Three questions on the future of quantum science and technology
The answers on the current status and future development of Quantum Science and Technology are presented.
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arXiv subjects
M. Dugic
Publications and source records attributed to M. Dugic.
Entropy dynamics for a harmonic propeller-shaped planar molecular quantum Brownian rotator
Dynamic stability is vital for the operation and control of molecular nanodevices, particularly molecular cogwheels in an external harmonic field. We used the relative change in rotator entropy as a measure of dynamical stability. This rotator dynamic is described by the Caldeira-Leggett quantum master equation: the main challenge is the absence of a general solution for this equation. As an alternative, we look for the initial states (pure or mixed) of the rotator that result in low entropy change. In order to create candidate initial states, we use an ansatz that align with the maximum entropy principle. We then find conditions for state preparation and system/bath parameters to achieve a small relative change in both linear and differential entropy in underdamped and non-underdamped regimes. We identify cases with relatively small entropy change and discuss their practical feasibility.
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Macroscopic quantum distinguishablity, identity and irreversibility
The basic characteristics of the classical many-particle (''macroscopic'') systems are notoriously hard to reproduce in quantum theory. In this paper we show that this is not the case for certain many-particle systems within the recently introduced theory of emergent local quantum times, the so-called, Local Time Scheme. For an isolated many-particle system consisting of large number of (approximately) isolated subsystems, distinguishability and individuality can be naturally and straightforwardly obtained. In effect, a single such many-particle system quickly evolves between the mutually approximately orthogonal states thus setting a trajectory in the state space that is not shared with any other such individual many-particle system. Irreversibility of such dynamical processes is justified for the individual systems but not for the statistical ensembles of such systems. As an application, we derive a genuine nonexponential law for decay of unstable systems, in accordance with some theoretical expectations. This, classically plausible, picture calls for detailed analysis regarding the relativistic causality and cosmological contexts.
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Is there any reasonable dynamics for quantum subsystems within the unitary-only quantum theory?
The foundational studies of the standard, unitary-only quantum theory revolve around the kinematical aspects of quantum entanglement and the improper quantum mixtures. In this paper, we introduce and argue for the foundational character of the question of dynamics of quantum subsystems (open quantum systems). In this context, for some typical and physically relevant Markovian processes, we technically prove non-existence of trajectories in the Hilbert state space of the open system. As a kind of no-go theorem for the unitary-only quantum theory, this finding suggests that the mixed quantum states may be joined to the individual (single) quantum subsystem dynamically described by the corresponding master equation. Then the problem of interpretation of improper mixtures dissolves while description of quantum measurement boils down to the problem of reduction of the mixed to the pure states-i.e. to the problem of actualization of definite values of certain observables of the single open systems, thus tackling the mathematical problem of interpreting probability for the single trials of an experiment. This kind of indeterminism may be the furthest we can go within the dynamical approach to quantum subsystems. As an alternative appears the possibility that the idea of dynamics of quantum subsystems may not be viable in the context of the unitary-only theory. As a direct consequence of our main finding appears the a priori impossibility to define "quantum history" in the Hilbert state space for the considered Markovian models.
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Complete positivity on the subsystems level
We consider complete positivity of dynamics regarding subsystems of an open composite quantum system, which is subject of a completely positive dynamics. By "completely positive dynamics", we assume the dynamical maps called the completely positive and trace preserving maps, with the constraint that domain of the map is the whole Banach space of the system's density matrices. We provide a technically simple and conceptually clear proof for the subsystems' completely positive dynamics. Actually, 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. An algorithm for obtaining the Kraus form for the subsystem's dynamical map is provided. As an illustrative example we consider a pair of mutually interacting qubits. The presentation is performed such that a student with the proper basic knowledge in quantum mechanics should be able to reproduce all the steps of the calculations.
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Axiomatic quantum mechanics: Necessity and benefits for the physics studies
The ongoing progress in quantum theory emphasizes the crucial role of the very basic principles of quantum theory. However, this is not properly followed in teaching quantum mechanics on the graduate and undergraduate levels of physics studies. The existing textbooks typically avoid the axiomatic presentation of the theory. We emphasize usefulness of the systematic, axiomatic approach to the basics of quantum theory as well as its importance in the light of the modern scientific-research context.
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A minimalist approach to conceptualization of time in quantum theory
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.
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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 analyze in depth a rather non-standard dynamical map that is imposed by the scheme. On 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, while an open system may reach a unique steady state given by the L\" uders-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.
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A top-down versus a bottom-up hidden-variables description of the Stern-Gerlach experiment
We employ the Stern-Gerlach experiment to highlight the basics of a minimalist, non-interpretational top-down approach to quantum foundations. Certain benefits of the here highlighted "quantum structural studies" are detected and discussed. While the top-down approach can be described without making any reference to the fundamental structure of a closed system, the hidden variables theory ?a la Bohm proves to be more subtle than it is typically regarded.
