Search Results (5)

Many of the most fundamental observables—position, momentum, phase point, and spin direction—cannot be measured by an instrument that obeys the orthogonal projection postulate. Continuous-in-time measurements provide the missing theoretical framework to make physical sense of such observables. The elements of the time-dependent instrument define a group called the instrumental group (IG). Relative to the IG, all of the time dependence is contained in a certain function called the Kraus-operator density (KOD), which evolves according to a classical Kolmogorov equation. Unlike the Lindblad master equation, the KOD Kolmogorov equation is a direct expression of how the elements of the instrument (not just the total quantum channel) evolve. Shifting from continuous measurements to sequential measurements more generally, the structure of combining instruments in sequence is shown to correspond to the convolution of their KODs. This convolution promotes the IG to an involutive Banach algebra (a structure that goes all the way back to the origins of POVM and C*-algebra theory), which will be called the instrumental group algebra (IGA). The IGA is the true home of the KOD, similar to how the dual of a von Neumann algebra is the true home of the density operator. Operators on the IGA, which play the analogous role for KODs as superoperators play for density operators, are called ultraoperators and various important examples are discussed. Certain ultraoperator–superoperator intertwining relationships are also considered throughout, including the relationship between the KOD Kolmogorov equation and the Lindblad master equation. The IGA is also shown to have actually two distinct involutions: one respected by the convolution ultraoperators and the other by the quantum channel superoperators. Finally, the KOD Kolmogorov generators are derived for jump processes and more general diffusive processes. Full article

Since a 1932 work from von Neumann, it has been considered that if two statistical mixtures are represented by the same density operator $\rho$, they should, in fact, be considered as the same mixture. In a 1970 paper, Zeh introduced a thought experiment with neutron spins, and suggested that, in that experiment, the density operator could not tell the whole story. Since then, no consensus has emerged yet, and controversies on the subject still presently develop. In his 1995 book, speaking of the use of the density operator, Peres spoke of a von Neumann postulate. In this paper, keeping the random variable used by von Neumann in his treatment of statistical mixtures, but also considering higher-order moments of this random variable, it is established that the two mixtures imagined by Zeh, with the same $\rho$, should however be distinguished. We show that the rejection of that postulate, installed on statistical mixtures for historical reasons, does not affect the general use of $\rho$, e.g., in quantum statistical mechanics, and the von Neumann entropy keeps its own interest and even helps clarifying that confusing consequence of the postulate identified by Peres. Full article

Quantum information mobilizes the description of quantum systems, their states, and their behavior. Since a measurement postulate introduced by von Neumann in 1932, if a quantum system has been prepared in two different mixed states represented by the same density operator $\rho ,$ these preparations are said to have led to the same mixture. For more than 50 years, there has been a lack of consensus about this postulate. In a 2011 article, considering variances of spin components, Fratini and Hayrapetyan tried to show that this postulate is unjustified. The aim of the present paper is to discuss major points in this 2011 article and in their reply to a 2012 paper by Bodor and Diosi claiming that their analysis was irrelevant. Facing some ambiguities or inconsistencies in the 2011 paper and in the reply, we first try to guess their aim, establish results useful in this context, and finally discuss the use or misuse of several concepts implied in this debate. Full article

Neuromorphic computing offers a promising solution to overcome the von Neumann bottleneck, where the separation between the memory and the processor poses increasing limitations of latency and power consumption. For this purpose, a device with analog switching for weight update is necessary to implement neuromorphic applications. In the diversity of emerging devices postulated as synaptic elements in neural networks, RRAM emerges as a standout candidate for its ability to tune its resistance. The learning accuracy of a neural network is directly related to the linearity and symmetry of the weight update behavior of the synaptic element. However, it is challenging to obtain such a linear and symmetrical behavior with RRAM devices. Thus, extensive research is currently devoted at different levels, from material to device engineering, to improve the linearity and symmetry of the conductance update of RRAM devices. In this work, the experimental results based on different programming pulse conditions of RRAM devices are presented, considering both voltage and current pulses. Their suitability for application as analog RRAM-based synaptic devices for neuromorphic computing is analyzed by computing an asymmetric nonlinearity factor. Full article

This work considers reasons for and implications of discarding the assumption of transitivity—the fundamental postulate in the utility theory of von Neumann and Morgenstern, the adiabatic accessibility principle of Caratheodory and most other theories related to preferences or competition. The examples of intransitivity are drawn from different fields, such as law, biology and economics. This work is intended as a common platform that allows us to discuss intransitivity in the context of different disciplines. The basic concepts and terms that are needed for consistent treatment of intransitivity in various applications are presented and analysed in a unified manner. The analysis points out conditions that necessitate appearance of intransitivity, such as multiplicity of preference criteria and imperfect (i.e., approximate) discrimination of different cases. The present work observes that with increasing presence and strength of intransitivity, thermodynamics gradually fades away leaving space for more general kinetic considerations. Intransitivity in competitive systems is linked to complex phenomena that would be difficult or impossible to explain on the basis of transitive assumptions. Human preferences that seem irrational from the perspective of the conventional utility theory, become perfectly logical in the intransitive and relativistic framework suggested here. The example of competitive simulations for the risk/benefit dilemma demonstrates the significance of intransitivity in cyclic behaviour and abrupt changes in the system. The evolutionary intransitivity parameter, which is introduced in the Appendix, is a general measure of intransitivity, which is particularly useful in evolving competitive systems. Full article