Entanglement Swapping Protocol Research Articles

Simplified entanglement swapping protocol for the quantum Internet

In this study, a simplified version of the entanglement-swapping protocol, commonly used in the deployment of quantum networks, is presented. Quantum repeaters are essential in extending the range of quantum networks, especially when they are implemented through the laying of optical fiber. The simplified version of the entanglement-swapping protocol does not require the use of unitary transforms to finish characterizing the shared Bell state at both ends to be connected, as happens in the traditional version of the protocol, facilitating and reducing costs in quantum repeater implementations. Both a theoretical demonstration and an experimental one on an optical table, based on two revealing experiments, show the excellent performance of the presented protocol.

Multistage entanglement swapping using superconducting qubits in the absence and presence of dissipative environment without Bell state measurement

In recent decades the entangled state generation is of great importance in the quantum information processing and technologies. In this paper, producing the distributed entangled state of superconducting (SC) qubits is considered using an entanglement swapping protocol in three successive stages. The SC qubit pairs (i,,i+1 with i=1,,3,,5,,7), where each pair of the qubits has been placed on a separate chip, are initially prepared in maximally entangled states. The external magnetic fields on capacitively coupled pairs (2,,3) and (6,,7) are implemented for modulating the frequency of qubits. Then, the SC qubits (1,,4) and (5,,8) are converted into entangled states via operating proper measurements instead of Bell state measurement (which is generally a hard task). Finally, the distributed entangled state of target SC qubits (1,,8) can be obtained by applying external magnetic fields on qubits (4,,5) and via operating suitable measurements. This process is studied in the absence and presence of thermal decoherence effects. The concurrence, as a measure of entanglement between two target qubits, success probability of the distributed entangled states and the corresponding fidelities are evaluated, by which we find that the state of target SC qubits (1,,8) is converted to Bell state with maximum entanglement at some moments of time. Under appropriate conditions the maximum of success probability of the obtained states in each stage approaches 1. However, the maxima of concurrence and success probability gradually decrease due to the thermal noise as time goes on. Moreover, compelling amounts of fidelity, success probability and entanglement can be obtained for the achieved entangled states.

Proposal for Optomagnonic Teleportation and Entanglement Swapping

A protocol for realizing discrete-variable quantum teleportation in an optomagnonic system is provided. Using optical pulses, an arbitrary photonic qubit state encoded in orthogonal polarizations is transferred onto the joint state of a pair of magnonic oscillators in two macroscopic yttrium-iron-garnet (YIG) spheres that are placed in an optical interferometer. We further show that optomagnonic entanglement swapping can be realized in an extended dual-interferometer configuration with a joint Bell-state detection. Consequently, magnon Bell states are prepared. We analyze the effect of the residual thermal occupation of the magnon modes on the fidelity in both the teleportation and entanglement swapping protocols. The work may find applications in the study of macroscopic quantum states, quantum information processing, and hybrid quantum networks based on magnonics.

Constraints on Gaussian Error Channels and Measurements for Quantum Communication.

Joint Gaussian measurements of two quantum systems are important for quantum communication between remote parties and are often used in continuous-variable teleportation or entanglement-swapping protocols. Many of the errors in real-world implementations can be modeled by independent Gaussian error channels acting prior to measurement. In this work we study independent single-mode Gaussian error channels on two modes A and B that take place prior to a joint Gaussian measurement. We determine the set of pairs of such channels that render all Gaussian measurements separable, and therefore unsuitable for entanglement swapping or teleportation of arbitrary input states. For example, if the error channels are loss with parameters followed by added noise with parameters then all Gaussian measurements are separable if and only if .

Deterministic entanglement distribution on series-parallel quantum networks

The performance of distributing entanglement between two distant nodes in a large-scale quantum network (QN) of partially entangled bipartite pure states is generally benchmarked against the classical entanglement percolation (CEP) scheme. Improvements beyond CEP were only achieved by nonscalable strategies for restricted QN topologies. This paper explores and amplifies a new and more effective mapping of a QN, referred to as concurrence percolation theory (ConPT), that suggests using deterministic rather than probabilistic protocols for scalably improving on CEP across arbitrary QN topology. More precisely, we implement ConPT via a deterministic entanglement transmission (DET) scheme that is fully analogous to resistor network analysis, with the corresponding series and parallel rules represented by deterministic entanglement swapping and concentration protocols, respectively. The main contribution of this paper is to establish a powerful mathematical framework, which is applicable to arbitrary $d$-dimensional information carriers (qudits), that provides different natural optimality metrics in terms of generalized $k$-concurrences (a family of fundamental entanglement measures) for different QN topologies. In particular, we conclude that the introduced DET scheme (a) is optimal over the well-known nested repeater protocol for distilling entanglement from partially entangled qubits and (b) leads to higher success probabilities of obtaining a maximally entangled state than using CEP. The implementation of the DET scheme is experimentally feasible as tested on IBM's quantum computation platform.

