Decoherence in the space of quantum operations: How to coherify a classical map?

Abstract: The theory of quantum information processing meets experiment: in view of the emerging field of quantum technologies future theoretical studies will be closer linked to the physical world by considering more realistic systems and putting even more emphasis on interaction of the system in question with environment and the effect of quantum decoherence. In this talk I will shortly review the standard notion of decoherence and its formal inverse: coherification of a classical probability vector denotes the search of all its preimages with respect to the coarse graining channel, which induces the decoherence. A similar problem can also be posed for channels: For a given classical map corresponding to a stochastic transition matrix T we look for quantum channel Φ, which induces the same classical transition matrix T, but is “more coherent”. To quantify the coherence of a channel Φ we measure the coherence of the corresponding Jamio kowski state J_Φ. We show that a classical transition matrix T can be coherified to a reversible unitary dynamics if and only if T is unistochastic. Otherwise the Jamio kowski state J_Φ of the optimally coherified channel is mixed, and the dynamics must necessarily be irreversible.

 

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