We analyse dissipation in quantum computation and its destructive impact on efficiency of quantum algorithms. Using a general model of decoherence we study the time evolution of a quantum register of arbitrary lenght coupled with an environment of arbitrary coherence lenght. We discuss relations between decoherence and computational complexity and show that the quantum factorisation algorithm must be modified in order to be regarded as efficient and realistic.

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We show that entanglement is a useful resource to enhance the mutual information of the depolarizing channel when the noise on consecutive uses of the channel has some partial correlations. We obtain a threshold in the degree of memory, depending on the shrinking factor of the channel, above which a higher amount of classical information is transmitted with entangled signals.The classical capacity of quantum channels, i.e. the amount of classical information which can be reliably transmitted by quantum states in the presence of a noisy environment has received renewed interest in recent years [1]. One of the main focuses of such interest is the study of entanglement as a useful resource to enhance the classical channel capacity. Although the theory does not rule this possibility out, the search for superaddivity of quantum channels has led sofar to the evidence that no such property is present in memoryless channels. This has been first proved analytically for the case of two entangled uses of the depolarizing channel [2] and then extended to a broader class of memoryless channels [3]. In this paper we will turn our attention to a different class of channels, namely to channels with partial memory. For such channels our results show that a higher mutual information can indeed be achieved above a certain memory threshold by entangling two consecutive uses of the channel. In the following each use of the channel will be a qubit, i.e will be a quantum state belonging to a twodimensional Hilbert space. The action of transmission channels is described by Kraus operators[4] A i , satisfying i A † i A i = 1l, such that if we send through the channel a qubit in a state described by the density operator π the corresponding output state is given by the mapAn interesting class of Kraus operators acting on individual qubits can be expressed in terms of the Pauli operators σ x,y,zwith i p i = 1 , i = 0, x, y, z and σ 0 = 1l. A noise model for these actions is for instance the application of a random rotation of the angle π around axisx,ŷ,ẑ with probability p x , p y , p z and the identity with probability p 0 .In the simplest scenario the transmitter can send one qubit at a time along the channel. In this case the codewords will be restricted to be the tensor products of the states of the individual qubits. Quantum mechanics however allows also the possibility to entangle multiple uses of the channel. For this more general strategy it has been shown that the amount of reliable information which can be transmitted per use of the channel is given by [1]where E = {P i , π i } with P i ≥ 0, P i = 1 is the input ensemble of states π i , transmitted with a priori probabilities P i , of n -generally entangled -qubits and I n (E) is the mutual information

We study the dynamics of quantum correlations in a class of exactly solvable Ising-type models. We analyze in particular the time evolution of initial Bell states created in a fully polarized background and on the ground state. We find that the pairwise entanglement propagates with a velocity proportional to the reduced interaction for all the four Bell states. Singlet-like states are favored during the propagation, in the sense that triplet-like states change their character during the propagation under certain circumstances. Characteristic for the anisotropic models is the instantaneous creation of pairwise entanglement from a fully polarized state; furthermore, the propagation of pairwise entanglement is suppressed in favor of a creation of different types of entanglement. The "entanglement wave" evolving from a Bell state on the ground state turns out to be very localized in space-time. Further support to a recently formulated conjecture on entanglement sharing is given.