Threshold effect for probabilistic entanglement swapping

The basic entanglement swapping protocol allows to project two qubits, which have never interacted, onto a maximally entangled state. For deterministic swapping, the key ingredient is the maximal entanglement that was initially contained in two pairs of qubits and the capacity of projecting onto a Bell basis. Thus the basic and deterministic entanglement swapping scheme involves three maximal level of entanglement. In this work we propose probabilistic entanglement swapping processes performed with different amounts of initial entanglement. Besides that we suggest a non Bell measuring-basis, to introduce a third entanglement level in the process. Additionally, we propose the unambiguous state extraction scheme as the local mechanism for probabilistically achieving the EPR projection. The combination of these three elements allows us to design four strategies for performing probabilistic entanglement swapping. Surprisingly, we find a twofold entanglement threshold effect related to the concurrence of the measuring-basis. Specifically, the maximal probability of accomplishing a EPR projection becomes a constant for concurrences higher than or equal to threshold entanglement value. Thus, we show that maximal entanglement in the measuring-basis is not required for attaining the EPR projection.

Local predictability and coherence versus distributed entanglement in entanglement swapping from partially entangled pure states

Complete complementarity relations, as e.g. P(ρA)2+C(ρA)2+E(|Ψ〉AB)2=1, constrain the local predictability and local coherence and the entanglement of bipartite pure states. For pairs of qubits prepared initially in a particular class of partially entangled pure states with null local coherence, these relations were used in Ref. [6] (Basso and Maziero (2022)) to provide an operational connection between local predictability of the pre-measurement states with the probability of the maximally entangled components of the states after the Bell-basis measurement of the entanglement swapping protocol (ESP). In this article, we extend this result for general pure initial states. We obtain a general relation between pre-measurement local predictability and coherence and the distributed entanglement in the ESP. We use IBM's quantum computers to verify experimentally some instances of these general theoretical results.

Open-Air Microwave Entanglement Distribution for Quantum Teleportation

Microwave technology plays a central role in current wireless communications, standing among them mobile communication and local area networks (LANs). The microwave range shows relevant advantages with respect to other frequencies in open-air transmission, such as low absorption losses and low energy consumption, and it is additionally the natural working frequency in superconducting quantum technologies. Entanglement distribution between separate parties is at the core of secure quantum communications. Therefore, understanding its limitations in realistic open-air settings, specially in the rather unexplored microwave regime, is crucial for transforming microwave quantum communications into a mainstream technology. Here, we investigate the feasibility of an open-air entanglement distribution scheme with microwave two-mode squeezed states. First, we study the reach of direct entanglement transmission in open-air, obtaining a maximum distance of approximately 500 meters in a realistic setting with state-of-the-art experimental parameters. Afterwards, we adapt entanglement distillation and entanglement swapping protocols to microwave technology in order to reduce environmental entanglement degradation. While entanglement distillation helps to increase quantum correlations in the short-distance low-squeezing regime by up to $46\%$, entanglement swapping increases the reach by $14\%$. Then, we compute the fidelity of a continuous-variable quantum teleportation protocol using open-air-distributed entanglement as a resource. Finally, we adapt the machinery to explore the limitations of quantum communication between satellites, where the thermal noise impact is substantially reduced and diffraction losses are dominant.

Quantum Zeno repeaters

Quantum repeaters pave the way for long-distance quantum communications and quantum Internet, and the idea of quantum repeaters is based on entanglement swapping which requires the implementation of controlled quantum gates. Frequently measuring a quantum system affects its dynamics which is known as the quantum Zeno effect (QZE). Beyond slowing down its evolution, QZE can be used to control the dynamics of a quantum system by introducing a carefully designed set of operations between measurements. Here, we propose an entanglement swapping protocol based on QZE, which achieves almost unit fidelity. Implementation of our protocol requires only simple frequent threshold measurements and single particle rotations. We extend the proposed entanglement swapping protocol to a series of repeater stations for constructing quantum Zeno repeaters which also achieve almost unit fidelity regardless of the number of repeaters. Requiring no controlled gates, our proposal reduces the quantum circuit complexity of quantum repeaters. Our work has potential to contribute to long distance quantum communications and quantum computing via quantum Zeno effect.

