We show the transition from a fully quantized interaction to a semiclassical one in entangled small number quantum systems using the quantum trajectories approach. In particular, we simulate the microwave Ramsey zones used in Rydberg atom interferometry, filling in the gap between the strongly entangling Jaynes Cummings evolution and the semiclassical rotation of the atomic internal states. We also correlate the information flowing with leaking photons to the entanglement generation between cavity field and flying atom and detail the roles played by the strong dissipation and the external driving force in preserving atomic coherence through the interaction.
Many non-classicality indicators are used to measure quantum effects of different systems. Kenfack's and Sadeghi's non-classicality indicators are introduced in terms of the amount of Wigner function's negativities and interferences in phase space quantum mechanics, respectively. They are, effectively, applied for some real distribution functions. In this paper, we compared these non-classicality indicators for the entangled state of photonic number states in the Wigner, Husimi and Rivier representations. It is shown that for a two-level entangled state, Sadeghi's indicator has more benefits w…
In the past ten-fifteen years, stochastic models of continuous wave function collapse were being proposed to describe the continuous emergence of classicality from quantum. We advocate that the hybrid dynamics of canonically coupled quantum and classical systems is a more basic concept. Continuous collapse formalisms are obtained as special cases. To illustrate our claim we show how von Neumann collapse follows from hybrid dynamical equations.
Can the computational complexity theory of computer science and mathematics say something new about unresolved problems in quantum physics? Particularly, can the P versus NP question in the computational complexity theory be a factor in the elucidation of the emergency of classicality in quantum mechanics? The paper compares two different ways of deriving classicality from the quantum formalism resulted from two differing hypotheses regarding the P versus NP question -- the approach of the quantum decoherence theory implying that P = NP and the computational complexity approach which assumes t…
In this paper, We investigate three-mode photon-added Greenberger-Horne-Zeilinger (GHZ) entangled coherent states by repeatedly operating the photon-added operator on the GHZ entangled coherent states. The product of two Laguerre polynomials is demonstrated to be connected to the normalizing constant. The influence of the operation on the non-classical and non-Gaussian behavior of the GHZ entangled coherent states is investigated. Sub-Poissonian statistics, such as Mandel's parameter and the negativity of the Wigner function, show that non-classical properties can enhance GHZ entangled coheren…
In this article, non-classical properties of Raman modes are investigated. The original goal, actually, is to identify how and by which method we can induce non-classicality in Raman modes. We introduce a plasmonic system in which Raman dye molecules are buried between two shells of the plasmonic materials similar to onion-like core/shell nanoparticle. This system is excited by the entangled photons, followed by analyzing its dynamics of motion using the Heisenberg-Langevin equations by which the time evolution of the signal-idler mode and Raman modes are derived. Interestingly, the entangled …
A unified formalism was developed in [S. Adhikary et. al., arXiv:1710.04371 [quant-ph]], for describing non-classicality of states by introducing pseudo projection operators in which both quantum logic and quantum probability are naturally embedded. In this paper we show, as the first practical application, how non-locality and entanglement emerge as two such important manifestations. It provides a perspective complementary to (i) the understanding of them that we have currently (in terms of LHV models) and (ii) to the algebraic approaches employed. The work also makes it possible to obtain, i…
We discuss the emergence of classical trajectories in Bohmian Mechanics (BM), when a macroscopic object interacts with an external environment. We show that in such a case the conditional wave function of the system follows a dynamics which, under reasonable assumptions, corresponds to that of the Ghirardi-Rimini-Weber (GRW) collapse model. As a consequence, Bohmian trajectories evolve classically. Our analysis also shows how the GRW (istantaneous) collapse process can be derived by an underlying continuous interaction of a quantum system with an external agent, thus throwing a light on how co…
We consider temporal correlations of particles with arbitrary spin. We show that the Leggett-Garg inequality can be maximally violated irrespective of the value of spin, thus improving upon an earlier result by Kofler and Brukner [Phys. Rev. Lett. \textbf{99}, 180403 (2007)]. Our proof is accomplished through a suitable adoption of a measurement scheme which has previously been employed for studying the spatial correlation in a system with arbitrary spin. We next consider generalized or unsharp measurements as a method for coarse graining in a quantitative manner, and show that classicality em…
One of the most striking features of quantum theory is the existence of entangled states, responsible for Einstein's so called "spooky action at a distance". These states emerge from the mathematical formalism of quantum theory, but to date we do not have a clear idea of the physical principles that give rise to entanglement. Why does nature have entangled states? Would any theory superseding classical theory have entangled states, or is quantum theory special? One important feature of quantum theory is that it has a classical limit, recovering classical theory through the process of decoheren…
Maximally predictive states, as defined in recent work by Zurek, Habib and Paz, are studied for more elaborate environment models than a linear coupling. An environment model which includes spatial correlations in the noise is considered in the non-dissipative regime. The Caldeira-Leggett model is also reconsidered in the context of an averaging procedure which produces a completely positive form for the quantum master equation. In both cases, the maximally predictive states for the harmonic oscillator are the coherent states, which is the same result found by Zurek,Habib and Paz for the Calde…
The discrepancy between maximally entangled states and maximally non-classical quantum correlations is well-known but still not well understood. We aim to investigate the relation between quantum correlations and entanglement in a family Bell inequalities with $N$-settings and $d$ outcomes. Using analytical as well as numerical techniques, we derive both maximal quantum violations and violations obtained from maximally entangled states. Furthermore, we study the most non-classical quantum states in terms of their entanglement entropy for large values of $d$ and many measurement settings. Inter…
An explicit dynamical model for non relativistic quantum mechanics with an effective gravitational interaction is proposed, which, as being well defined, allows in principle for the evaluation of every physical quantity. Its non unitary dynamics results from a unitary one in a space with twice as many degrees of freedom as the ordinary ones. It exhibits a threshold for the emergence of classical behavior for bodies of ordinary density on rather long times or instantaneously, respectively at around 10^11 or 10^20 proton masses.
