Open Systems & Information Dynamics

We present the geometry of pure states of an ensemble of N spin-J systems using a generalisation of the Majorana representation. The approach is based on Schur-Weyl duality that allows for simple interpretation of the state transformation under the action of general linear and permutation groups. We show an exemplary application in the theory of decoherence-free subspaces and noiseless subsystems.

Quantum state transfer is a procedure, which allows to exchange quantum information between stationary qubit systems. It is anticipated that the transfer will find applications in solid-state quantum computing. In this contribution, we discuss the effects of various, physically relevant models of decoherence on a toy model of six qubit linearly coupled by the exchange interaction. In many cases we observe the advantage of the two-qubit encoding, which can be associated with the fact that this encoding does not require the state initialization.

By using an appropriate one-mode type interacting Fock spaces, , introduced in [1], we define a nuclear triple of test and generalized functions, with θ being a suitable Young function. Moreover, we prove general characterization theorems for the fundamental nuclear spaces. For the applications, we introduce new renormalized products for the generators of the renormalized higher powers of white noise ⋆-Lie algebra and the Virasoro-Zamolodchikov-w_∞ ⋆-Lie algebra. Then we show that these new renormalized products lead to nuclear realizations of these Lie algebras in terms of quantum Meixner white noise operators.

One of the main activities of the brain is the recognition of signals. As it was pointed out in [22, 25] the procedure of recognition can be described as follows: There is a set of complex signals stored in the memory. Choosing one of these signals may be interpreted as generating a hypothesis concerning an "expected view of the world". Then the brain compares a signal arising from our senses with the signal chosen from the memory. That changes the state of both signals in such a manner that after the procedure the signals coincide in a certain sense. Furthermore, measurements of that procedure like EEG or MEG are based on the fact that recognition of signals causes a certain loss of excited neurons, i.e. the neurons change their state from "excited" to "nonexcited". For that reason a statistical model of the recognition process should reflect both — the change of the signals and the loss of excited neurons. Now, [5] represents the first attempt to explain the process of recognition in terms of quantum statistics. According to the general conception of quantum theory, the procedure of recognition should be described by an operator on a certain Hilbert space. In [5] we proposed two candidates for such an operator. One of them reflects in a clear sense the mentioned change of the signals. The other one reflects the loss of excited neurons. We will prove (cf. Theorem 4) that for sufficiently high intensities of the signals both operators are approximately equal.

A recent method for causal discovery is in many cases able to infer whether X causes Y or Y causes X for just two observed variables X and Y. It is based on the observation that there exist (non-Gaussian) joint distributions P(X,Y) for which Y may be written as a function of X up to an additive noise term that is independent of X and no such model exists from Y to X. Whenever this is the case, one prefers the causal model X → Y. Here we justify this method by showing that the causal hypothesis Y → X is unlikely because it requires a specific tuning between P(Y) and P(X|Y) to generate a distribution that admits an additive noise model from X to Y. To quantify the amount of tuning, needed we derive lower bounds on the algorithmic information shared by P(Y) and P(X|Y). This way, our justification is consistent with recent approaches for using algorithmic information theory for causal reasoning. We extend this principle to the case where P(X,Y)almost admits an additive noise model. Our results suggest that the above conclusion is more reliable if the complexity of P(Y) is high.