Creating quantum correlations in generalized entanglement swapping

We study how different types of quantum correlations can be established as the consequence of a generalized entanglement swapping protocol where, starting from two Bell pairs (1,2) and (3,4), a general quantum measurement [denoted by a positive operator-valued measure (POVM)] is performed on the pair (2,3), which results in creating quantum correlation in (1,4) shared between two spatially separated observers. Contingent upon using different kinds of POVMs, we show generation or destruction of different quantum correlations in the pairs (1,4), (1,2), and (3,4). This thus reflects nontrivial transfer of quantum correlations from the pairs (1,2) and (3,4) to the pair (1,4). As an offshoot, this paper provides an operational tool to generate different types of single parameter families of quantum correlated states [for example, entangled but not Einstein-Podolsky-Rosen (EPR) steerable, or EPR steerable but not Bell nonlocal, or Bell nonlocal] by choosing different quantum measurements in the basic entanglement swapping setup. We further extend our paper by taking mixed initial states shared by the pairs (1,2) and (3,4). Finally, we study network nonlocality in our scenario. Here, we find the appropriate POVM measurement for which the generated correlation demonstrates or does not demonstrate network nonlocality for the whole range of the measurement parameter.

Rabi Oscillations, Entanglement and Teleportation in the Anti-Jaynes-Cummings Model

This paper provides a scheme for generating maximally entangled qubit states in the anti-Jaynes-Cummings interaction mechanism, so called entangled anti-polariton qubit states. We demonstrate that in an initial vacuum-field, Rabi oscillations in a cavity mode in the anti-Jaynes-Cummings interaction process, occur in the reverse sense relative to the Jaynes-Cummings interaction process and that time evolution of entanglement in the anti-Jaynes-Cummings interaction process takes the same form as in the Jaynes-Cummings interaction process. With the generated anti-polariton qubit state as one of the initial qubits, we present quantum teleportation of an atomic quantum state by applying entanglement swapping protocol achieving an impressive maximal teleportation fidelity~$F_\rho=1$.

Experimental Diagnostics of Entanglement Swapping by a Collective Entanglement Test

The paper reports on experimental diagnostics of entanglement swapping protocol by means of collective entanglement witness. Our approach is suitable to detect disturbances occurring in the preparation of quantum states, quantum communication channel and imperfect Bell-state projection. More specifically we demonstrate that our method can distinguish disturbances such as depolarization, phase-damping, amplitude-damping and imperfect Bell-state measurement by observing four probabilities and estimating collective entanglement witness. Since entanglement swapping is a key procedure for quantum repeaters, quantum relays, device-independent quantum communications or entanglement assisted error correction, this can aid in faster and practical resolution of quality-of-transmission related problems as our approach requires less measurements then other means of diagnostics.

Information-disturbance trade-off in generalized entanglement swapping

We study information-disturbance trade-off in generalized entanglement swapping protocols wherein starting from Bell pairs $\left(1,2\right)$ and $\left(3,4\right)$, one performs an arbitrary joint measurement on $\left(2,3\right)$, so that $\left(1,4\right)$ now becomes correlated. We obtain trade-off inequalities between information gain in correlations of $\left(1,4\right)$ and residual information in correlations of $\left(1,2\right)$ and $\left(3,4\right)$ respectively and argue that information contained in correlations (information) is conserved if each inequality is an equality. We show that information is conserved for a maximally entangled measurement but is not conserved for any other complete orthogonal measurement and Bell measurement mixed with white noise. However, rather surprisingly, we find that information is conserved for rank-two Bell diagonal measurements, although such measurements do not conserve entanglement. We also show that a separable measurement on $\left(2,3\right)$ can conserve information, even if, as in our example, the post-measurement states of all three pairs $\left(1,2\right)$, $\left(3,4\right)$, and $\left(1,4\right)$ become separable. This implies correlations from an entangled pair can be transferred to separable pairs in nontrivial ways so that no $information$ is lost in the process.

Photonic hybrid state entanglement swapping using cat state superpositions.

We propose the use of hybrid entanglement in an entanglement swapping protocol, as means of distributing a Bell state with high fidelity to two parties. The hybrid entanglement used in this work is described as a discrete variable (Fock state) and a continuous variable (cat state super- position) entangled state. We model equal and unequal levels of photonic loss between the two propagating continuous variable modes, before detecting these states via a projective vacuum-one-photon measurement, and the other mode via balanced homodyne detection. We investigate homodyne measurement imperfections, and the associated success probability of the measurement schemes chosen in this protocol. We show that our entanglement swapping scheme is resilient to low levels of photonic losses, as well as low levels of averaged unequal losses between the two propagating modes, and show an improvement in this loss resilience over other hybrid entanglement schemes using coherent state superpositions as the propagating modes. Finally, we conclude that our protocol is suitable for potential quantum networking applications which require two nodes to share entanglement separated over a distance of , when used with a suitable entanglement purification scheme.

