Optimal quantum cloning via spin networks

Abstract

In this paper we present an approach to quantum cloning via free dynamical evolution of spin networks. By properly designing the network and the couplings between spins, we show that optimal 1 → M phase covariant cloning can be achieved without any external control. Especially, when M is an odd number, the optimal phase-covariant cloning can be achieved without ancillas. Moreover, we demonstrate that the same framework is capable for optimal 1 → 2 universal cloning.PACS numbers: 03.67. Hk, The no-cloning theorem [1] presents that quantum mechanics prohibits perfect cloning of an arbitrary state, which is one of the most fundamental differences between classical and quantum information processing. This nogo theorem plays an important role in the security of quantum cryptography [2]. Since ideal replication of information is forbidden, it is then interesting to discuss how close to ideality one can afford to copy an unknown quantum state, namely the upper bound to the fidelity of approximate cloning [3,4,5,6,7,8]. In a pioneering work of Bužek and Hillery [3], they proposed an optimal 1 → 2 universal cloning scheme. Later, Gisin and Massar presented the unitary transformation leading to optimal 1 → M universal cloning [4]. Other than universal cloning, Bruß et al proposed state-dependent cloning, where partial information of the input state is priorly known [5]. An interesting example is the phase covariant cloning (PCC) [6], where the input states can be expressed as |ψ = 1 √ 2 (|0 + e iφ |1 ), namely equatorial states (in the case of qubits). Since the input state is confined in a subset of the Bloch sphere, higher optimal fidelity is expected, which has been demonstrated in relevant papers [7,8].Currently, approximate quantum cloning machine has been implemented experimentally within several approaches [9,10,11,12]. However, most of these proposals are based on quantum logic gates and post-selection methods. In fact, there are other routes to implement the required quantum protocols. In previous work, quantum computation for a spin network based on Heisenberg couplings was reported [13,14,15,16,17,18,19,20,21,22]. For example, with unmodulated Heisenberg chains, high fidelity quantum state transfer can be achieved [14,15,16,17,18,19]. One attracting feature of this approach is that it does not require time modulation for the qubits couplings. Once the initial states and the evolutional hamiltonian is determined, the system can faithfully im- * Electronic address: chenqing@mail.ustc.edu.cn † Electronic address: djf@ustc.edu.cn plement designated computation task through dynamical evolution. Thus, except the preparation of initial states and the readout of computation results, the whole computation process does not involve external controlling, which provides relatively longer decoherence time for the system. Recently, Chiara et al [21,22] proposed the implementation of 1 → M and N → M PCC (numerically for several special cases) within this approach. Nevertheless, in their proposal, the 1 → M PCC can reach the op...

Factorization and Criticality in Finite XXZ Systems of Arbitrary Spin

“…For a spin-star geometry, where a central spin is coupled to N − 1 noninteracting spins (Refs. [55,48]), there are again 2 N −1 FF configurations, according to the signs chosen in (7) For an open 3 × N array a similar procedure leads to a system of first-order linear recurrences, from which we find a number of configurations given by…”

Improving fidelity of quantum cloning via the Dzyaloshinskii-Moriya interaction in a spin network

“…The spin system including DM couplings in this paper is a spin star network [16] as shown in Fig. 1.…”

“…(3) describes a resonant interaction between a spin-1 2 and a higher spin-J system. Since the total z component of the spin commutes with H , the supplementary states can be rewritten as eigenstates of J 2 and J z , i.e., |S(M,k) = |M/2, k − M/2 according to Clebsch-Gordan coefficients [16]. Then the state at time t of the system can be written as…”

“…In Table I, F c is calculated from the expression of the maximum fidelity obtained by Chen et al [16] where no DM interaction is introduced. F max is the maximal fidelity obtained by the present paper.…”

“…Among these works, De Chiara et al introduced an approach to quantum cloning based on spin networks using XY coupling and reached relatively high fidelities [14,15]. In 2006, Chen et al proposed a protocol of 1 → M PCCM based on star spin networks [16]. They demonstrated that near-optimal fidelities * adzhu@ybu.edu.cn can be reached by properly preparing a special symmetric state as the initial state in Heisenberg models.…”