Communication via an entangled coherent quantum network

This study investigates controlled bidirectional transmission of two low-dimensional unknown single-particle quantum states through high-dimensional entangled channels. Initially, complete orthogonal non-symmetric bases in -dimensional Hilbert space and five-particle maximally entangled states in d-dimensional Hilbert space are constructed, with -dimensional non-symmetric bases and 3-dimensional 5-qutrit entangled states serving as specific instances. We then propose a controlled bidirectional teleportation (CBT) protocol wherein a 3-dimensional 5-qutrit maximally entangled channel enables simultaneous exchange of two 2-dimensional single-qubit states under supervisor authorization, implemented via non-symmetric basis measurements. Subsequent replacement of the maximally entangled channel with a 3-dimensional 5-qutrit non-maximally entangled state facilitates probabilistic reconstruction of the original states through auxiliary particle introduction and appropriate unitary operations, still under supervisory control. The success probabilities are analytically derived, demonstrating that the non-maximally entangled protocol generalizes the former scheme. Furthermore, these protocols admit dual extensions: (i) quantum channel dimensionality scalable from 3-dimensional to arbitrary d dimensions; (ii) transmitted state dimensionality extendable from 2-dimensional to arbitrary f-dimensional Hilbert space (f < d).

A scheme for probabilistic teleportation of an unknown three-atom entangled state via a five-atom non-maximally entangled cluster state as quantum channel is proposed. In this scheme, the sender performs two Bell state and a single-atom measurements on the atoms, the receiver can reconstruct the original state with a certain probability by introducing an auxiliary atom and operating appropriate unitary transformations and controlled-not (C-not) operations according to the sender Alice's measurement results. As a result, the probability of successful teleportation is determined by the smallest two of the coefficients' absolute values of the cluster state. The considerable advantage of our scheme is that we employ a non-maximally entangled cluster state as quantum channel in the scheme, which can greatly reduce the amount of entanglement resources and need less classical bits. If we employ a maximally entangled cluster state as quantum channel, the probabilistic teleportation scheme becomes usual teleportation, the successful probability being 100%.

An experimentally feasible scheme for teleportation of an unknown two-atom entangled state is proposed. Our scheme uses a cluster state as the quantum channel, where we do not need any joint Bell-state measurement. Moreover the successful probability and fidelity of teleportation can both reach 1.0. The current scheme can be realized within the current experimental technology.

The purpose of this paper is to explore how to teleport a low-dimensional (two-dimensional) arbitrary unknown two-qubit cat-like state through a high-dimensional entangled state constituting the quantum channel. We first present a scheme employing a maximally entangled three-qutrit state as the channel. Within this scheme, the sender performs a single-qubit projective measurement and a non-symmetric basis measurement on their particles. Based on these measurement outcomes, the receiver applies specific unitary operations to reconstruct the original cat-like state. Subsequently, the maximally entangled channel is replaced with a non-maximally entangled three-qutrit state. For this probabilistic teleportation scheme, the target state is reconstructed by introducing an auxiliary qubit and performing appropriate operations; the corresponding success probability is derived. Analysis indicates that the non-maximally entangled scheme generalizes the previous maximally entangled approach. Furthermore, both schemes are shown to be directly extendable to quantum channels formed by arbitrary high-dimensional entangled states.

Quantum networks are composed of quantum nodes which coherently interact by way of quantum channels. They offer powerful capabilities for quantum computation, communication, and metrology. A generic requirement for these realizations is the capability to generate and store quantum states among multiple quantum nodes, and to disseminate these resources throughout the network via the quantum channels. In this thesis, I describe a series of experiments whereby single excitations in atomic ensembles are strongly coupled to optical modes and provide efficient means for the coherent control of entangled states between matter and light. By following the seminal proposal by Duan et al., we have generated measurement-induced entanglement of an excitation between two cold atomic ensembles. Using this system, we investigated the relationship for the global bipartite entanglement and local correlations in its subsystems. In addition, we achieved functional quantum nodes for entanglement distribution. Two pairs of remote ensembles at two quantum nodes were prepared into entangled states in a heralded and asynchronous fashion by the conditional controls of the entanglement. The quantum states of the ensembles were then distributed into polarization entangled states of photons. We also prepared an analogous quantum state and transferred the nonlocal coherence between two pairs of heralded entangled atomic ensembles, providing a step towards entanglement connection. Beyond such probabilistic approaches, we demonstrated an experiment where entanglement between two quantum memories is created by the reversible and deterministic mapping of an entangled state of light via dynamic electromagnetically induced transparency. This experiment opens novel prospects of integrating hybrid quantum systems by way of reversible quantum interfaces between light and matter. Then, we extended our work to multipartite quantum systems. We theoretically investigated the characterization of multipartite mode-entangled states by way of quantum uncertainty relations, and introduced theoretical tools to verify the entanglement orders in multipartite systems. In particular, we achieved entanglement for one delocalized photon among multiple optical modes (N > 2). Finally, we have achieved measurement-induced entanglement of spin waves among four quantum memories. The individual atomic components for the entangled W state of the four ensembles were then coherently converted into four propagating entangled beams of light via superradiant emissions. We observed the statistical and dynamic transitions for the multipartite entangled spin waves. Experiments described in this thesis thereby represent significant advances of experimental and theoretical capabilities to generate, store, transfer, and characterize entanglement of matter and light over quantum networks.

