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 ...

Contextuality is central to both the foundations of quantum theory and to the novel information processing tasks. Despite some recent proposals, it still faces a fundamental problem: how to quantify its presence? In this work, we provide a universal framework for quantifying contextuality. We conduct two complementary approaches: (i) the bottom-up approach, where we introduce a communication game, which grasps the phenomenon of contextuality in a quantitative manner; (ii) the top-down approach, where we just postulate two measures, relative entropy of contextuality and contextuality cost, analogous to existent measures of nonlocality (a special case of contextuality). We then match the two approaches by showing that the measure emerging from the communication scenario turns out to be equal to the relative entropy of contextuality. Our framework allows for the quantitative, resource-type comparison of completely different games. We give analytical formulas for the proposed measures for some contextual systems, showing in particular that the Peres-Mermin game is by order of magnitude more contextual than that of Klyachko et al. Furthermore, we explore properties of these measures such as monotonicity or additivity.

The superposition principle is one of the landmarks of quantum mechanics. The importance of quantum superpositions provokes questions about the limitations that quantum mechanics itself imposes on the possibility of their generation. In this work we systematically study the problem of creation of superpositions of unknown quantum states. First, we prove a no-go theorem that forbids the existence of a universal probabilistic quantum protocol producing a superposition of two unknown quantum states. Secondly, we provide an explicit probabilistic protocol generating a superposition of two unknown states, each having a fixed overlap with the known referential pure state.The protocol can be applied to generate coherent superposition of results of independent runs of subroutines in a quantum computer. Moreover, in the context of quantum optics it can be used to efficiently generate highly nonclassical states or non-gaussian states.The existence of superpositions of pure quantum states is one of the most intriguing consequences of the postulates of quantum mechanics. Quantum superpositions are crucial for the path-integral formulation of quantum mechanics [1] and are responsible for numerous nonclassical phenomena that are considered to be the key features of quantum theory [2]. The prominent examples are: quantum interference [3][4][5] and quantum entanglement [6]. Coherent addition of wavefunctions is also responsible for quantum coherence, a feature of quantum states that recently received a lot of attention [7][8][9]. Quantum superpositions are not only important from the foundational point of view but also a feature of quantum mechanics that underpins the existence of ultra-fast quantum algorithms (such as Shor factoring algorithm [10] or Grover search algorithm [11]), quantum cryptography [12] and efficient quantum metrology [13].The importance of quantum superpositions provokes questions about the restrictions that quantum mechanics itself imposes on the possibility of their generation. Studies of the limitations of the possible operations allowed by quantum mechanics have a long tradition are important both from the fundamental perspective as well as for the applications in quantum information theory. On one hand quantum mechanics offers a number of protocols that either outperform all existing classical counterparts or even allow to perform tasks that are impossible in the classical theory (such as quantum teleportation [14]). On the other hand a number of no-go theorems [15][16][17][18][19][20] restrict a class of protocols that are possible to realise within quantum mechanics. Finally, such no-go theorems can be themselves useful for practical purposes. For instance a no-clonning theorem can be used to certify the security of quantum cryptographic protocols [12].In this paper, we consider the scenario in which we are given two unknown pure quantum states and our task is to create, using the most general operations allowed by quantum mechanics, their superposition with some complex weights. Essentially the sam...

We study the ordering of two-qubit states with respect to the degree of bipartite entanglement using the Wootters concurrence -- a measure of the entanglement of formation, and the negativity -- a measure of the entanglement cost under the positive-partial-transpose-preserving operations. For two-qubit pure states, the negativity is the same as the concurrence. However, we demonstrate analytically on simple examples of various mixtures of Bell and separable states that the entanglement measures can impose different orderings on the states. We show which states, in general, give the maximally different predictions, (i) when one of the states has the concurrence greater but the negativity smaller than those for the other state, and (ii) when the states are entangled to the same degree according to one of the measures, but differently according to the other.Comment: 4 pages, 3 figures, slightly revised (including new title and comments on general structure of family of states exhibiting the discussed properties), to appear in Phys. Rev.

A lot of research has been done on multipartite correlations. However, it seems strange that there is no definition of so called genuine multipartite correlations. In this paper we propose three reasonable postulates which each measure or indicator of genuine multipartite correlations (or genuine multipartite entanglement) should satisfy. We also introduce degree of correlations which gives partial characterization of multipartite correlations. Then, we show that covariance does not satisfy two postulates and hence, it cannot be used as an indicator of genuine multipartite correlations. Finally, we propose candidate for a measure of genuine multipartite correlations based on the work that can be drawn from local bath by means of a multipartite state.