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...

The uncertainty principle, originally formulated by Heisenberg 1 , clearly illustrates the difference between classical and quantum mechanics. The principle bounds the uncertainties about the outcomes of two incompatible measurements, such as position and momentum, on a particle. It implies that one cannot predict the outcomes for both possible choices of measurement to arbitrary precision, even if information about the preparation of the particle is available in a classical memory. However, if the particle is prepared entangled with a quantum memory, a device that might be available in the not-too-distant future 2 , it is possible to predict the outcomes for both measurement choices precisely. Here, we extend the uncertainty principle to incorporate this case, providing a lower bound on the uncertainties, which depends on the amount of entanglement between the particle and the quantum memory. We detail the application of our result to witnessing entanglement and to quantum key distribution.Uncertainty relations constrain the potential knowledge one can have about the physical properties of a system. Although classical theory does not limit the knowledge we can simultaneously have about arbitrary properties of a particle, such a limit does exist in quantum theory. Even with a complete description of its state, it is impossible to predict the outcomes of all possible measurements on the particle. This lack of knowledge, or uncertainty, was quantified by Heisenberg 1 using the standard deviation (which we denote by R for an observable R). If the measurement on a given particle is chosen from a set of two possible observables, R and S, the resulting bound on the uncertainty can be expressed in terms of the commutator 3 :In an information-theoretic context, it is more natural to quantify uncertainty in terms of entropy rather than the standard deviation. Entropic uncertainty relations for position and momentum were derived in ref. 4 and later a relation was developed that holds for any pair of observables 5 . An improvement of this relation was subsequently conjectured 6 and then proved 7 . The improved relation iswhere H (R) denotes the Shannon entropy of the probability distribution of the outcomes when R is measured. The term 1/c quantifies the complementarity of the observables. For non-degenerate observables, c := max j,k | ψ j |φ k | 2 , where |ψ j and |φ k are the eigenvectors of R and S, respectively. One way to think about uncertainty relations is through the following game (the uncertainty game) between two players, Alice and Bob. Before the game commences, Alice and Bob agree on two measurements, R and S. The game proceeds as follows. Bob prepares a particle in a quantum state of his choosing and sends it to Alice. Alice then carries out one of the two measurements and announces her choice to Bob. Bob's task is to minimize his uncertainty about Alice's measurement outcome. This is illustrated in Fig. 1.Equation (1) bounds Bob's uncertainty in the case that he has no quantum memory-all information Bob hold...

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].

In this paper, we present a new entanglement monotone for bipartite quantum states. Its definition is inspired by the so-called intrinsic information of classical cryptography and is given by the halved minimum quantum conditional mutual information over all tripartite state extensions. We derive certain properties of the new measure which we call "squashed entanglement": it is a lower bound on entanglement of formation and an upper bound on distillable entanglement. Furthermore, it is convex, additive on tensor products, and superadditive in general.Continuity in the state is the only property of our entanglement measure which we cannot provide a proof for. We present some evidence, however, that our quantity has this property, the strongest indication being a conjectured Fannes type inequality for the conditional von Neumann entropy. This inequality is proved in the classical case.

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 propose a general method for studying properties of quantum channels acting on an n-partite system, whose action is invariant under permutations of the subsystems. Our main result is that, in order to prove that a certain property holds for an arbitrary input, it is sufficient to consider the case where the input is a particular de Finetti-type state, i.e., a state which consists of n identical and independent copies of an (unknown) state on a single subsystem. Our technique can be applied to the analysis of information-theoretic problems. For example, in quantum cryptography, we get a simple proof for the fact that security of a discrete-variable quantum key distribution protocol against collective attacks implies security of the protocol against the most general attacks. The resulting security bounds are tighter than previously known bounds obtained with help of the exponential de Finetti theorem.

When n − k systems of an n-partite permutation-invariant state are traced out, the resulting state can be approximated by a convex combination of tensor product states. This is the quantum de Finetti theorem. In this paper, we show that an upper bound on the trace distance of this approximation is given by 2 kd 2 n , where d is the dimension of the individual system, thereby improving previously known bounds. Our result follows from a more general approximation theorem for representations of the unitary group. Consider a pure state that lies in the irreducible representation Uµ+ν ⊂ Uµ ⊗ Uν of the unitary group U(d), for highest weights µ, ν and µ + ν. Let ξµ be the state obtained by tracing out Uν. Then ξµ is close to a convex combination of the coherent states Uµ(g)|vµ , where g ∈ U(d) and |vµ is the highest weight vector in Uµ.For the class of symmetric Werner states, which are invariant under both the permutation and unitary groups, we give a second de Finetti-style theorem (our "half" theorem). It arises from a combinatorial formula for the distance of certain special symmetric Werner states to states of fixed spectrum, making a connection to the recently defined shifted Schur functions [1]. This formula also provides us with useful examples that allow us to conclude that finite quantum de Finetti theorems (unlike their classical counterparts) must depend on the dimension d. The last part of this paper analyses the structure of the set of symmetric Werner states and shows that the product states in this set do not form a polytope in general.

Abstract:The Quantum Reverse Shannon Theorem states that any quantum channel can be simulated by an unlimited amount of shared entanglement and an amount of classical communication equal to the channel's entanglement assisted classical capacity. In this paper, we provide a new proof of this theorem, which has previously been proved by Bennett, Devetak, Harrow, Shor, and Winter. Our proof has a clear structure being based on two recent information-theoretic results: one-shot Quantum State Merging and the Post-Selection Technique for quantum channels.