Perfect transfer of arbitrary states in quantum spin networks

Abstract

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].

Perfect state transfer: Beyond nearest-neighbor couplings

“…To minimise this scaling, we therefore want to choose a spectrum whose maximum eigenvalue is O(N ), and not O(N 2 ), for example. Note that the uniformly coupled chain has a spectrum λ k = 2 cos(kπ/ (N + 1)), which has a minimum spacing ∼ 1 N 2 for large N [3]. This minimum spacing corresponds to an upper bound to 1 t0 i.e.…”

“…Firstly, by assuming the Hamiltonian is spin preserving, [ σ z , H] = 0, the problem is reduced to subspaces, and we can concentrate only on the first excitation subspace [3]. By ensuring a single excitation is correctly transferred, a quantum state is also transferred because the state |00 .…”

“…This wire would be a chain of qubits, with a fixed interaction, capable of transferring a quantum state from one end of the chain to the other. Following the initial investigation of wires [1], and subsequent demonstration that perfect quantum wires exist [2,3], a large number of papers have been published about optimising the schemes over a variety of parameters such as the robustness against errors, or a restricted ability to engineer the state (see, for example, [4,5,6,7]). Novel modifications of such chains have also been presented for the generation of entangled states or the application of unitary operations during the transfer [8].…”

Quantum channels with memory

“…Recently, an unmodulated spin chain has been proposed as a model for short distance quantum communication [3,4,5,6]. In such a scheme, the state to be communicated over the channel is placed on one of the spins of the chain, propagates for a specific amount of time, and is then received at a distant spin of the chain (cf.…”

Noise effects in perfect transmission of quantum states

“…the stochastic process θ; the disturbances affecting the time-intervals between pulses, described by the process τ , can be similarly treated and will be briefly discussed at the end of the section. 4 In presence of correlations among pulses, the probability density P pulse (θ) can no longer be written as the product of independent probabilities as in (30). The simplest generalization of (30) involves joint probabilities with one-step correlations based on the conditional probabilities…”