非对称经济相位协变量子克隆的最优性

我们严格的证明两维空间中1→2非对称经济型相位协变量子克隆的最优性。证明中,我们得出另一种独立的幺正变换。我们的结果涵盖了以前的结果[Durt T, et, al, Phys. Rev. A, 2004, 69: 062316]。     

Optimal symmetric economical phase-covariant quantum cloning

We derive the explicit transformation of the optimal symmetric economical 1→M$1\to M$ phase-covariant quantum cloning machine (EPCCM), which works without ancilla, as well as the corresponding fidelities in 2-dimension. The fidelity (1→M=2k+1 EPCCM$1\to M=2k+1\text{EPCCM}$) is covered with previous contributions [G.M. D'Ariano, et al., Phys. Rev. A 71 (2005) 042327]. Meanwhile, the explicit transformation of the optimal symmetric 1→M$1\to M$ phase-covariant quantum cloning machine (PCCM) (working with ancilla) as well as the corresponding fidelities in 2-dimension is also derived. The results of the PCCM agree with previous contributions [H. Fan, et al., Phys. Rev. A 65 (2001) 012304].     

Scheme for implementing an economical phase-covariant quantum cloning machine of distant atomic qubits with single-photon interference

By means of cavity-assisted photon interference, a simple scheme is proposed to implement a symmetric economical phase-covariant quantum cloning machine of two remote qubits, with each in a separate cavity. With our present scheme, a high-fidelity cloning machine is realized. Our scheme may be quite useful in terms of distributed quantum information processing.     

腔QED技术实现最优非对称经济型1到3的相位协变克隆方案

本文提出一个在腔QED中实现最优非对称经济型1到3相位协变克隆的可行性方案,这种克隆不需要辅助粒子.在这个方案中,三个原子中的两个同时与腔场发生作用,并且受经典场的作用.此方案不受腔场的态和腔衰变的影响,因此,在实验上是可能实现的.     

利用腔QED技术实现最优非对称经济型1到3的相位协变克隆

本文提出一个在腔QED中实验上可行的方案来实现最优非对称经济型1到3相位协变克隆,这种克隆是不需要辅助粒子的。在这个的方案中,三个原子中的两个同时与腔场发生作用,并且它们受经典场的作用。并且此方案不受腔场的态和腔衰变的影响,因此,在实验上是可能实现的。     

在腔QED中实现最优非对称经济型1到3的相位协变克隆方案

本文提出一个在腔QED中实验上可行的方案来实现最优非对称经济型1到3相位协变克隆,这种克隆是不需要辅助粒子的。在这个的方案中,三个原子中的两个同时与腔场发生作用,并且它们受经典场的作用。并且此方案不受腔场的态和腔衰变的影响,因此,在实验上是可能实现的。     

Scheme for the implementation of 1→3 optimal phase-covariant quantum cloning in ion-trap systems

This paper proposes a scheme for the implementation of 1→ 3 optimal phase-covariant quantum cloning with trapped ions. In the present protocol, the required time for the whole procedure is short due to the resonant interaction, which is important in view of decoherence. Furthermore, the scheme is feasible based on current technologies.     

Scheme to Implement Optimal Asymmetric Economical Phase-Covariant Quantum Cloning in Cavity QED

We propose an experimentally feasible scheme to implement the optimal asymmetric economical 1→2 phase-covariant quantum cloning in two dimensions based on the cavity QED technique. The protocol is very simple and only two atoms are required. Our scheme is insensitive to the cavity field states and cavity decay. During the processes, the cavity is only virtually excited and it thus greatly prolongs the efficient decoherent time. Therefore, it may be realized in experiment.     

Optimal Phase-Covariant Cloning in 3 Dimensions

In this paper, we present the explicit transformations of the optimal 1 → 3, 4, 5 phase-covariant cloning in 3 dimensions. The cloning fidelities are covered by the theoretical bounds of the optimal 1 → 3k, 3k + 1, 3k + 2 phase-covariant cloning of qutrits, where k ≥ 1 is the integral [Phys. Rev. A 67 (2003) 042306].     

Optimal 1 → M phase-covariant cloning in three dimensions

In this paper, we derive the explicit transformations of the optimal 1 → 3, 4, 5 phase-covariant cloning in three dimensions, and then generalize them to the cases of 1 → M = 3n, 3n + 1, 3n + 2(n ≥ 1 integer) cloning. The clone fidelities are coincident with the theoretical bounds found.     

Implementing phase-covariant cloning in circuit quantum electrodynamics

An efficient scheme is proposed to implement phase-covariant quantum cloning by using a superconducting transmon qubit coupled to a microwave cavity resonator in the strong dispersive limit of circuit quantum electrodynamics (QED). By solving the master equation numerically, we plot the Wigner function and Poisson distribution of the cavity mode after each operation in the cloning transformation sequence according to two logic circuits proposed. The visualizations of the quasi-probability distribution in phase-space for the cavity mode and the occupation probability distribution in the Fock basis enable us to penetrate the evolution process of cavity mode during the phase-covariant cloning (PCC) transformation. With the help of numerical simulation method, we find out that the present cloning machine is not the isotropic model because its output fidelity depends on the polar angle and the azimuthal angle of the initial input state on the Bloch sphere. The fidelity for the actual output clone of the present scheme is slightly smaller than one in the theoretical case. The simulation results are consistent with the theoretical ones. This further corroborates our scheme based on circuit QED can implement efficiently PCC transformation.     