We investigate the universal programmable unambiguous discrimination of two unknown quantum states with two copies. We first present the optimal positive-operator valued measure (POVM) elements that determine the individual success probabilities. In terms of the positivity of an inconclusive operator, we derive the average success probability, which is higher than the average success probability of discriminating two unknown states with one copy given in the reference [Bergou and Hillery, Phys. Rev. Lett. 94, 160501 (2005)].

Dynamics of coded information over Bloch channels is investigated. We show that the coded information is sent with high accuracy over the Bloch channel by increasing the absolute equilibrium value of the information carrier or decreasing the ratio of relaxation time. The robustness of coded information in maximum and partial entangled states is discussed. It is shown that, the maximum entangled states are more robust than the partial entangled state over these types of channels. The dynamics of the local and the non-local information is investigated for different values of the channel's parameters and the initial state setting. It is found that by increasing the absolute equilibrium values for both qubits, the local information of both qubits decreases faster and consequently the information gained by the eavesdropper increases.

The magnetofluid dynamic stability of two streaming fluids cylindrical interface has been developed based on the linear perturbation technique. Each of the two fluids is perfectly conducting, non-viscous and incompressible. The model is acting upon the capillary, inertia, pressure gradient and electromagnetic forces. The outer fluid is bounded by a solid cylindrical interface. A general dispersion relation is derived and studied analytically and the results are confirmed numerically. The capillary force is, acting along the fluids interface, destabilizing only for long symmetric wavelengths while it is stabilizing for all others. The electromagnetic forces are strongly stabilizing in each fluid. Above a certain value of the applicable magnetic field strength, the stabilizing influence of a magnetic field suppresses completely the capillary instability. The thicker the outer fluid cylinder the greater is the destabilizing influence of surface tension for the same values of the magnetic field intensity and the densities ratio of (outer-interior) fluids. The latter is strongly stabilizing for the same values of the magnetic field intensity and the outer fluid thickness.

The noise and complexity inherent to quantum communication networks leads to technical challenges in designing quantum network protocols using classical methods. We address this issue with a hybrid variational quantum optimization framework (VQO) that simulates quantum networks on quantum hardware and optimizes the simulation using differential programming. We maximize nonlocality in noisy quantum networks to showcase our VQO framework. Using a classical simulator we investigate the noise robustness of quantum nonlocality. Our VQO methods reproduce known results and uncover novel phenomena. We find that maximally entangled states maximize nonlocality in the presence of unital qubit channels, while nonmaximally entangled states can maximize nonlocality in the presence of nonunital qubit channels. Thus, we show VQO to be a practical design tool for quantum networks even when run on a classical simulator. Finally, using IBM quantum computers we demonstrate that our VQO framework can maximize nonlocality on noisy quantum hardware. In the long-term, our VQO techniques show promise of scaling beyond classical approaches and can be deployed on quantum network hardware to optimize network protocols against their inherent noise.

Quantum networks provide a prominent platform for realizing quantum information processing and quantum communication, with entanglement being a key resource in such applications. Here, we describe the dissipative transport protocol for entangled states, where entanglement stored in the first node of quantum network can be transported with high fidelity to the second node via a 1D chiral waveguide. In particular, we exploit the directional asymmetry in chirally-coupled single-mode ring resonators to transport entangled states. For the fully chiral waveguide, Bell states, multipartite $W$-states and and Dicke states can be transported with fidelity as high as $0.954$, despite the fact that the communication channel is noisy. Our proposal can be utilized for long-distance distribution of multipartite entangled states between the quantum nodes of the open quantum network.

