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.

Quantum cloning machines and their implementation in physical systems

We review the basic theory of approximate quantum cloning for discrete variables and some schemes for implementing quantum cloning machines. Several types of approximate quantum clones and their expansive quantum clones are intro- duced. As for the implementation of quantum cloning machines, we review some design methods and recent experimental results.

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 Cloning of Steering

Quantum steering in a global state allows an observer to remotely steer a subsystem into different ensembles by performing different local measurements on the other part. We show that, in general, this property cannot be perfectly cloned by any joint operation between a steered subsystem and a third system. Perfect cloning is viable if and only if the initial state is of zero discord. We also investigate the process of cloning the steered qubit of a Bell state using a universal cloning machine. Einstein–Podolsky–Rosen(EPR) steering, which is a type of quantum correlation existing in the states without a local-hidden-state model, is observed in the two copy subsystems. This contradicts the conclusion of no-cloning of quantum steering(EPR steering) [C. Y. Chiu et al.,npj Quantum Inf. 2, 16020(2016)] based on a mutual information criterion for EPR steering.

Maximum confidence measurements via probabilistic quantum cloning

Probabilistic quantum cloning（PQC） cannot copy a set of linearly dependent quantum states.In this paper,we show that if incorrect copies are allowed to be produced,linearly dependent quantum states may also be cloned by the PQC.By exploiting this kind of PQC to clone a special set of three linearly dependent quantum states,we derive the upper bound of the maximum confidence measure of a set.An explicit transformation of the maximum confidence measure is presented.

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.

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.

Quantum logic networks for cloning a quantum state near a given state

Two quantum logic networks are proposed to simulate a cloning machine that copies the states near a given one. Probabilistie cloning based on the first network is realized and the cloning probability of success based on the second network is lOOe/0. Therefore, the second network is more motivative than the first one.

Balancing four-state continuous-variable quantum key distribution with linear optics cloning machine

We show that the secret key generation rate can be balanced with the maximum secure distance of four-state continuous-variable quantum key distribution（CV-QKD） by using the linear optics cloning machine（LOCM）. Benefiting from the LOCM operation, the LOCM-tuned noise can be employed by the reference partner of reconciliation to achieve higher secret key generation rates over a long distance. Simulation results show that the LOCM operation can flexibly regulate the secret key generation rate and the maximum secure distance and improve the performance of four-state CV-QKD protocol by dynamically tuning parameters in an appropriate range.

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.

Scheme for realizing assisted cloning of an unknown two-atom entangled state via cavity QED

This paper proposes a scheme where one can realize quantum cloning of an unknown two-atom entangled state with assistance of a state preparer in cavity QED. The first stage of the scheme requires usual teleportation. In the second stage of the scheme, with the assistance of the preparer, the perfect copies of an unknown atomic entangled state can be produced.

Economical phase-covariant cloning with multiclones

This paper presents a very simple method to derive the explicit transformations of the optimal economical 1 to M phase-covariant cloning. The fidelity of clones reaches the theoretic bound [D＇Ar]ano G M and Macchiavello C 2003 Phys. Rev. A 67 042306]. The derived transformations cover the previous contributions [Delgado Y, Lamata Let al, 2007 Phys. Rev. Lett. 98 150502] in which M must be odd.

Fidelity between Gaussian mixed states with quantum state quadrature variances

In this paper, from the original definition of fidelity in a pure state, we first give a well-defined expansion fidelity between two Gaussian mixed states. It is related to the variances of output and input states in quantum information pro- cessing. It is convenient to quantify the quantum teleportation （quantum clone） experiment since the variances of the input （output） state are measurable. Furthermore, we also give a conclusion that the fidelity of a pure input state is smaller than the fidelity of a mixed input state in the same quantum information processing.

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.

Quantum superreplication of states and gates

Although the no-cloning theorem forbids perfect replication of quantum information, it is sometimes possible to produce large numbers of replicas with vanishingly small error. This phenomenon, known as quantum superreplication, can occur for both quantum states and quantum gates. The aim of this paper is to review the central features of quantum superreplication and provide a unified view of existing results. The paper also includes new results. In particular, we show that when quantum superreplication can be achieved, it can be achieved through estimation up to an error of size O（M/N2）, where N and M are the number of input and output copies, respectively. Quantum strategies still offer an advantage for superreplication in that they allow for exponentially faster reduction of the error. Using the relation with estimation, we provide i） an alternative proof of the optimality of Heisenberg scaling in quantum metrology, ii） a strategy for estimating arbitrary unitary gates with a mean square error scaling as log N/N2, and iii） a protocol that generates O（N2） nearly perfect copies of a generic pure state U｜0） while using the corresponding gate U only N times. Finally, we point out that superreplication can be achieved using interactions among k systems, provided that k is large compared to M2/N2.