A generalization of quantum teleportation and splitting of entanglement via local cloning

In the original one-to-one teleportation protocol of Bennett et al. [1], an observer, Alice, transmits the information of a d-level system to another observer, Bob, with perfect fidelity, by using a maximally entangled state. We introduce a generalization called the many-to-many teleportation, where the information is sent from N observers to M receivers situated at different locations. One of the most interesting applications of quantum cloning is the symmetric broadcasting of entanglement proposed by Buzek et al. [2]. We propose the splitting of entanglement based on a local optimal universal asymmetric cloning machine and, then, by applying the Peres-Horodecki criterion, we analyze the inseparability of the final states. The text was submitted by the author in English.     

Implementing 2→<Emphasis Type="Italic">M</Emphasis> Phase-covariant Cloning in Spin Networks

We propose a scheme to implement 2→M phase-covariant quantum cloning machine by using a M+2 spin star network in which the two central spins interact with the M outer spins respectively. The effect of the magnetic field on the fidelity of the cloning is also investigated. By applying an external magnetic field on the spin system, the fidelity of the cloning machine can be largely improved.     

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〉.     

Template matching of mixed quantum states

We consider the problem of optimal classification of an unknown input mixed quantum state with respect to a set of predefined patterns C_i, each represented by a known mixed quantum template . The performance of the matching strategy is addressed within a Bayesian formulation where the cost function, as suggested by the theory of monotone distances between quantum states, is chosen to be the fidelity or the relative entropy between the input and the templates. We investigate various examples of quantum template matching for the case of a finite number of copies of a two-level input state and for a generic, group covariant, set of two-level template states.     

Superbroadcasting of harmonic oscillators mixed states

We consider the problem of broadcasting quantum information encoded in the displacement parameter for an harmonic oscillator, from N to M > N copies of a thermal state. We show the Weyl-Heisenberg covariant broadcasting map that optimally reduces the thermal photon number, and we prove that it minimizes the noise in conjugate quadratures at the output for general input states. We find that from two input copies broadcasting is feasible, with the possibility of simultaneous purification (superbroadcasting). The text was submitted by the authors in English.     

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].     

Quantum teleportation via a two-qubit Heisenberg <Emphasis Type="Italic">XXZ</Emphasis> chain – effects of anisotropy and magnetic field

We study quantum teleportation via a two-qubit Heisenberg XXZ chain under an inhomogeneous magnetic field. We first consider entanglement teleportation, and then focus on the teleportation fidelity under different conditions. The effects of anisotropy and the magnetic field, both uniform and inhomogeneous, are discussed. We also find that, though entanglement teleportation does require an entangled quantum channel, a nonzero critical value of minimum entanglement is not always necessary.     

A Proposal of Telecloning for a Three-Particle Entangled?W?State

A 1→2 telecloning solution for an arbitrary three-particle entangled W state is proposed in which two four-particle entangled states are used as quantum channels. It is proposed that the three-particle W state can be telecloned based on the quantum teleportation and the local copying of entanglement, and the fidelity of each clone depends on the input state. This scheme can be generalized into the case of 1→N (N>2) telecloning of an arbitrary three-particle W state. Furthermore, another scheme for 1→N (N≥2) telecloning of an arbitrary n-particle (n≥4) W state is proposed, the multi-bit controlled-NOT (CNOT) gates and additional particles are needed in this case. Project 10574060 supported by the National Natural Science Foundation of China.     

Super Universality of the Quantum Hall Effect and the?“Large N Picture” of the ? Angle

It is shown that the “massless chiral edge excitations” are an integral and universal aspect of the low energy dynamics of the ϑ vacuum that has historically gone unnoticed. Within the SU(M+N)/S(U(M)×U(N)) non-linear sigma model we introduce an effective theory of “edge excitations” that fundamentally explains the quantum Hall effect. In sharp contrast to the common beliefs in the field our results indicate that this macroscopic quantization phenomenon is, in fact, a super universal strong coupling feature of the ϑ angle with the replica limit M=N=0 only playing a role of secondary importance. To demonstrate super universality we revisit the large N expansion of the CP ^N−1 model. We obtain, for the first time, explicit scaling results for the quantum Hall effect including quantum criticality of the quantum Hall plateau transition. Consequently a scaling diagram is obtained describing the cross-over between the weak coupling “instanton phase” and the strong coupling “quantum Hall phase” of the large N theory. Our results are in accordance with the “instanton picture” of the ϑ angle but fundamentally invalidate all the ideas, expectations and conjectures that are based on the historical “large N picture.”     

Optimal asymmetric economical state-dependent cloners

We present the optimal asymmetric economical 1-3 phase-covariant and real state cloning in two-dimensions. The fidelity distributions of copies of two state-dependent cloners are the same, and higher than that of the optimal asymmetric universal quantum cloning. Using a quantum network, we calculate the single-qubit rotation angles to implement two symmetric economical state-dependent cloners. We also propose an experimentally feasible scheme to implement the optimal asymmetric economical 1-3 phase-covariant cloner. The scheme can be realized with the success probability of 100%.     

