Three-dimensional Entangled State Research Articles

Spatial-spectral mapping to prepare frequency entangled qudits.

Entangled qudits, the high-dimensional entangled states, play an important role in the study of quantum information. How to prepare entangled qudits in an efficient and easy-to-operate manner is still a challenge in quantum technology. Here, we demonstrate a method to engineer frequency entangled qudits in a spontaneous parametric downconversion process. The proposal employs an angle-dependent phase-matching condition in a nonlinear crystal, which forms a classical-quantum mapping between the spatial (pump) and spectral (biphotons) degrees of freedom. In particular, the pump profile is separated into several bins in the spatial domain, and thus shapes the down-converted biphotons into discrete frequency modes in the joint spectral space. Our approach provides a feasible and efficient method to prepare a high-dimensional frequency entangled state. As an experimental demonstration, we generate a three-dimensional entangled state by using a homemade variable slit mask.

Experimental High-Dimensional Greenberger-Horne-Zeilinger Entanglement with Superconducting Transmon Qutrits

Multipartite entanglement is one of the core concepts in quantum information science with broad applications that span from condensed matter physics to quantum physics foundation tests. Although its most studied and tested forms encompass two-dimensional systems, current quantum platforms technically allow the manipulation of additional quantum levels. We report the experimental demonstration and certification of a high-dimensional multipartite entangled state in a superconducting quantum processor. We generate the three-qutrit Greenberger-Horne-Zeilinger state by designing the necessary pulses to perform high-dimensional quantum operations. We obtain the fidelity of $76\mathrm{%}\ifmmode\pm\else\textpm\fi{}1\mathrm{%}$, proving the generation of a genuine three-partite and three-dimensional entangled state. To this date, only photonic devices have been able to create and certify the entanglement of these high-dimensional states. Our work demonstrates that another platform, superconducting systems, is ready to exploit genuine high-dimensional entanglement and that a programmable quantum device accessed on the cloud can be used to design and execute experiments beyond binary quantum computation.

Fast dissipative preparation of three-dimensional entangled states for two Rydberg atoms via Lyapunov control

By using the Lyapunov control approach—an optimization algorithm, we propose a dissipative scheme for efficiently preparing the three-dimensional entangled state of two Rydberg atoms, which subject to Rydberg–Rydberg interactions at the antiblockade regime. The steady target state is the unique dark state of the two-atom system, and is achieved with high fidelity under the Rydberg pumping and the atomic spontaneous emission. The time required to settle into the high-fidelity steady state is greatly accelerated by the help of Lyapunov control, which takes effects while the system is initially prepared in the states containing coherence between the dark state and decoherence-sensitive bright states. The numerical results show that a fidelity of the steady three-dimensional entangled state above 0.99 can be achieved around 2.2 ms with the current experimental conditions. We study in detail the optimal control parameters and show the robustness of the scheme against random noises. The scheme may be generalized for preparation of more complicate multi-atom entangled states.

Rapid generation of a three-dimensional entangled state for two atoms trapped in a cavity via shortcuts to adiabatic passage

We present an efficient protocol to rapidly generate a three-dimensional entangled state for two atoms trapped in a cavity with quantum Zeno dynamics and Lewis---Riesenfeld invariants. The required time for the protocol is much shorter than that with adiabatic passage. The influence of various decoherence processes such as atomic spontaneous emission and photon loss on the fidelity of the three-dimensional entangled state is investigated. Numerical simulation demonstrates that the protocol is robust against both the atomic spontaneous emission and cavity decay. Different from Lin et al. (J Opt Soc Am B 33(4):519---524, 2016), the three-dimensional entangled state can be fast generated with only one step. Furthermore, the protocol can be generalized to generate N-dimensional entanglement state. Therefore, we hope the protocol may be useful in quantum information field.

Fast generations of tree-type three-dimensional entanglement via Lewis-Riesenfeld invariants and transitionless quantum driving.

