M. Arsenijevic

A local-time-induced unique pointer basis

There is a solution to the problem of asymptotic completeness in many-body scattering theory that offers a specific view of the quantum unitary dynamics which allows for the straightforward introduction of local time for every, at least approximately closed, many-particle system. In this approach, time appears as a hidden classical parameter of the unitary dynamics of a many-particle system. We show that a closed many-particle system can exhibit behaviour that is characteristic for open quantum systems and there is no need for the ‘state collapse’ or environmental influence. On the other hand, closed few-particle systems bear high quantum coherence. This local-time scheme encompasses concepts including ‘emergent time’, ‘relational time’ as well as the ‘hybrid system’ models with possibly induced gravitational uncertainty of time.

Dynamical emergence of Markovianity in local time scheme.

Recently we pointed out the so-called local time scheme as a novel approach to quantum foundations that solves the preferred pointer-basis problem. In this paper, we introduce and analyse in depth a rather non-standard dynamical map that is imposed by the scheme. On the one hand, the map does not allow for introducing a properly defined generator of the evolution nor does it represent a quantum channel. On the other hand, the map is linear, positive, trace preserving and unital as well as completely positive, but is not divisible and therefore non-Markovian. Nevertheless, we provide quantitative criteria for dynamical emergence of time-coarse-grained Markovianity, for exact dynamics of an open system, as well as for operationally defined approximation of a closed or open many-particle system. A closed system never reaches a steady state, whereas an open system may reach a unique steady state given by the Lüders–von Neumann formula; where the smaller the open system, the faster a steady state is attained. These generic findings extend the standard open quantum systems theory and substantially tackle certain cosmological issues.

Generalized Kraus Operators for the One-Qubit Depolarizing Quantum Channel

Microscopic Hamiltonian models of the composite system “open system + environment” typically do not provide the operator-sum Kraus form of the open system’s dynamical map. With the use of a recently developed method (Andersson et al. J. Mod. Opt. 54, 1695 2007), we derive the Kraus operators starting from the microscopic Hamiltonian model, i.e., from the proper master equation, of the one-qubit depolarizing channel. Those Kraus operators generalize the standard counterparts, which are widely used in the literature. Comparison of the standard and the here obtained Kraus operators is performed via investigating dynamical change of the Bloch sphere volume, entropy production, and the open system’s state trace distance. We compare the generalized with the standard Kraus operators for both single qubit and regarding the occurrence of the entanglement sudden death for a pair of initially correlated qubits. We find that the generalized Kraus operators describe the less deteriorating quantum channel than the standard ones.

Kraus Operators for a Pair of Interacting Qubits: a Case Study

The Kraus form of the completely positive dynamical maps is appealing from the mathematical and the point of the diverse applications of the open quantum systems theory. Unfortunately, the Kraus operators are poorly known for the two-qubit processes. In this paper, we derive the Kraus operators for a pair of interacting qubits, while the strength of the interaction is arbitrary. One of the qubits is subjected to the x-projection spin measurement. The obtained results are applied to calculate the dynamics of the entanglement in the qubits system. We obtain the loss of the correlations in the finite time interval; the stronger the inter-qubit interaction, the longer lasting entanglement in the system.

Complete Positivity on the Subsystems Level

We provide a conceptually clear and technically simple presentation of certain subtleties of the concept of complete positivity of the quantum dynamical maps. The presentation is performed by addressing complete positivity of dynamics of certain subsystems of an open composite system, which is subject of a completely positive map. We prove that every subsystem of a composite open system can be subject of a completely positive dynamics if and only if the initial state of the composite open system is tensor-product of the initial states of the subsystems. A general algorithm for obtaining the Kraus form for a subsystem’s dynamical map is designed for the finite-dimensional systems. As an illustrative example we consider a pair of mutually interacting qubits.

A minimalist approach to conceptualization of time in quantum theory

Abstract Ever since Schrodinger, Time in quantum theory is postulated Newtonian for every reference frame. With the help of certain known mathematical results, we show that the concept of the so-called Local Time allows avoiding the postulate. In effect, time appears as neither fundamental nor universal on the quantum-mechanical level while being consistently attributable to every, at least approximately, closed quantum system as well as to every of its (conservative or not) subsystems.