Quantum Computer Algorithm for Parity Determination Based on Quantum Counting

A new quantum computer algorithm is proposed for determining the parity of function f(x) by using quantum counting algorithm. The parity of function f(x) can be determined by counting exactly the number of satisfying f(x)=−1, which is equivalent to determine the number of solutions, M, to an N item search problem. The algorithm can be accomplished in time of order .     

Quantum rotors with regular frustration and the quantum Lifshitz point

We have discussed the zero-temperature quantum phase transition in n-component quantum rotor Hamiltonian in the presence of regular frustration in the interaction. The phase diagram consists of ferromagnetic, helical and quantum paramagnetic phase, where the ferro-para and the helical-para phase boundary meets at a multicritical point called a (d,m) quantum Lifshitz point where (d,m) indicates that the m of the d spatial dimensions incorporate frustration. We have studied the Hamiltonian in the vicinity of the quantum Lifshitz point in the spherical limit and also studied the renormalisation group flow behaviour using standard momentum space renormalisation technique (for finite n). In the spherical limit ()one finds that the helical phase does not exist in the presence of any nonvanishing quantum fluctuation for m =d though the quantum Lifshitz point exists for all d > 1+m/2, and the upper critical dimensionality is given by d _u = 3 +m/2. The scaling behaviour in the neighbourhood of a quantum Lifshitz point in d dimensions is consistent with the behaviour near the classical Lifshitz point in (d+z) dimensions. The dynamical exponent of the quantum Hamiltonian z is unity in the case of anisotropic Lifshitz point (d>m) whereas z=2 in the case of isotropic Lifshitz point (d=m). We have evaluated all the exponents using the renormalisation flow equations along-with the scaling relations near the quantum Lifshitz point. We have also obtained the exponents in the spherical limit (). It has also been shown that the exponents in the spherical model are all related to those of the corresponding Gaussian model by Fisher renormalisation. Received: 23 December 1997 / Received in final form: 6 January 1998 / Accepted: 7 January 1998     

Quantum leakage of collective excitations of atomic ensemble induced by spatial motion

We generalize the conception of quantum leakage for the atomic collective excitation states. By making use of the atomic coherence state approach, we study the influence of the atomic spatial motion on the symmetric collective states of 2-level atomic ensemble due to inhomogeneous coupling. In the macroscopic limit, we analyze the quantum decoherence of the collective atomic state by calculating the quantum leakage for a very large ensemble at a finite temperature. Our investigations show that the fidelity of the atomic system will not be good in the case of atom numberN→∞. Therefore, quantum leakage is an inevitable problem in using the atomic ensemble as a quantum information memory. The detailed calculations shed theoretical light on quantum processing using atomic ensemble collective qubit.     

Probabilistic teleportation of an M-quNit state by a single non-maximally entangled quNit-pair

In this work we devise a scheme to teleport a type of unknown M-quNit state using only a single non-maximally entangled quNit-pair as the quantum channel. The fidelity is one while the success probability is less than one and depends on N but not on M. The scheme requires M−1 ancillary quNits and 1 qubit at the receiver's and the receiver should be capable of performing some quNit-quNit/qubit operations. The classical message that the teleporter must announce consists only of 2 Nits, though the full set of his/her measurement outcome is as huge as M+1 Nits.     

Generalized Teleportation of a <Emphasis Type="Italic">d</Emphasis>-Level <Emphasis Type="Italic">N</Emphasis>-Particle GHZ State with One Pair of Entangled Particles as the Quantum Channel

With one pair of entangled particles as the quantum channel, we present an explicit generalized protocol for perfectly teleporting a d-level N-particle GHZ state from a sender to a receiver. This protocol has the advantage of transmitting much less particles and classical information for teleporting the d-level N-particle GHZ state than others.     

Cloning of continuous quantum variables

The cloning of quantum variables with continuous spectra is analyzed. A Gaussian quantum cloning machine is exhibited that copies equally well the states of two conjugate variables such as position and momentum. It also duplicates all coherent states with a fidelity of 2/3. More generally, the copies are shown to obey a no-cloning Heisenberg-like uncertainty relation.     

Controlled teleportation of an arbitrary n-qudit state using nonmaximally entangled GHZ states

In this paper, we explicitly present a general scheme for controlled quantum teleportation of an arbitrary multi-qudit state with unit fidelity and non-unit successful probability using d-dimensional nonmaximally entangled GHZ states as the quantum channel and generalized d-dimensional Bell states as the measurement basis. The expression of successful probability for controlled teleportation is present depending on the degree of entanglement matching between the quantum channel and the generalized Bell states. And the formulae for the selection of operations performed by the receiver are given according to the results measured by the sender and the controller.      

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.     

ZN-Graded Noncommutative Differential Calculus

We consider the algebra M _N (C) ofN × N matrices as a cyclic quantum plane.We also analyze the coaction of the quantum group F and the action of its dualquantum algebra H on it. Then we study the decomposition ofM _N (C) in termsof the quantum algebra representations. Finally, we develop the differential algebraof the cyclic group Z _N with d ^N = 0, where Z _N is viewed as the the subalgebraof diagonal N × N complex matrices, and treat the particularcase N = 3.