Simultaneous certification of entangled states and measurements in bounded dimensional semiquantum games

Certification of quantum systems and operations is a central task in quantum information processing. Most current schemes rely on a tomography with fully characterized devices, while this may not be met in real experiments. Device characterizations can be removed with device-independent tests, but it is technically challenging at the moment. In this paper, we investigate the problem of certifying entangled states and measurements via semiquantum games, a type of nonlocal quantum games with well characterized quantum inputs, balancing practicality and device independence. We first design a specific bounded-dimensional semiquantum game, with which any pure entangled state and Bell state measurement operators can be simultaneously certified. Afterward via a duality treatment of state and measurement, we interpret the dual form of this game as a source-independent bounded-dimensional entanglement swapping protocol and show the whole process, including any entangled projector and Bell states, can be certified with this protocol. In particular, our results do not require a complete Bell state measurement, which is beneficial for experiments and practical use.Received 11 February 2020Accepted 12 August 2020DOI:https://doi.org/10.1103/PhysRevResearch.2.033400Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasEntanglement detectionNonlocalityQuantum correlations in quantum informationQuantum entanglementQuantum Information

Connecting heterogeneous quantum networks by hybrid entanglement swapping.

Recent advances in quantum technologies are rapidly stimulating the building of quantum networks. With the parallel development of multiple physical platforms and different types of encodings, a challenge for present and future networks is to uphold a heterogeneous structure for full functionality and therefore support modular systems that are not necessarily compatible with one another. Central to this endeavor is the capability to distribute and interconnect optical entangled states relying on different discrete and continuous quantum variables. Here, we report an entanglement swapping protocol connecting such entangled states. We generate single-photon entanglement and hybrid entanglement between particle- and wave-like optical qubits and then demonstrate the heralded creation of hybrid entanglement at a distance by using a specific Bell-state measurement. This ability opens up the prospect of connecting heterogeneous nodes of a network, with the promise of increased integration and novel functionalities.

Relativity of quantum states in entanglement swapping

The entanglement swapping protocol is analyzed in a relativistic setting, where shortly after the entanglement swapping is performed, a Bell test is performed. For an observer in the laboratory frame, a Bell violation is observed between the qubits with the swapped entanglement. In a moving frame, the order of the measurements is reversed, and a Bell violation is observed even though the particles are not entangled, directly or indirectly, or at any point in time. Although the measurement results are identical, the wavefunctions for the two frames are starkly different — one is entangled and the other is not. Furthermore, for boosts in a perpendicular direction, in the presence of decoherence, we show that the maximum Bell violation can occur across non-simultaneous points in time. This is a signature of entanglement that is spread across both space and time, showing both non-local and non-simultaneous aspects of entanglement.

Correction to: Demonstration of entanglement purification and swapping protocol to design quantum repeater in IBM quantum computer

The article Demonstration of entanglement purification and swapping protocol to design quantum repeater in IBM quantum computer, written by Bikash K. Behera, Swarnadeep Seth, Antariksha Das, Prasanta K. Panigrahi, was originally published electronically on the publisher’s internet portal (currently SpringerLink) on 1 March 2019 with open access.

Demonstration of entanglement purification and swapping protocol to design quantum repeater in IBM quantum computer

Quantum communication is a secure way to transfer quantum information and to communicate with legitimate parties over distant places in a network. Although communication over a long distance has already been attained, technical problem arises due to unavoidable loss of information through the transmission channel. Quantum repeaters can extend the distance scale using entanglement swapping and purification scheme. Here we demonstrate the working of a quantum repeater by the above two processes. We use IBM’s real quantum processor ‘ibmqx4’ to create two pair of entangled qubits and design an equivalent quantum circuit which consequently swaps the entanglement between the two pairs. We then develop a novel purification protocol which enhances the degree of entanglement in a noisy channel that includes combined errors of bit-flip, phase-flip and phase-change error. We perform quantum state tomography to verify the entanglement swapping between the two pairs of qubits and working of the purification protocol.

Some Numerical Cases of Entanglement Concentration Using Entanglement Swapping

The quantum information network is important in establishing next-generation technology. In particular, maximal and long-distance entangled states are important in realizing a number of quantum information technologies, such as teleportation, key distribution and so forth. Entanglement swapping is a scheme that creates a long-distance network by using multiple short ones. Entanglement swapping protocols applied to non-maximal correlations have been thoroughly investigated by various people. Rather than providing any new analytic results, some examples of a numerical approach will be provided in this paper. In particular, the paper reveals the existence of different classes of coefficients that approximate the optimal outcome (i.e., the weaker average maximal entanglement between the two initial states). The new class of states is non-trivial in the sense that their coefficients are just as widely distributed as the coefficients of states satisfying optimality conditions are. Moreover, we will numerically examine entanglement swapping methods and show the distribution of optimal and general coefficients for three and four 2-level correlations.