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Entanglement Relativity in the Foundations of The Open Quantum Systems Theory
Realistic many-particle systems dynamically exchange particles with their environments. In classical physics, small variations in the number of constituent particles are commonly considered practically irrelevant. However, in the quantum mechanical context, such and similar structural variations are generically taxed due to the so-called Entanglement Relativity. In this paper we point out difficulties in deriving master equation for a subsystem of an alternative partition of the closed quantum system. We find that the Nakajima-Zwanzig projection method cannot be straightforwardly used to solve the problem. The emerging tasks and prospects for the consistent foundations are examined.
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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 behavior 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.
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Quantum Structures of the Hydrogen Atom
Modern quantum theory introduces quantum structures (decompositions into subsystems) as a new discourse that is not fully comparable with the classical-physics counterpart. To this end, so-called Entanglement Relativity appears as a corollary of the universally valid quantum mechanics that can provide for a deeper and more elaborate description of the composite quantum systems. In this paper we employ this new concept to describe the hydrogen atom. We offer a consistent picture of the hydrogen atom as an open quantum system that naturally answers the following important questions: (a) how do the so called "quantum jumps" in atomic excitation and de-excitation occur? and (b) why does the classically and seemingly artificial "center-of-mass + relative degrees of freedom" structure appear as the primarily operable form in most of the experimental reality of atoms?
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Classicality from zero discord for continuous-variables bipartite systems
Quantum information resources quantified by non-zero discord are ubiquitous for the continuous-variables bipartite systems. Complementary to this, we formally construct a model characterized by zero two-way discord for arbitrarily long time interval. The model is classical in the sense it does not support quantum information processing. We point out some interesting physical features of the model.
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Quantum Structures of a Model-Universe: An Inconsistency with Everett Interpretation of Quantum Mechanics
We observe a Quantum Brownian Motion (QBM) Model Universe in conjunction with recently established Entanglement Relativity and Parallel Occurrence of Decoherence. The Parallel Occurrence of Decoherence establishes the simultaneous occurrence of decoherence for two mutually irreducible structures (decomposition into subsystems) of the total QBM model universe. First we find that Everett world branching for one structure excludes branching for the alternate structure and in order to reconcile this situation branching cannot be allowed for either of the structures considered. Second, we observe the non-existence of a third, "emergent structure", that could approximate both structures and also be allowed to branch. Ultimately we find unless world-branching requires additional criteria or conditions, or there is a privileged structure, that we provide a valid model that cannot be properly described by the Everett Interpretation of Quantum Mechanics.
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A Limitation of the Nakajima-Zwanzig projection method
There is current interest in dynamical description of dif- ferent decompositions of a quantum system into subsystems. We investi- gate usefulness of the Nakajima-Zwanzig projection method in this context. Particularly, we are interested in simultaneous description of dynamics of open systems pertaining to dierent system-environment splits (decompo- sitions). We find that the Nakajima-Zwanzig and related projection meth- ods are system-environment split specific, that every system-environment split requires specific projector, and that projector adapted to a split nei- ther provides information about nor commute with a projector adapted to an alternative system-environment split. Our findings refer to finite- and infinite-dimensional systems and to arbitrary kinds of system-environment splitting. These findings are a direct consequence of the recently established quantum correlations relativity. We emphasize the subtlety and delicacy re- quired of the task of simultaneously describing the dynamics of alternate system-environment splits.
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Delayed choice without choice
A critical note on some of the existing proposals for performing the "delayed choice" experiment is placed. By abandoning the original idea and intention, some modern theoretical proposals and experimental evidence are simply incorrectly understood/interpreted. In effect, the Complementarity principle remains practically intact.
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The "Ghostly" Quantum Worlds
We present the foundations of a new emerging interpretation of quantum theory bearing wide-range implications. Physical basis of the interpretation is non-questionable yet relatively new--it relies on the different structures (decompositions into parts, subsystems) of the quantum Universe. We compare the mutually irreducible structures of the Universe and recognize them as the different facets of the one and the same quantum Universe. Physical picture is interesting and non-reducible to the existing interpretations. As a particularly interesting topic in this context appears the 'free will' topic of current interest in the interpretation of quantum theory. To this end, we arrive at the following interesting observation. The freely chosen actions (e.g. quantum measurements) performed by a (conscious) agent that are still locally observable in the alternate Worlds could seem physically unexplainable ('non-physical', 'ghostly').
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Asymptotic dynamics of the alternate degrees of freedom for a two-mode system: an analytically solvable model
The composite systems can be non-uniquely decomposed into parts (subsystems). Not all decompositions (structures) of a composite system are equally physically relevant. In this paper we answer on theoretical ground why it may be so. We consider a pair of mutually un-coupled modes in the phase space representation that are subjected to the independent quantum amplitude damping channels. By investigating asymptotic dynamics of the degrees of freedom, we find that the environment is responsible for the structures non-equivalence. Only one structure is distinguished by both locality of the environmental in uence on its subsystems and a classical-like description.
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