We propose a class of qubit networks that admit perfect transfer of any quantum state in a fixed period of time. Unlike many other schemes for quantum computation and communication, these networks do not require qubit couplings to be switched on and off. When restricted to N -qubit spin networks of identical qubit couplings, we show that 2 log 3 N is the maximal perfect communication distance for hypercube geometries. Moreover, if one allows fixed but different couplings between the qubits then perfect state transfer can be achieved over arbitrarily long distances in a linear chain. The transfer of quantum states from one location (A) to another (B) is an important feature in many quantum information processing systems. Depending on technology at hand, this task can be accomplished in a number of ways. Optical systems, typically employed in quantum communication and cryptography applications, transfer states from A to B directly via photons. These photons could contain an actual message or could be used to create entanglement between A and B for future quantum teleportation between the two sites [1]. Quantum computing applications with trapped atoms use a variety of information carriers to transfer states from A to B, e.g. photons in cavity QED [2] and phonons in ion traps [3]. These photons and phonons may be viewed as individual quantum carriers. However, many promising technologies for the implementation of quantum information processing, such as optical lattices [4], and arrays of quantum dots [5] rely on collective phenomena to transfer quantum states. In this case a "quantum wire", the most fundamental unit of any quantum processing device, is made out of many interacting components. In the sequel we focus on quantum channels of this type. Insight into the physics of perfect quantum channels is of special significance for technologies that route entanglement and quantum states on networks. These technologies range from the very small, like the components of a quantum cellular automaton, to the medium-sized, like the data bus of a quantum computer, to the truly grand, like a quantum Internet spanning many quantum computers.In this Letter, we address the problem of arranging N interacting qubits in a network which allows the perfect transfer of any quantum state over the longest possible distance. The transfer is implemented by preparing the input qubit A in a prescribed quantum state and, some time later, by retrieving the state from the output qubit B. The network is described by a graph G in which the vertices V (G) represent locations of the qubits and a set of edges E(G) specifies which pairs of qubits are coupled. The graph is characterized by its adjacency matrix A(G),It has two special vertices, labelled as A and B, which mark the input and the output qubits respectively. We define the distance between A and B to be the number of edges constituting the shortest path between them. Although this distance is defined on a graph, it is directly related to the physical separation between the input and outp...

We propose a class of qubit networks that admit perfect state transfer of any two-dimensional quantum state in a fixed period of time. We further show that such networks can distribute arbitrary entangled states between two distant parties, and can, by using such systems in parallel, transmit the higher dimensional systems states across the network. Unlike many other schemes for quantum computation and communication, these networks do not require qubit couplings to be switched on and off. When restricted to N -qubit spin networks of identical qubit couplings, we show that 2 log 3 N is the maximal perfect communication distance for hypercube geometries. Moreover, if one allows fixed but different couplings between the qubits then perfect state transfer can be achieved over arbitrarily long distances in a linear chain. This paper expands and extends the work done in [1].

Two new relative entropy quantities, called the min-and max-relative entropies, are introduced and their properties are investigated. The well-known min-and max-entropies, introduced by Renner [1], are obtained from these. We define a new entanglement monotone, which we refer to as the max-relative entropy of entanglement, and which is an upper bound to the relative entropy of entanglement. We also generalize the min-and max-relative entropies to obtain smooth minand max-relative entropies. These act as parent quantities for the smooth Rényi entropies [1], and allow us to define the analogues of the mutual information, in the Smooth Rényi Entropy framework. Further, the spectral divergence rates of the Information Spectrum approach are shown to be obtained from the smooth min-and max-relative entropies in the asymptotic limit.

Transfer of data in linear quantum registers can be significantly simplified with preengineered but not dynamically controlled interqubit couplings. We show how to implement a mirror inversion of the state of the register in each excitation subspace with respect to the center of the register. Our construction is especially appealing as it requires no dynamical control over individual interqubit interactions. If, however, individual control of the interactions is available then the mirror inversion operation can be performed on any substring of qubits in the register. In this case, a sequence of mirror inversions can generate any permutation of a quantum state of the involved qubits.

We consider a two-parameter family of Rényi relative entropies D α, z (ρ∥σ) that are quantum generalisations of the classical Rényi divergence D α (p∥q). This family includes many known relative entropies (or divergences) such as the quantum relative entropy, the recently defined quantum Rényi divergences, as well as the quantum Rényi relative entropies. All its members satisfy the quantum generalizations of Rényi's axioms for a divergence. We consider the range of the parameters α, z for which the data-processing inequality holds. We also investigate a variety of limiting cases for the two parameters, obtaining explicit formulas for each one of them. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4906367]  D α (ρ∥σ) for 1/2 ≤ α ≤ 1. 16