Classical and quantum speed limits

The new bound on quantum speed limit (in terms of relative purity) is derived by applying the original Mandelstam-Tamm one to the evolution in the space of Hilbert-Schmidt operators acting in the initial space of states. It is shown that it provides the quantum counterpart of the classical speed limit derived in Phys. Rev. Lett. 120 (2018), 070402 and the ℏ→0 limit of the former yields the latter. The existence of classical limit is related to the degree of mixing of the quantum state.

A Unifying Coalgebraic Semantics Framework for Quantum Systems

As a quantum counterpart of labeled transition system (LTS), quantum labeled transition system (QLTS) is a powerful formalism for modeling quantum programs or protocols, and gives a categorical understanding for quantum computation. With the help of quantum branching monad, QLTS provides a framework extending some ideas in non-deterministic or probabilistic systems to quantum systems. On the other hand, quantum finite automata (QFA) emerged as a very elegant and simple model for resolving some quantum computational problems. In this paper, we propose the notion of reactive quantum system (RQS), a variant of QLTS capturing reactive system behavior, and develop a coalgebraic semantics for QLTS, RQS and QFA by an endofunctor on the category of convex sets, which has a final coalgebra. Such a coalgebraic semantics provides a unifying abstract interpretation for QLTS, RQS and QFA. The notions of bisimulation and simulation can be employed to compare the behavior of different types of quantum systems and judge whether a coalgebra can be behaviorally simulated by another.

Quantum Stochastic Products and the Quantum Convolution

A quantum stochastic product is a binary operation on the space of quantum states preserving the convex structure. We describe a class of associative stochastic products, the twirled products, that have interesting connections with quantum measurement theory. Constructing such a product involves a square integrable group representation, a probability measure and a fiducial state. By extending a twirled product to the full space of trace class operators, one obtains a Banach algebra. This algebra is commutative if the underlying group is abelian. In the case of the group of translations on phase space, one gets a quantum convolution algebra, a quantum counterpart of the classical phase-space convolution algebra. The peculiar role of the fiducial state characterizing each quantum convolution product is highlighted.

Otto Engine: Classical and Quantum Approach

In this paper, we analyze the total work extracted and the efficiency of the magnetic Otto cycle in its classic and quantum versions. As a general result, we found that the work and efficiency of the classical engine is always greater than or equal to its quantum counterpart, independent of the working substance. In the classical case, this is due to the fact that the working substance is always in thermodynamic equilibrium at each point of the cycle, maximizing the energy extracted in the adiabatic paths. We apply this analysis to the case of a two-level system, finding that the work and efficiency in both the Otto’s quantum and classical cycles are identical, regardless of the working substance, and we obtain similar results for a multilevel system where a linear relationship between the spectrum of energies of the working substance and the external magnetic field is fulfilled. Finally, we show an example of a three-level system in which we compare two zones in the entropy diagram as a function of temperature and magnetic field to find which is the most efficient region when performing a thermodynamic cycle. This work provides a practical way to look for temperature and magnetic field zones in the entropy diagram that can maximize the power extracted from an Otto magnetic engine.

A novel approach to quantum gravity in the presence of matter without the problem of time

An approach to the quantization of gravity in the presence of matter is examined which starts from the classical Einstein–Hilbert action and matter approximated by “point” particles minimally coupled to the metric. Upon quantization, the Hamilton constraint assumes the form of the Schrödinger equation: it contains the usual Wheeler–DeWitt term and the term with the time derivative of the wave function. In addition, the wave function also satisfies the Klein–Gordon equation, which arises as the quantum counterpart of the constraint among particles’ momenta. Comparison of the novel approach with the usual one in which matter is represented by scalar fields is performed, and shown that those approaches do not exclude, but complement each other. In final discussion it is pointed out that the classical matter could consist of superparticles or spinning particles, described by the commuting and anticommuting Grassmann coordinates, in which case spinor fields would occur after quantization.

Quantum Shannon theory with superpositions of trajectories

Shannon's theory of information was built on the assumption that the information carriers were classical systems. Its quantum counterpart, quantum Shannon theory, explores the new possibilities arising when the information carriers are quantum systems. Traditionally, quantum Shannon theory has focused on scenarios where the internal state of the information carriers is quantum, while their trajectory is classical. Here we propose a second level of quantization where both the information and its propagation in space–time is treated quantum mechanically. The framework is illustrated with a number of examples, showcasing some of the counterintuitive phenomena taking place when information travels simultaneously through multiple transmission lines.