Recently, a novel three-dimensional entangled state called tree-type entanglement, which is likely to have applications for improving quantum communication security, was prepared via adiabatic passage by Song et al. Here we propose two schemes for fast generating tree-type three-dimensional entanglement among three spatially separated atoms via shortcuts to adiabatic passage. With the help of quantum Zeno dynamics, two kinds of different but equivalent methods, Lewis-Riesenfeld invariants and transitionless quantum driving, are applied to construct shortcuts to adiabatic passage. The comparisons between the two methods are discussed. The strict numerical simulations show that the tree-type three-dimensional entangled states can be fast prepared with quite high fidelities and the two schemes are both robust against the variations in the parameters, atomic spontaneous emissions and the cavity-fiber photon leakages.

Generation of tree-type three-dimensional entangled states via adiabatic passage

We propose a scheme for generating a type of novel tree-type three-dimensional entangled state. In the scheme, an atom and two Bose--Einstein condensates (BECs) are individually trapped in three spatially separated optical cavities which are connected by two optical fibers. Because the system evolves along the dark state via adiabatic passage, the populations of the intermediate excited states of the atom and BECs are so negligible that the influence of atomic spontaneous radiation on the fidelity is restrained. In addition, because of the certain limit condition used, the cavity decay and fiber loss are efficiently suppressed. This novel three-dimensional entangled state is likely to have applications for improving quantum communication security.

Simplified scheme for entanglement preparation with Rydberg pumping via dissipation

Inspired by recent work [A. W. Carr and M. Saffman, Phys. Rev. Lett. 111, 033607 (2013)], we propose a simplified scheme to prepare the two-atom maximally entangled states via dissipative Rydberg pumping. Compared with the former scheme, the simplified one involves less classical laser fields and Rydberg interactions, and the asymmetric Rydberg interactions are avoided. Master equation simulations demonstrate that the fidelity and the Clauser-Horne-Shimony-Holt correlation of the maximally entangled state could reach up to 0.999 and 2.821, respectively, under certain conditions. Furthermore, we extend the physical thoughts to prepare the three-dimensional entangled state, the numerical simulations show that, in theory, both the fidelity and the Negativity of the desired entanglement could be very close to unity under certain conditions.

Preparation of three-dimensional entanglement for distant atoms in coupled cavities via atomic spontaneous emission and cavity decay.

We propose a dissipative scheme to prepare a three-dimensional entangled state for two atoms trapped in separate coupled cavities. Our work shows that both atomic spontaneous emission and cavity decay, which are two typical obstacles in unitary-dynamics-based schemes, are no longer detrimental, but necessary for three-dimensional entangled state preparation without specifying initial state and controlling the evolution time precisely. Final numerical simulation with one group of experimental parameters indicates that the performance of our scheme could be better than the unitary-dynamics-based scheme.

Dissipative preparation of a steady three-dimensional entangled state via quantum-jump-based feedback

A robust and scalable scheme to generate a steady three-dimensional entangled state for a V-type atom and a Λ-type atom trapped in a strongly dissipative bimodal cavity is proposed by direct feedback control based on quantum-jump detection. The robustness of this scheme reflects in the insensitivity to detection inefficiencies and the strong ability against the parameter fluctuations in the feedback, driving, and coupling strengths. The influence of atomic spontaneous emission can be suppressed by using the local feedback control. The scalability is ensured that N-dimensional entangled states of two atoms can be deterministically generated.

Dissipative creation of three-dimensional entangled state in optical cavity via spontaneous emission

We present a dissipative protocol to engineer two $^{87}Rb$ atoms into a form of three-dimensional entangled state via spontaneous emission. The combination of coupling between ground states via microwave fields and dissipation induced by spontaneous emission make the current scheme deterministic and a stationary entangled state can always be achieved without state initialization. Moreover, this scheme can be straightforwardly generalized to preparation of an $N$-dimensional entangled state in principle.

Generating Three-Dimensional Entanglement for Atomic Ensembles Trapped in Two Separated Cavity via an Optical Fiber

We propose a scheme for generating high fidelity three-dimensional entangled state for two atomic ensembles in spatially separated cavities coupled by an optical fiber. By employing multiple atoms in a cavity and resonant interaction between atoms and photons, the interaction time can be shortened greatly. Furthermore, we study the effects of spontaneous emission of atoms and photon leakage.