We propose a quantum state protection scheme via quantum feedforward control combined with environment-assisted measurement to protect arbitrary unknown initial states from the finite-temperature thermal noise (FTTN). The main strategy is to transfer the quantum system to a noise-robust state by weak measurement and feedforward control before the noise channel. Then we apply the environment-assisted measurement on the noise channel to select our desired damped states that are invertible to the initial state. After the noise channel, the reversal operations are applied to restore the initial state. We consider the protection of a single-qubit system, derive the analytical expressions of the success probability and the fidelity, and analyze the influence of key parameters on the performance of the proposed scheme. Unlike previous studies, there is no trade-off between the fidelity and the success probability in the proposed scheme; hence one could maximize them separately. Simulation results show that the proposed scheme can greatly improve the fidelity of the quantum state with a certain success probability. Moreover, the proposed scheme is successfully applied to improving the fidelity of controlled quantum teleportation through two independent FTTN channels from the perspective of protecting the shared entanglement.

The multipartite correlations derived from local measurements on some composite quantum systems are inconsistent with those reproduced classically. This inconsistency is known as quantum nonlocality and shows a milestone in the foundations of quantum theory. Still, it is NP hard to decide a nonlocal quantum state. We investigate an extended question: how to characterize the nonlocal properties of quantum states that are distributed and measured in networks. We first prove the generic tripartite nonlocality of chain-shaped quantum networks using semiquantum nonlocal games. We then introduce a new approach to prove the generic activated nonlocality as a result of entanglement swapping for all bipartite entangled states. The result is further applied to show the multipartite nonlocality and activated nonlocality for all nontrivial quantum networks consisting of any entangled states. Our results provide the nonlocality witnesses and quantum superiorities of all connected quantum networks or nontrivial hybrid networks in contrast to classical networks.

A model of two 2-level atoms interacts with a single quantized electromagnetic field is considered. We study the effect of the mean photon number and the structure of the initial states of the two atoms on the dynamics of the atomic system from the separability point of view. It is found that, if we start from a product mixed atomic state, the probability of generating long living entangled states is increased as the mean photon number increases. Starting from excited atomic system in product state, one generates a more stable entangled states with high degree of entanglement. Also, the effect of the mean photon number on atomic system prepared initially in entangled states is investigated. It is found that the entangled state generated from the initially partial entangled states are more robust than those obtained from a maximum entangled state. The Pancharatnam phase for the separable and entangled states is studied under the effect of the mean photon number and the structure of the initial state. We find that for the separable states, the collapses decrease and the amplitude of the revivals is smaller than that for the entangled state, so there are long-living entangled phases. This property give us a great chances to store safely information in entangled state.

Quantum communication in the presence of noise local environments

It is pointed out that the possibility of teleporting an arbitrary unknown one-particle spin state is crucially connected with the maximal entanglement of the Einstein-Podolsky-Rosen pair, whose one-particle reduced density matrix is $\ensuremath{\rho}(i)=\frac{1}{2}{\mathbf{I}}_{2}$ $(i=1,2).$ It is shown that, to teleport an arbitrary k-particle spin state, one must prepare an ancillary N-particle $(N&gt;~2k)$ entangled state, whose k-particle reduced density matrix has the form ${(1/2}^{k}){\mathbf{I}}_{{2}^{k}}$ $({\mathbf{I}}_{{2}^{k}}$ is the ${2}^{k}\ifmmode\times\else\texttimes\fi{}{2}^{k}$ identity matrix). An alternative approach to constructing many-particle entangled states is developed by using ${R}_{x}(\ensuremath{\pi}),$ the collective rotation of $\ensuremath{\pi}$ around a given axis (say, x axis). The entangled states constructed by using ${R}_{x}(\ensuremath{\pi})$ operating on the basis of angular momentum uncoupling representation are just the GHZ states, which cannot be used for the teleportation of an arbitrary k $(&gt;~2)$ particle spin state. The entangled states constructed by using ${R}_{x}(\ensuremath{\pi})$ operating on the basis of angular momentum coupling representation turn out to be effective for the teleportation of an arbitrary multiparticle state. A formal extension of the scheme of Bennett et al. to deal with the teleportation of an arbitrary two (or more) particle spin state is discussed.