and fundamental tests of quantum science. In the context of spatial modes of light, high-dimensional entanglement provides an avenue to increase the bandwidth of quantum communications and provides more stringent limits for tests of quantum foundations. Here we simultaneously swap the entanglement of multiple orbital angular momentum states of light. The system is based on a degenerate filter that cannot distingu…
We propose a curious protocol for swapping the intra-photon entanglement between path and polarization degrees of freedom of a single photon to inter-photon entanglement between two spatially separated photons which have never interacted. This is accomplished by using an experimental setup consisting of three suitable Mach-Zehnder interferometers along with number of beam splitters, polarization rotators and detectors. Using the same setup, we have also demonstrated an interesting quantum state transfer protocol, symmetric between Alice and Bob. Importantly, the Bell-basis discrimination is no…
The entanglement swapping protocol is analyzed in a relativistic setting, where shortly after the entanglement swapping is performed, a Bell violation measurement is performed. From an observer in the laboratory frame, a Bell violation is observed due to entanglement swapping taking place, but in a moving frame the order of the measurements is reversed, and a Bell violation is observed even though no entanglement is present. Although the measurement results are identical, the wavefunctions for the two frames are different--- one is entangled and the other is not. Furthermore, for boosts in a p…
In this paper, we study the effect of classical driving field on the spontaneous emission spectrum of a qubit embedded in a dissipative cavity. Furthermore, we monitor the entanglement dynamics of the driven qubit with its radiative decay under the action of the classical field. Afterwards, we carry out an investigation on the possibility of entanglement swapping between two such distinct driven qubits. The swapping will be feasible with the aid of a Bell state measurement performing on the photons leaving the cavities. It is demonstrated that the classical driving field has a beneficial effec…
We report an experimental demonstration of entanglement swapping over two quantum stages. By successful realizations of two cascaded photonic entanglement swapping processes, entanglement is generated and distributed between two photons, that originate from independent sources and do not share any common past. In the experiment we use three pairs of polarization entangled photons and conduct two Bell-state measurements (BSMs) one between the first and second pair, and one between the second and third pair. This results in projecting the remaining two outgoing photons from pair 1 and 3 into an …
Entanglement swapping between photon pairs is a fundamental building block in schemes using quantum relays or quantum repeaters to overcome the range limits of long-distance quantum key distribution. We develop a closed-form solution for the actual quantum states prepared by realistic entanglement swapping, which takes into account experimental deficiencies due to inefficient detectors, detector dark counts, and multiphoton-pair contributions of parametric down-conversion sources. We investigate how the entanglement present in the final state of the remaining modes is affected by the real-worl…
We show that the possibility of distinguishing between single and two photon detection events is not a necessary requirement for the proof that recent operational realization of entanglement swapping cannot find a local realistic description. We propose a simple modification of the experiment, which gives a richer set of interesting phenomena.
In this paper, an optimal scheme of four-level quantum teleportation and swapping of quantum entanglement is given. We construct a complete orthogonal basis of the bipartite ququadrit systems. Using this basis, the four-level quantum teleportation and swapping can be achieved according to the standard steps. In addition, associate the above bases with the unextendible product bases and the exact entanglement bases, we prove that in the $2\times 2\times 2$ systems or $3\times 3$ systems the collective translations of multipartite quantum entanglement can be realized. PACC numbers: 03.67.Mn, 03.…
Entanglement swapping, the process to entangle two particles without coupling them in any way, is one of the most striking manifestations of the quantum-mechanical nonlocal characteristic. Besides fundamental interest, this process has applications in complex entanglement manipulation and quantum communication. Here we report a high-fidelity, unconditional entanglement swapping experiment in a superconducting circuit. The measured concurrence characterizing the qubit-qubit entanglement produced by swapping is above 0.75, confirming most of the entanglement of one qubit with its partner is dete…
In quant-ph/0201134 Jennewein et al. report experiments demonstrating entanglement swapping under various conditions. In one instance, they claim to have exhibited Bell inequality violations by a pair of photons prior to performing any entangling operations on the pair. However, the Bell inequality violation results in this case from post-selection of the data, not from quantum non-locality.
A theoretical scheme for bidirectional swapping quantum controlled teleportation is presented using the entanglement property of maximally entangled five-qubit state, i.e., Alice wants to transmit a entangled state of particle a to Bob and Bob wants to transmit a entangled state of particle b to Alice via the control of the supervisor Charlie.
Complementarity and entanglement are fundamental features of Quantum Mechanics that were recently related in triality equalities that involve quantum coherence, the wave aspect of a qubit, and quantum predictability and quantum entanglement, the particle aspect of a qubit. In this article, we give an operational connection between redictability and entanglement in entanglement swapping from initially partially entangled states. For this, we show that the predictability of the pre-measurement one-qubit density matrix is directly related to the probability of the partially entangled component of…
Based on a general unitary operation of two-qubit system, we investigate the dynamics of entanglement, entropy and purity. Distinctive features in the different initial states settings of an interacting bipartite system are explored. The striking effects of initial product states on entanglement shows that zeros entanglement can be obtained during the development of the interaction.
