Quantum Weak Invariants: Dynamical Evolution of Fluctuations and Correlations

On Nonuniqueness of Quantum Channel for Fixed Input-Output States: Case of Decoherence Channel

For a fixed pair of input and output states in the space HA of a system A, a quantum channel, i.e., a linear, completely positive and trace-preserving map, between them is not unique, in general. Here, this point is discussed specifically for a decoherence channel, which maps from a pure input state to a completely decoherent state like the thermal state. In particular, decoherence channels of two different types are analyzed: one is unital and the other is not, and both of them can be constructed through reduction of B in the total extended space HA⊗HB, where HB is the space of an ancillary system B that is a replica of A. The nonuniqueness is seen to have its origin in the unitary symmetry in the extended space. It is shown in an example of a two-qubit system how such symmetry is broken in the objective subspace HA due to entanglement between A and B. A comment is made on possible relevance of the present work to nanothermodynamics in view of quantum Darwinism.

On the effect of decoherence on quantum tunnelling

This work proposes a series of quantum experiments that can, at least in principle, allow for examining microscopic mechanisms associated with decoherence. These experiments can be interpreted as a quantum-mechanical version of non-equilibrium mixing between two volumes separated by a thin interface. One of the principal goals of such experiments is in identifying non-equilibrium conditions when time-symmetric laws give way to time-directional, irreversible processes, which are represented by decoherence at the quantum level. The rate of decoherence is suggested to be examined indirectly, with minimal intrusions—this can be achieved by measuring tunnelling rates that, in turn, are affected by decoherence. Decoherence is understood here as a general process that does not involve any significant exchanges of energy and governed by a particular class of the Kraus operators. The present work analyses different regimes of tunnelling in the presence of decoherence and obtains formulae that link the corresponding rates of tunnelling and decoherence under different conditions. It is shown that the effects on tunnelling of intrinsic decoherence and of decoherence due to unitary interactions with the environment are similar but not the same and can be distinguished in experiments.