We analyze the class of single qubit channels with the environment modeled by a one-qubit mixed state. The set of affine transformations for this class of channels is computed analytically, employing the canonical form for the two-qubit unitary operator. We demonstrate that, 3 8 of the generalized depolarizing channels can be simulated by the one-qubit mixed state environment by explicitly obtaining the shape of the volume occupied by this class of channels within the tetrahedron representing the generalized depolarizing channels. Further, as a special case, we show that the twoPauli Channel cannot be simulated by a one-qubit mixed state environment.

We describe a new implementation of the Bernstein-Vazirani algorithm which relies on the fact that the polarization states of classical light beams can be cloned. We explore the possibility of computing with waves and discuss a classical optical model capable of implementing any algorithm (on n qubits) that does not involve entanglement. The Bernstein-Vazirani algorithm (with a suitably modified oracle), wherein a hidden n bit vector is discovered by one oracle query as against n oracle queries required classically, belongs to this category. In our scheme, the modified oracle is also capable of computing f (x) for a given x, which is not possible with earlier versions used in recent NMR and optics implementations of the algorithm.

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We investigate the effect of different types of non-unitary quantum channels on multi-qubit quantum systems. For an n-qubit system and a particular channel, in order to draw unbiased conclusions about the system as a whole as opposed to specific states, we evolve a large number of randomly generated states under the given channel. We increase the number of qubits and study the effect of system size on the decoherence processes. The entire scheme is repeated for various types of environments which include dephasing channel, depolarising channel, collective dephasing channel and zero temperature bath. Non-unitary channels representing the environments are modeled via their Karus operator decomposition or master equation approach. Further, for a given n we restrict ourselves to the study of particular subclasses of entangled states, namely the GHZ-type and W-type states. We generate random states within these classes and study the class behaviors under different quantum channels for various values of n.