In this work we study the production and swapping of non-gaussian multipartite entanglement in a setup containing a parametric amplifier which generates three photons in different modes coupled to three qubits. We prove that the entanglement generated in this setup is of nongaussian nature. We introduce witnesses of genuine tripartite nongaussian entanglement, valid both for mode and qubit entanglement. Moreover, those witnesses show that the entanglement generated among the photons can be swapped to the qubits, and indeed the qubits display nongaussian genuine tripartite entanglement over a w…
In this paper, we propose a scheme to generate entanglement between two distant qubits (two-level atom) which are separately trapped in their own (in general) non-Markovian dissipative cavities by utilizing entangling swapping. We consider the case in which the qubits can move along their cavity axes rather than a static state of motion. We first examine the role of movement of the qubit by studying the entropy evolution for each subsystem. We calculate the average entropy over the initial states of the qubit. Then by performing a Bell state measurement on the fields leaving the cavities, we s…
Extending the eavesdropping strategy devised by Zhang, Li and Guo [Phys. Rev. A 63, 036301 (2001)], we show that the multiparty quantum communication protocol based on entanglement swapping, which was proposed by Cabello [quant-ph/0009025], is not secure. We modify the protocol so that entanglement swapping can secure multiparty quantum communication, such as multiparty quantum key distribution and quantum secret sharing of classical information, and show that the modified protocol is secure against the Zhang-Li-Guo's strategy for eavesdropping as well as the basic intercept-resend attack.
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…
A basic problem of quantum communication is to generate entangled states between distant sites. Using entanglement swapping, we are able to generate an entangled state of the desired distance from connecting many short distance entangled states. We investigate the entanglement swapping of the Valence-Bond Solid state with un-identical local filtering operations. It is found that not only a long distance entangled state can be generated from the VBS state, but also there is a trade-off between the probability and the degree of the entanglement in the resultant state. The results are also genera…
Kang et al. [Chin. Phys. B 24 (2015) 090306] proposed a controlled mutual quantum entity authentication protocol. We find that the proposed protocol is not secure, that is, Charlie can eavesdrop the shared keys between Alice and Bob without being detected.
We consider an analogue of entanglement-swapping for a set of black boxes with the most general non-local correlations consistent with relativity (including correlations which are stronger than any attainable in quantum theory). In an attempt to incorporate this phenomenon, we consider expanding the space of objects to include not only correlated boxes, but `couplers', which are an analogue for boxes of measurements with entangled eigenstates in quantum theory. Surprisingly, we find that no couplers exist for two binary-input/binary-output boxes, and hence that there is no analogue of entangle…
Based on a scheme that produces an entanglement between the spin and the path variables of a single spin-1/2 particle (qubit) using a beam-splitter and a spin-flipper, we formulate a procedure for transferring this intraparticle hybrid entanglement to an interparticle entanglement between the spin variables of two other spatially separated spin-1/2 particles which never interact with each other during the entire process. This procedure of entanglement swapping is accomplished by a Mach-Zehnder setup in conjunction with the Stern-Gerlach measuring device, using suitable unitary operations. The …
In this paper we consider the generation of a three-qubit GHZ-like thermal state by applying the entanglement swapping scheme of Zukowski {\it et al.} [Ann. N. Y. Acad. Sci. {\bf 755}, 91 (1995)] to three pairs of two-qubit Heisenberg XY chains. The quality of the resulting three-qubit entanglement is studied by analyzing the teleportation fidelity, when it is used as a resource in the teleportation protocol of Karlsson {\it et al.}[Phys. Rev. A {\bf 58}, 4394 (1998)]. We show that even though thermal noise in the original two-qubit states is amplified by the entanglement swapping process, we …
We experimentally realize "hybrid" entanglement swapping between discrete-variable (DV) and continuous-variable (CV) optical systems. DV two-mode entanglement as obtainable from a single photon split at a beam splitter is robustly transferred by means of efficient CV entanglement and operations, using sources of squeezed light and homodyne detections. The DV entanglement after the swapping is verified without post-selection by the logarithmic negativity of up to 0.28$\pm$0.01. Furthermore, our analysis shows that the optimally transferred state can be post-selected into a highly entangled stat…
We propose a very simple scheme to test the quantum enatanglement swapping in a priori. In the scheme, we only assume the photon detector can distinguish the vacuum and non-vacuum Fock state rather than the exact Fock number states.
It is shown that, concerning the experiment described by the authors, their extension to the situation in which Alice's measurement occurs after Bob's is unnecessary and their interpretation misleading.