Scheme for Implementation of Ancillary-Free 1→3 Optimal Phase-Covariant Quantum Cloning with Trapped Ions

We propose a simple scheme for the implementation of the ancillary-free 1→3 optimal phase-covariant quantum cloning for x-y equatorial qubits in ion-trap system. In the scheme, the vibrational mode is only virtually excited, which is very important in view of decoherence. The present proposal can be realized based on current available technologies.     

Probabilistic quantum cloning of real states

We construct the explicit formulation of the probabilistically perfect quantum cloning machine that perfectly duplicates the input states chosen from the special set consisting of the linearly independent and nonorthogonal quantum states with 〈φ_i ∣φ_j〉 = r ∈ (0, 1)(i ≠ j). The success probabilities of cloning the input states are equal and maximal. As two examples, we present the explicit transformations of the optimal 1 → 2 probabilistically perfect quantum cloning of the real states in 2 and 3 dimensions. The success probabilities of each of two cloning machines are equal and maximal.     

A quantum network for implementation of the optimal quantum cloning

This paper presents a quantum network to implement the optimal 1→2 quantum cloning in 2 dimensions, including the optimal asymmetric universal, the optimal symmetric phase-covariant, and the asymmetric real state cloning. By only choosing different angles of the single-qubit rotations, the quantum network can implement three optimal quantum cloning.     

Quantum deleting and cloning in a pseudo-unitary system

In conventional quantum mechanics, quantum no-deleting and no-cloning theorems indicate that two different and nonorthogonal states cannot be perfectly and deterministically deleted and cloned, respectively. Here, we investigate the quantum deleting and cloning in a pseudo-unitary system. We first present a pseudo-Hermitian Hamiltonian with real eigenvalues in a two-qubit system. By using the pseudo-unitary operators generated from this pseudo-Hermitian Hamiltonian, we show that it is possible to delete and clone a class of two different and nonorthogonal states, and it can be generalized to arbitrary two different and nonorthogonal pure qubit states. Furthermore, state discrimination, which is strongly related to quantum no-cloning theorem, is also discussed. Last but not least, we simulate the pseudo-unitary operators in conventional quantum mechanics with post-selection, and obtain the success probability of simulations. Pseudo-unitary operators are implemented with a limited efficiency due to the post-selections. Thus, the success probabilities of deleting and cloning in the simulation by conventional quantum mechanics are less than unity, which maintain the quantum no-deleting and no-cloning theorems.     

Nonlocal quantum cloning via quantum dots trapped in distant cavities

A scheme for implementing nonlocal quantum cloning via quantum dots trapped in cavities is proposed.By modulating the parameters of the system,the optimal 1 → 2 universal quantum cloning machine,1 → 2 phase-covariant cloning machine,and 1 → 3 economical phase-covariant cloning machine are constructed.The present scheme,which is attainable with current technology,saves two qubits compared with previous cloning machines.     

腔QED中相位协变量子克隆机的实现及纠错

应用N个二能级原子和单模真空腔场相互作用,提出了一个1→2的相位协变量子克隆机的方案.同时,基于这种克隆机,我们也提出了量子纠错方案,考虑了由相位和比特反转错误所产生的消相干影响,通过对后两个比特位进行Bell测量,并沿着合适的轴旋转第一比特,就可以恢复初始态.     

Probabilistically perfect quantum cloning and unambiguous state discrimination

We consider the N → M probabilistically perfect quantum cloning machine that perfectly produces M faithful copies from N identical input states, where the input states are selected, with prior probabilities η₁and η₂ = 1 − η₁, from a given set of the two linearly independent states |ψ₁〉^⊗ N = (cosθ|0〉 + sinθ|1〉)^⊗ N and |ψ₂〉^⊗ N = (sinθ|0〉 + cosθ|1〉)^⊗ N (θ∈(0,π/2)). We derive the optimal distribution of the success probabilities. When M approaches infinite, the probabilistically perfect quantum cloning can be regarded as a kind of the unambiguous state discrimination, and theoretically provides the upper bound of the unambiguous state discrimination. By using the optimal distribution of the success probabilities of the optimal asymmetric 1 → M probabilistically perfect quantum cloning, we can derive the maximum average success probability of the unambiguous discrimination of two nonorthogonal quantum states |ψ₁〉and|ψ₂〉. As an example, we give the explicit transformation of the optimal symmetric 1 → M probabilistically perfect quantum cloning to copy the two input states |ψ₁〉 and |ψ₂〉.