Non-Perfect Propagation of Information to a Noisy Environment with Self-Evolution

Abstract

We study the non-perfect propagation of information for evolving a low-dimensional environment that includes self-evolution as well as noisy initial states and analyse the interrelations between the degree of objectivization and environment parameters. In particular, we consider an analytical model of three interacting qubits and derive its objectivity parameters. The numerical analysis shows that the quality of the spectrum broadcast structure formed during the interaction may exhibit non-monotonicity both in the speed of self-dynamics of the environment as well as its mixedness. The former effect is particularly strong, showing that—considering part of the environment as a measurement apparatus—an increase of the external magnetic field acting on the environment may turn the vague measurement into close to ideal. The above effects suggest that quantum objectivity may appear after increasing the dynamics of the environment, although not with respect to the pointer basis, but some other, which we call the generalized pointer or indicator basis. Furthermore, it seems also that, when the objectivity is poor, it may be improved, at least by some amount, by increasing the thermal noise. We provide further evidence of this by analysing the upper bounds on distance to the set of states representing perfect objectivity in the case of a higher number of qubits.

Quantum security and theory of decoherence

“…Now, let us use the above results to analyze a case of the environment consisting of N qubits. We follow the standard approach [16,90] and model the U (AE) interaction as N independent imperfect CNOT defined as…”

“…Thus, stating that the measuring device interacts with the environment via some interaction U (AE) is not restrictive. Next, we perform the calculations using a particular form of U (AE) used in [16,90]; we leave considerations with more general U (AE) as an important new engineering task of designing cryptographical devices in a way more secure against Van Eck's attacks. The considered form of the interaction U (EV) does not restrict the generality of our results, as it is sufficient for the trade-off relation to occur.…”