Practically state-independent test of contextuality with 9 observables

We propose a test of quantum contextuality for a single three-level system that uses nine projective measurements. It has a form of an inequality that has to be satisfied by any non-contextual theory and which is violated by any quantum state, except for the maximally mixed one. Due to the fact that there is only a single state that does not exhibit contextuality, it is natural to ask what the difference between state-independent tests and the one proposed here is.Comment: 3 pages, 1 figur

Information processing in biological molecular machines

Biological molecular machines are bi-functional enzymes that simultaneously catalyze two processes: one providing free energy and second accepting it. Recent studies show that most protein enzymes have a rich dynamics of stochastic transitions between the multitude of conformational substates that make up their native state. It often manifests in fluctuating rates of the catalyzed processes and the presence of short-term memory resulting from the preference of selected conformations. For any stochastic protein machine dynamics we proved a generalized fluctuation theorem that leads to the extension of the second law of thermodynamics. Using them to interpret the results of random walk on a complex model network, we showed the possibility of reducing free energy dissipation at the expense of creating some information stored in memory. The subject of our analysis is the time course of the catalyzed processes expressed by sequences of jumps at random moments of time. Since similar signals can be registered in the observation of real systems, all theses of the paper are open to experimental verification. From a broader physical point of view, the division of free energy into the operation and organization energies is worth emphasizing. Information can be assigned a physical meaning of a change in the value of both these functions of state.Comment: The manuscript contains 14 pages, 7 figure