Entanglement Transmission Research Articles

Multi-party quantum key distribution protocol in quantum network

This study proposes a measurement property of graph states and applies it to design a mediated multiparty quantum key distribution (M-MQKD) protocol for a repeater-based quantum network in a restricted quantum environment. The protocol enables remote classical users, who cannot directly transmit qubits, to securely distribute a secret key with the assistance of potentially dishonest quantum repeaters. Classical users only require two quantum capabilities, while quantum repeaters handle entanglement transmission through single-photon measurements. The one-way transmission approach eliminates the need for additional defenses against quantum Trojan horse attacks, reducing maintenance costs compared to round-trip or circular transmission methods. As a result, the M-MQKD protocol is lightweight and easy to implement. The study also evaluates the security of the protocol and demonstrates its practicality through quantum network simulations.

Enhancement of Nonreciprocal Entanglement and Transmission via Phase‐Dependent Unidirectional Coupling

AbstractThe nonreciprocal property of quantum systems is crucial for chiral quantum networks. In this study, a phase‐controlled scheme is proposed to enhance the nonreciprocal quantum entanglement and optical transmission in a cavity optomechanical system by introducing a phase‐dependent unidirectional coupling between two whispering‐gallery‐mode (WGM) resonators. The Sagnac effect induced by the spinning resonator generates nonreciprocity, while the interference effect between direct evanescent coupling and indirect phase‐dependent unidirectional coupling significantly enhances entanglement under the anti‐Stokes sideband. For specific coupling phases, ideal nonreciprocity can be achieved in both entanglement and transmission. The proposed phase‐controlled nonreciprocity presented offers an effective strategy for constructing a unidirectional quantum channel and implementing an optical diode in chiral quantum networks, thereby opening up new possibilities for applications in quantum technologies.

Port-based entanglement teleportation via noisy resource states

Port-based teleportation (PBT) represents a variation of the standard quantum teleportation and is currently being employed and explored within the field of quantum information processing owing to its various applications. In this study, we focus on PBT protocol when the resource state is disrupted by local Pauli noises. Here, we fully characterise the channel of the noisy PBT protocol using Krauss representation. Especially, by exploiting the application of PBT for entanglement distribution necessary in realizing quantum networks, we investigate entanglement transmission through this protocol for each qubit considering noisy resource states, denoted as port-based entanglement teleportation (PBET). Finally, we derive upper and lower bounds for the teleported entanglement as a function of the initial entanglement and the noises. Our study demonstrates that quantum entanglement can be efficiently distributed by protocols utilizing large-sized resource states in the presence of noise and is expected to serve as a reliable guide for developing optimized PBET protocols. To obtain these results, we address that the order of entanglement of two qubit states is preserved through the local Pauli channel, and identify the boundaries of entanglement loss through this teleportation channel.

Verifiable anonymous quantum communication with authentication based on d-level single-particle states

Anonymous quantum communication (AQC) enables the secure transmission of classical and quantum messages while preserving the anonymity of the sender, receiver, or both. Qudits, quantum states with more advantages than qubits in terms of information transmission rate and eavesdropping detection, offer promising capabilities. In this paper, we propose a verifiable AQC (VAQC) protocol utilizing d-level single-particle states, establishing anonymous entanglement between a public sender and an anonymous receiver. By using quantum teleportation, the public sender can transmit private information to his/her chosen anonymous receiver. The verifiable function of the proposed protocol guarantees the legitimacy of all participants’ identities and verifies the correctness of the anonymous entanglement. Furthermore, we demonstrate that the proposed VAQC protocol satisfies the requirements of correctness, anonymity, and security. The proposed VAQC protocol exhibits extensibility and can be extended to enable private communication between an anonymous sender and an anonymous receiver, as well as anonymous entanglement among multiple participants. This work lays the foundation for practical applications in achieving d-level anonymous entanglement and anonymous transmission of qudits.

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.

