We study a quantum state transfer between two qubits interacting with the ends of a quantum wire consisting of linearly arranged spins coupled by an excitation conserving, time-independent Hamiltonian. We show that if we control the coupling between the source and the destination qubits and the ends of the wire, the evolution of the system can lead to an almost perfect transfer even in the case in which all nearest-neighbour couplings between the internal spins of the wire are equal.PACS numbers: 03.67. Hk, 03.67.Pp, 05.50.+q The problem of designing quantum networks which enable efficient high-fidelity transfer of quantum states has recently been addressed by a number of authors (see ). Ideally, such a network should meet both the simplicity and the minimal control requirements. By simplicity we mean that the network consists of typical elements coupled in a standard way so that a few networks can be combined together to form more complex systems. The minimal control requirement says that the transmission of a quantum state through the network should be possible without performing many control operations (as switching interactions on and off, measuring, encoding and decoding, etc.). A 1D quantum network (quantum wire) which fulfills both above requirements was proposed by Bose [1] who considered a spin chain with the nearest neighbour Heisenberg Hamiltonian; here the transmission of quantum state between the ends of the chain was achieved simply by a free evolution of the network. However, as was shown by Bose, if all neighbour couplings have the same strength the fidelity of a transmission decreases with the chain length n. A similar model (with the Heisenberg Hamiltonian replaced by XY one) was considered by Christandl et al. in [2]. They show that one can transfer quantum states through arbitrary long chains if spin couplings are carefully chosen in a way depending on the chain length n (see also [3][4][5][6][7][8]). Note however that this approach does not meet the simplicity requirement since one cannot merge several "modulated" quantum wires into a longer one.Here, we study a transfer of quantum states between two qubits attached to the ends of a quantum wire consisting of n linearly arranged spins. In order to fulfill the requirement of simplicity we assume that all couplings between neighbouring spins forming the quantum wire are the same (and equal to 1), while the couplings between the source and the destination qubits and the ends of the wire are equal to a. We show that one can significantly improve of the fidelity of the transfer be- * Corresponding author. Phone: +48 (61) 829-5394, fax: +48 (61) 829-5315. E-mail: tomasz@amu.edu.pl tween the source and the destination qubits by selecting the value of a appropriately. In particular, choosing a small enough, one can achieve a transfer whose fidelity can be arbitrarily close to one, even for large n.We assume that the Hamiltonian of the whole system of n + 2 qubits conserves the number of excitation (e.g., it is a XY Hamiltonian), so the state n+1 ...

In this Letter, we demonstrate that the property of monogamy of Bell violations seen for no-signaling correlations in composite systems can be generalized to the monogamy of contextuality in single systems obeying the Gleason property of no disturbance. We show how one can construct monogamies for contextual inequalities by using the graph-theoretic technique of vertex decomposition of a graph representing a set of measurements into subgraphs of suitable independence numbers that themselves admit a joint probability distribution. After establishing that all the subgraphs that are chordal graphs admit a joint probability distribution, we formulate a precise graph-theoretic condition that gives rise to the monogamy of contextuality. We also show how such monogamies arise within quantum theory for a single four-dimensional system and interpret violation of these relations in terms of a violation of causality. These monogamies can be tested with current experimental techniques.

We study a quantum state transfer between spins interacting with an arbitrary network of spins coupled by uniform XX interactions. It is shown that in such a system under fairly general conditions, we can expect a nearly perfect transfer of states. Then we analyze a generalization of this model to the case of many network users, where the sender can choose which party he wants to communicate with by appropriately tuning his local magnetic field. We also remark that a similar idea can be used to create an entanglement between several spins coupled to the network.