Generation of multiparticle three-dimensional entanglement state via adiabatic passage

A scheme is proposed for generating a multiparticle three-dimensional entangled state by appropriately adiabatic evolutions, where atoms are respectively trapped in separated cavities so that individual addressing is needless. In the ideal case, losses due to the spontaneous transition of an atom and the excitation of photons are efficiently suppressed since atoms are all in ground states and the fields remain in a vacuum state. Compared with the previous proposals, the present scheme reduces its required operation time via simultaneously controlling four classical fields. This advantage would become even more obvious as the number of atoms increases. The experimental feasibility is also discussed. The successful preparation of a high-dimensional multiparticle entangled state among distant atoms provides better prospects for quantum communication and distributed quantum computation.

Generation of three-dimensional entangled state between a single atom and a Bose-Einstein condensate via adiabatic passage

Inspired by a recently experiment by M. Lettner et al. [Phys. Rev. Lett. 106, 210503 (2011)], we propose a robust scheme to prepare three-dimensional entanglement state between a single atom and a Bose-Einstein condensate (BEC) via stimulated Raman adiabatic passage (STIRAP) technique. The atomic spontaneous radiation, the cavity decay, and the fiber loss are efficiently suppressed by the engineering adiabatic passage. Our strictly numerical simulation shows our proposal is good enough to demonstrate the generation of three-dimensional entanglement with high fidelity and within the current experimental technology.

One-step generation of qutrit entanglement via adiabatic passage in cavity quantum electrodynamics

A scheme is proposed for generating a three-dimensional entangled state for two atoms trapped in a cavity by one step via adiabatic passage. In the scheme, the two atoms are always in ground states and the field mode of the cavity excited is negligible under a certain condition. Therefore, the scheme is very robust against decoherence. Furthermore, it needs neither the exact control of all parameters nor the accurate control of the interaction time. It is shown that qutrit entanglement can be generated with a high fidelity.

Deterministic generation of a three-dimensional entangled state via quantum Zeno dynamics

A scheme is proposed for the generation of a three-dimensional entangled state for two atoms trapped in a cavity via quantum Zeno dynamics. Because the scheme is based on the resonant interaction, the time required to produce entanglement is very short compared with the dispersive protocols. We show that the resulting effective dynamics allows for the creation of robust qutrit-qutrit entanglement. The influence of various decoherence processes such as spontaneous emission and photon loss on the fidelity of the entangled state is investigated. Numerical results show that the scheme is robust against the cavity decay since the evolution of the system is restricted to a subspace with null-excitation cavity fields. Furthermore, the present scheme has been generalized to realize $N$-dimensional entanglement for two atoms.

Distributed qutrit–qutrit entanglement via quantum Zeno dynamics

A scheme is proposed to generate a three-dimensional entangled state for two atoms trapped in two distant cavities via quantum Zeno dynamics. We study such system in the regime of resonant atom–field interactions, which makes the scheme work very fast. We also investigate the influence of dissipation, due to atomic spontaneous emission and photon leakage, on the qutrit–qutrit entanglement.

Quantum Computation and Entangled-State Generation Through Photon Emission and Absorption Processes in Separated Cavities

We propose a scheme to implement a two-bit conditional quantum phase gate and generate a multi-atom cluster state and a two-atom three-dimensional entangled state based on photon emission and absorption processes. In the scheme, a Λ-type atom and a V-type atom are individually trapped in two spatially separated cavities connected by an optical fiber. By choosing the interaction time and the ratio of coupling parameters appropriately, the gate operation and entanglement generation can be determinately achieved. We also discuss the influence of photon Leakage on the fidelities of the gate and entanglement and show that the scheme is scalable and feasible in the experimental realization and further utilization.

Schemes for Teleportation of an Unknown Single-Qubit Quantum State by Using an Arbitrary High-Dimensional Entangled State

We propose a scheme to teleport an unknown single-qubit state by using a high-dimensional entangled state as the quantum channel. As a special case, a scheme for teleportation of an unknown single-qubit state via three-dimensional entangled state is investigated in detail. Also, this scheme can be directly generalized to an unknown f-dimensional state by using a d-dimensional entangled state (d > f) as the quantum channel.