Entanglement transmission due to the Dzyaloshinskii–Moriya interaction

We revisited the effectiveness of state and entanglement transmission through a spin-chain-based quantum channel while altering the system parameters and the channel’s initial state. Our research is focused on the spin-1/2 XX chain with Dzyaloshinskii–Moriya (DM) interaction and the aim is to measure entanglement dynamics between different part of the chain. The speed of entanglement propagation is utilized to probe the evolution of the system via three scenarios: (i) pure Heisenberg interaction, (ii) pure DM interaction, and (iii) collaboration of both types of couplings. To accomplish this, we employ the fermionization approach to obtain an exact solution to the problem. Aside from investigating the influence of magnetic interaction type on entanglement transfer, the effect of selecting the initial state has also been studied. As a result, we discovered that the phase factor regulating the system’s initial state induces sharp drops in the propagation speed of entanglement. We also showed how to predict the location of these dramatic drops using the language of wave interference. In addition, the fastest transmission occurs at a special value of the phase factor in which the highest amount of entanglement reaches the system’s different pairs. On the other hand, we observe a continuous and flat range of this factor in which the least amount of entanglement is transmitted and for them we have a sharp drop in the speed profile.

The transfer of entanglement negativity at the onset of interactions

Quantum information, in the form of entanglement with an ancilla, can be transmitted to a third system through interaction. Here, we investigate this process of entanglement transmission perturbatively in time. Using the entanglement monotone negativity, we determine how the proclivity of an interaction to either generate, transfer or lose entanglement depends on the choice of Hamiltonians and initial states. These three proclivities are captured by Hamiltonian- and state-dependent quantities that we call negativity susceptibility, negativity transmissibility and negativity vulnerability respectively. These notions could serve, for example, as cost functions in quantum technologies such as machine-learned quantum error correction.

A Heuristic Remote Entanglement Distribution Algorithm on Memory-Limited Quantum Paths

Remote entanglement distribution plays a crucial role in large-scale quantum networks, and the key enabler for entanglement distribution is quantum routers (or repeaters) that can extend the entanglement transmission distance. However, the performance of quantum routers is far from perfect yet. Amongst the causes, the limited quantum memories in quantum routers largely affect the rate and efficiency of entanglement distribution. To overcome this challenge, this paper presents a new modeling for the maximization of entanglement distribution rate (EDR) on a memory-limited path, which is then transformed into entanglement generation and swapping sub-problems. We propose a greedy algorithm for short-distance entanglement generation so that the quantum memories can be efficiently used. As for the entanglement swapping sub-problem, we model it using an Entanglement Graph (EG), whose solution is yet found to be at least NP-complete. In light of it, we propose a heuristic algorithm by dividing the original EG into several sub-problems, each of which can be solved using dynamic programming (DP) in polynomial time. By conducting simulations, the results show that our proposed scheme can achieve a high EDR, and the developed algorithm has a polynomial-time upper bound and reasonable average runtime complexity.

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.

Enhancing quantum teleportation fidelity under decoherence via weak measurement with flips

Noiseless quantum channels are critical to share a pure maximally entangled state for performing an ideal teleportation protocol. However, in reality the shared entanglement severely degraded due to decoherence. In this paper, we propose a quantum teleportation channel protection scheme to enhance the teleportation fidelity in presence of decoherence. Before the entangled pair enters the decoherence channel, the weak measurement and flip operations are applied to transfer the qubit to a more robust state to the effects of the noise. After the decoherence channel the reversed flip operations and weak measurement reversal are applied to recover the initial state. We illustrate our protected teleportation scheme and compare it with a protocol based on weak measurement reversal. The numerical results show that the average teleportation fidelity of our proposed scheme can be significantly improved. Although the proposed entanglement protection scheme is probabilistic, after a successful entanglement transmission, we use the standard teleportation protocol which has probability one.

Concurrence Percolation in Quantum Networks.

