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 [Formula: see text] with [Formula: see text], 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 [Formula: see text] and [Formula: see text] are implemented for modulating the frequency of qubits. Then, the SC qubits [Formula: see text] and [Formula: see text] 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 [Formula: see text] can be obtained by applying external magnetic fields on qubits [Formula: see text] 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 [Formula: see text] 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.
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 [Formula: see text] with [Formula: see text], 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 [Formula: see text] and [Formula: see text] are implemented for modulating the frequency of qubits. Then, the SC qubits [Formula: see text] and [Formula: see text] 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 [Formula: see text] can be obtained by applying external magnetic fields on qubits [Formula: see text] 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 [Formula: see text] 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.
Abstract An efficient scheme is proposed to teleport an entangled state of two superconducting (SC) qubits from Alice's to Bob's lab. This type of two-level systems has recently attracted a lot of attention due to the possible tunability of the coupling strength of the qubits with each other. To achieve the purpose, we first generate the GHZ state as the necessary teleportation channel. Then, appropriate interactions are performed in two processes between two of the five qubits, each with a certain frequency modulative external magnetic field which is applied on specific one of the qubits. Next, via applying proper gates and measurements in each lab, we observe that the teleportation can be successfully performed with maximum possible values of fidelity and success probability. At last, to make the protocol close to reality, decay rates of SC qubits are also taken into account, showing that our protocol still works well, satisfactorily.
Important tasks in cavity quantum electrodynamics include the generation and control of quantum states of spatially separated particles distributed in different cavities. An interesting question in this context is how to prepare entanglement among particles located in different cavities, which are important for large-scale quantum information processing. We here consider a multi-cavity system where cavities are coupled to a superconducting (SC) qubit and each cavity hosts many SC qubits. We show that all intra-cavity SC qubits plus the coupler SC qubit can be prepared in an entangled Greenberger–Horne–Zeilinger (GHZ) state, by using a single operation and without the need of measurements. The GHZ state is created without exciting the cavity modes; thus greatly suppressing the decoherence caused by the cavity-photon decay and the effect of unwanted inter-cavity crosstalk on the operation. We also introduce two simple methods for entangling the intra-cavity SC qubits in a GHZ state. As an example, our numerical simulations show that it is feasible, with current circuit-QED technology, to prepare high-fidelity GHZ states, for up to nine SC qubits by using SC qubits distributed in two cavities. This proposal can in principle be used to implement a GHZ state for an arbitrary number of SC qubits distributed in multiple cavities. The proposal is quite general and can be applied to a wide range of physical systems, with the intra-cavity qubits being either atoms, NV centers, quantum dots, or various SC qubits.
When a two-qubit system is initially maximally entangled, two independent decoherence channels, one per qubit, would greatly reduce the entanglement of the two-qubit system when it reaches its stationary state. We propose a method on how to minimize such a loss of entanglement in open quantum systems. We find that the quantum entanglement of general two-qubit systems with controllable parameters can be controlled by tuning both the single-qubit parameters and the two-qubit coupling strengths. Indeed, the maximum fidelity Fmax between the stationary entangled state, ${\ensuremath{\rho}}_{\ensuremath{\infty}}$, and the maximally entangled state, ${\ensuremath{\rho}}_{m}$, can be about $2/3\ensuremath{\approx}\text{max}{\text{tr}({\ensuremath{\rho}}_{\ensuremath{\infty}}{\ensuremath{\rho}}_{m})}={F}_{\text{max}}$, corresponding to a maximum stationary concurrence, Cmax, of about $1/3\ensuremath{\approx}C({\ensuremath{\rho}}_{\ensuremath{\infty}})={C}_{\text{max}}$. This is significant because the quantum entanglement of the two-qubit system can be produced and kept, even for a long time. We apply our proposal to several types of two-qubit superconducting circuits and show how the entanglement of these two-qubit circuits can be optimized by varying experimentally controllable parameters.
Hybrid W entangled states are essential in quantum information processing, quantum communication, and quantum technology. In this Letter, we propose a simple method to prepare hybrid W entangled states between n superconducting (SC) qubits and n microwave resonators (MRs) in circuit QED. Only two basic operations are needed for the preparation of hybrid W states. The operational time decreases as the number of qubits increases. Since no ancillary cavity is required, the hardware resources for the state preparation are minimized. Because the state preparation does not involve any measurements, the hybrid W entangled states are generated in a deterministic way. Moreover, during the entire preparation, the high-energy levels of the SC qutrits remain unexcited, which greatly reduces decoherence of the SC qutrits. As an example, our numerical simulation demonstrates that high-fidelity preparation of the hybrid W entangled state of three SC qubits and three MRs is feasible within the current circuit QED technique. This method is universal and can be applied to generate hybrid W states of n matter qubits (e.g., atomic qubits, NV center qubits, quantum dot qubits, and magnon qubits) and n photonic qubits in various physical systems.
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, considering 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. The average entropy over the initial states of the qubit is calculated. Then by performing a Bell state measurement on the fields leaving the cavities, we swap the entanglement between qubit-field in each cavity into qubit-qubit and field-field subsystems. The entangling power is used to measure the average amount of swapped entanglement over all possible pure initial states. Our results are presented in two weak and strong coupling regimes, illustrating the positive role of movement of the qubits on the swapped entanglement. It is revealed that by considering certain conditions for the initial state of qubits, it is possible to achieve a maximally long-leaving stationary entanglement (Bell state) which is entirely independent of the environmental variables as well as the velocity of qubits. This happens when the two qubits have the same velocities.
The basic entanglement swapping protocol allows to achieve the main aim of deterministically projecting two qubits, which have never interacted, onto a maximally entangled state. For deterministic swapping the key ingredient is the maximal entanglement initially contained in two pairs of qubits and the ability to measure onto a Bell basis. In other words, the basic and deterministic entanglement swapping scheme involves three maximal level of entanglement. In this work we address probabilistic entanglement swapping processes performed with different amounts of initial entanglement. Besides, we suggest a non Bell measuring-basis, thus we introduce a third entanglement level in the process. Additionally, we propose the \emph{unambiguous state extraction} scheme as the local mechanism for probabilistically achieving the main aim. Amalgamating these three elements allows us to design four strategies for performing probabilistic entanglement swapping. Surprisingly, we encountered an twofold entanglement matching effect related to the concurrence of the measuring-basis. Specifically, the maximal probability of accomplishing the main aim becomes a constant for concurrences higher than or equal to the matching entanglement values. Thus, we show that maximal entanglement in the measuring-basis is not required for attaining the main aim with optimal probability.