We propose a scheme to realize entanglement swapping via superradiance, entangling two distant cavities without a direct interaction. The successful Bell-state-measurement outcomes are performed naturally by the electromagnetic reservoir, and we show how, using a quantum trajectory method, the non-local properties of the state obtained after the swapping procedure can be verified by the steering inequality. Furthermore, we discuss how the unsuccessful measurement outcomes can be used in an experiment of delayed-choice entanglement swapping. An extension of testing the quantum steering inequali…
We generalize the procedure of entanglement swapping to obtain a scheme for manipulating entanglement in multiparticle systems. We describe how this scheme allows to establish multiparticle entanglement between particles belonging to distant users in a communication network through a prior distribution of singlets followed by only local measurements. We show that this scheme can be regarded as a method of generating entangled states of many particles and compare it with existing schemes using simple quantum computational networks. We highlight the practical advantages of using a series of enta…
Entanglement swapping allows to establish entanglement between independent particles that never interacted nor share any common past. This feature makes it an integral constituent of quantum repeaters. Here, we demonstrate entanglement swapping with time-synchronized independent sources with a fidelity high enough to violate a Clauser-Horne-Shimony-Holt inequality by more than four standard deviations. The fact that both entangled pairs are created by fully independent, only electronically connected sources ensures that this technique is suitable for future long-distance quantum communication …
The transactional interpretation of quantum mechanics, which uses retarded and advanced solutions of the Schrodinger equation and its complex conjugate, offers an original way to visualize and understand quantum processes. After a brief review, we show how it can be applied to different quantum situations, emphasizing the importance of specifying a complete configuration of absorbers. We consider in more detail the phenomenon of entanglement swapping, and see how the apparent retroactive enforcement of entanglement can be understood in the transactional interpretation.
We experimentally demonstrate continuous-variable quantum teleportation beyond the no-cloning limit. We teleport a coherent state and achieve the fidelity of 0.70$\pm$0.02 that surpasses the no-cloning limit of 2/3. Surpassing the limit is necessary to transfer the nonclassicality of an input quantum state. By using our high-fidelity teleporter, we demonstrate entanglement swapping, namely teleportation of quantum entanglement, as an example of transfer of nonclassicality.
Using the information content of correlations between multipartite systems, together with the notion of partitioning, we show that some general results about the evolution of correlations in quantum systems can be derived with only elementary methods. In particular, we show that for 2 quantum systems A and B, each comprised of a number of sub-systems, in which a partition of A interacts unitarily with a partition of B, then the total correlation can only increase (or remain unchanged) and is given simply by the sum of the initial correlation and the correlation that develops as a result of the…
Entanglement swapping at telecom wavelengths is at the heart of quantum networking in optical fiber infrastructures. Although entanglement swapping has been demonstrated experimentally so far using various types of entangled photon sources both in near-infrared and telecom wavelength regions, the rate of swapping operation has been too low to be applied to practical quantum protocols, due to limited efficiency of entangled photon sources and photon detectors. Here we demonstrate drastic improvement of the efficiency at telecom wavelength by using two ultra-bright entangled photon sources and f…
Swapped Entanglement in High-Dimensional Quantum Systems
University of Sargodha（萨格达大学）；Institute for Research in Fundamental Sciences (IPM)（伊朗基础科学研究院）；Interdisciplinary Centre for Security, Reliability and Trust (SnT), University of Luxembourg（卢森堡大学交叉安全、可靠性与信任中心（SnT））；QSpace SecureTech S.à r.l.-S
We present our approach for sharing photons and assessing resultant four-photon visibility between two distant parties using concatenated entanglement swapping. In addition we determine the corresponding key generation rate and the quantum bit-error rate. Our model is based on practical limitations of resources, including multipair parametric down-conversion sources, inefficient detectors with dark counts and lossy channels. Through this approach, we have found that a trade-off is needed between experimental run-time, pair-production rate and detector efficiency. Concatenated entanglement swap…
We analyze entanglement swapping (ES) of partially entangled pure states with arbitrary Schmidt rank from the perspective of quantum state discrimination. It is shown that the standard deterministic ES protocol is related with an optimal minimum-error strategy. In this case the amount of entanglement of the states resulting from swapping is, in general, lower than the maximum achievable for the quantum channels involved. In this regard, we show that the ES protocol can be probabilistically improved resorting to optimal maximum-confidence (MC) discrimination strategy. Additionally, we show that…
In a recent paper [Z. J. Zhang and Z. X. Man, Phys. Rev. A 72, 022303(2005)], a multiparty quantum secret sharing protocol based on entanglement swapping was presented. However, as we show, this protocol is insecure in the sense that an unauthorized agent group can recover the secret from the dealer. Hence, we propose an improved version of this protocol which can stand against this kind of attack.