Establishing long-distance quantum entanglement, i.e., entanglement transmission, in quantum networks (QN) is a key and timely challenge for developing efficient quantum communication. Traditional comprehension based on classical percolation assumes a necessary condition for successful entanglement transmission between any two infinitely distant nodes: they must be connected by at least a path of perfectly entangled states (singlets). Here, we relax this condition by explicitly showing that one can focus not on optimally converting singlets but on establishing concurrence-a key measure of bipartite entanglement. We thereby introduce a new statistical theory, concurrence percolation theory (ConPT), remotely analogous to classical percolation but fundamentally different, built by generalizing bond percolation in terms of "sponge-crossing" paths instead of clusters. Inspired by resistance network analysis, we determine the path connectivity by series and parallel rules and approximate higher-order rules via star-mesh transforms. Interestingly, we find that the entanglement transmission threshold predicted by ConPT is lower than the known classical-percolation-based results and is readily achievable on any series-parallel networks such as the Bethe lattice. ConPT promotes our understanding of how well quantum communication can be further systematically improved versus classical statistical predictions under the limitation of QN locality-a "quantum advantage" that is more general and efficient than expected. ConPT also shows a percolationlike universal critical behavior derived by finite-size analysis on the Bethe lattice and regular two-dimensional lattices, offering new perspectives for a theory of criticality in entanglement statistics.

Nonlocal generalized quantum measurements of bipartite spin products without maximal entanglement

Measuring a nonlocal observable on a space-like separated quantum system is a resource-hungry and experimentally challenging task. Several theoretical measurement schemes have already been proposed to increase its feasibility, using a shared maximally-entangled ancilla. We present a new approach to this problem, using the language of generalized quantum measurements, to show that it is actually possible to measure a nonlocal spin product observable without necessarily requiring a maximally-entangled ancilla. This approach opens the door to more economical arbitrary-strength nonlocal measurements, with applications ranging from nonlocal weak values to possible new tests of Bell inequalities. The relation between measurement strength and the amount of ancillary entanglement needed is made explicit, bringing a new perspective on the links that tie quantum nonlocality, entanglement and information transmission together.

Entanglement performance of light through the composite free space channel

Entanglement transmission is utilized widely in quantum communication. In this paper we establish a model, which characterizes the performance of entanglement state passing through the composite free space channel. This free space channel is compounded with atmosphere, sea surface and underwater channel. Based on the model, the entanglement photon pairs transmitted through composite channel are simulated. Simulation results show that the beam wandering, the incident angle of the beam on the sea surface, the concentration of chlorophyll in the seawater and other factors will lead to the degradation of the entanglement and these factors have a nonlinear relationship with transmittance. Moreover, the increase of the chlorophyll concentration is found to be a relatively heavy impact on the entanglement. In addition, expanding the aperture size of the receiving telescope will improve entanglement. The research of this paper has momentous meaning to the transmission of quantum entanglement in free space. What’s more, the results have an extremely vital reference value for quantum communications in diverse natural environments.

Entanglement transmission through dense scattering medium

Scattering effects are ubiquitous in practical wireless optical links. Here a transmission model with complete consideration of scattered light and beam wandering effects for underwater link is developed, with the aim to completely characterize the received quantum state of light through dense scattering medium. Based on this model, we show the influence of scattered photons on the improvement of the entanglement after transmission through turbid water may vary for different copropagation scenarios, i.e., the contribution of scattered light on entanglement transmission may be turned from positive to negative, with increase of the strength of underwater beam wandering. And the attenuation coefficient and aperture size are found to be the dominant factors affecting the entanglement through underwater link. While for the counterpropagation scenario, the scattered photons will severely deteriorate the entanglement transmission especially for the high-loss scattering links. These findings may shed light on quantum entanglement transmission and help to develop its applications through dense scattering medium.

Entanglement transmission through turbulent atmosphere for modes of Gaussian beam

Transmission of entangled state through turbulent atmosphere is studied. The qubits are encoded by modes of the Gaussian beam. The quality of the entanglement transmission is estimated using the distance between the density matrix and the subspace of non-entangled states. It is shown that the values of the distances depend on chosen modes numbers.

Self-error-rejecting quantum state transmission of entangled photons for faithful quantum communication without calibrated reference frames

We propose an alignment-free two-party polarization-entanglement transmission scheme for entangled photons by using only linear-optical elements, requiring neither ancillary photons nor calibrated reference frames. The scheme is robust against both the random channel noise and the instability of reference frames. Furthermore, the success probabilities for entanglement transmission are, in principle, improved to unity when active polarization controllers are used. The distinct characters of a simple structure, being easy to implement, and the high fidelity and efficiency make our protocol very useful for long-distance quantum communications and distributed quantum networks in practical applications. As an example, we give its application in a reference-frame-alignment-free quantum key distribution protocol with entanglement.

A Poisson Model for Entanglement Optimization in the Quantum Internet

We define a nature-inspired model for entanglement optimization in the quantum Internet. The optimization model aims to maximize the entanglement fidelity and relative entropy of entanglement for the entangled connections of the entangled network structure of the quantum Internet. The cost functions are subject of a minimization defined to cover and integrate the physical attributes of entanglement transmission, purification, and storage of entanglement in quantum memories. The method can be implemented with low complexity that allows a straightforward application in the quantum Internet and quantum networking scenarios.

Energy-Constrained Private and Quantum Capacities of Quantum Channels

This paper establishes a general theory of energy-constrained quantum and private capacities of quantum channels. We begin by defining various energy-constrained communication tasks, including quantum communication with a uniform energy constraint, entanglement transmission with an average energy constraint, private communication with a uniform energy constraint, and secret key transmission with an average energy constraint. We develop several code conversions, which allow us to conclude non-trivial relations between the capacities corresponding to the above tasks. We then show how the regularized, energy-constrained coherent information is equal to the capacity for the first two tasks and is an achievable rate for the latter two tasks, whenever the energy observable satisfies the Gibbs condition of having a well defined thermal state for all temperatures and the channel satisfies a finite output-entropy condition. For degradable channels satisfying these conditions, we find that the single-letter energy-constrained coherent information is equal to all of the capacities. We finally apply our results to degradable quantum Gaussian channels and recover several results already established in the literature (in some cases, we prove new results in this domain). Contrary to what may appear from some statements made in the literature recently, proofs of these results do not require the solution of any kind of minimum output entropy conjecture or entropy photon-number inequality.

Entanglement-Gradient Routing for Quantum Networks

We define the entanglement-gradient routing scheme for quantum repeater networks. The routing framework fuses the fundamentals of swarm intelligence and quantum Shannon theory. Swarm intelligence provides nature-inspired solutions for problem solving. Motivated by models of social insect behavior, the routing is performed using parallel threads to determine the shortest path via the entanglement gradient coefficient, which describes the feasibility of the entangled links and paths of the network. The routing metrics are derived from the characteristics of entanglement transmission and relevant measures of entanglement distribution in quantum networks. The method allows a moderate complexity decentralized routing in quantum repeater networks. The results can be applied in experimental quantum networking, future quantum Internet, and long-distance quantum communications.

Amending entanglement-breaking channels via intermediate unitary operations

We report a bulk optics experiment demonstrating the possibility of restoring the entanglement distribution through noisy quantum channels by inserting a suitable unitary operation (filter) in the middle of the transmission process. We focus on two relevant classes of single-qubit channels consisting in repeated applications of rotated phase damping or rotated amplitude damping maps, both modeling the combined Hamiltonian and dissipative dynamics of the polarization state of single photons. Our results show that interposing a unitary filter between two noisy channels can significantly improve entanglement transmission. This proof-of-principle demonstration could be generalized to many other physical scenarios where entanglement-breaking communication lines may be amended by unitary filters.