We describe a set of measurement protocols for performing non-classicality tests and the verification of entangled superposition states of macroscopic continuous variable systems, such as nanomechanical resonators. Following earlier works, we first consider a setup where a two-level system is used to indirectly probe the motion of the mechanical system via Ramsey measurements and discuss the application of this methods for detecting non-classical mechanical states. We then show that the generalization of this techniques to multiple resonator modes allows the conditioned preparation and the det…
With the emerging possibility to obtain emissions of triples of GHZ-entangled photons via a direct parametric generation we study here bright emissions of this kind which involve higher order emissions of two triples, three triples, etc. Such states would constitute a natural generalization of the four mode (two beams plus polarization) squeezed vacuum. We have three beam process of emission generalized bright GHZ states, which a are superpositions of one, two, three, and so on GHZ entangled triples of photons. We show how to avoid technical difficulties related with straight ahead generalizat…
The origin of classical reality in our quantum world is a long-standing mystery. Here, we examine a nitrogen vacancy center evolving naturally in the presence of its environment to study quantum Darwinism - the proliferation of information about preferred quantum states throughout the world via the environment. This redundantly imprinted information accounts for the perception of objective reality, as it is independently accessible by many without perturbing the system of interest. To observe the emergence of redundant information, we implement a novel dynamical decoupling scheme that enables …
Regarding the limit hbar-->0 as the classical limit of quantum mechanics seems to be silly because hbar is a definite constant of physics, but it was successfully used in the derivation of the WKB approximation. A superseded version of the WKB approximation is proposed in the classical limit alpha-->0 where alpha=m/M is the screening parameter of an object in which m is the mass of the effective screening layer and M the total mass. This version is applicable to not only approximate solution of Schrodinger equation of a quantum particle but also that of a nanoparticle. Moreover, the version sh…
We consider the claim that decoherence explains the emergence of classicality in quantum systems, and conclude that it does not. We show that, given a randomly chosen universe composed of a variety of subsystems, some of which are macroscopic and subject to decoherence-inducing interactions, and some of which are microscopic, the macroscopic subsystems will not display any distinctively classical behavior. Therefore, a universe in which macroscopic and microscopic do display distinct behavior must be in a very special, highly nongeneric quantum state.
Emergence of classicality from quantum mechanics, a hotly debated topic, has had no satisfactory resolution so far. Various approaches including decoherence and gravitational interactions have been suggested. In the present work, the Schrödinger-Newton model is used to study the role of semi-classical self-gravity in the evolution of massive spin-1/2 particles in a Stern-Gerlach experiment. For small mass, evolution of the initial wavepacket in a spin superposition shows a splitting in the magnetic field gradient into two trajectories as in the standard Stern-Gerlach experiment. For larger mas…
In a series of comments, Bonder et al. criticized our work on decoherence due to time dilation [Nature Physics 11, 668-672 (2015)]. First the authors erroneously claimed that our results contradict the equivalence principle, only to "resolve" the alleged conflict in a second note. The resolution - relativity of simultaneity - was already explained in our reply [arXiv:1508.03296], which Bonder et al. now essentially reiterate. The newly raised points were also already extensively clarified in our note. The physical prediction of our work remains valid: systems with internal dynamics decohere if…
According to the so-called ``Quantum Darwinist'' approach, the emergence of ``classical islands'' from a quantum background is assumed to obey a (selection) principle of maximal information. We illustrate this idea by considering the coupling of two particles that interact through a position-dependent potential. This approach sheds a new light on the emergence of classical logics and of our classical preconceptions about the world. The distinction between internal and external world, the Cartesian prejudice according to which the whole can be reduced to the sum of its parts and the appearance …
We have studied the emergence of classical states in the perturbative interaction model. The states which interact with many other degrees of freedom, such as the center of mass of a macro-object, play important role. Although the random phase mechanism is effective as same as Zurek's strong correlation model, there are enormous states, each of which independently developes due to the orthogonality of the environmental states. In these privileged states, the subsystem picture with the separability is stable.
There have been recent attempts at justifying, from first principles, and within the standard framework, the emergence of classical behavior in the post-inflationary cosmological context. Accounting for this emergence is an important issue, as it underlies the extraordinary empirical success of our current understanding of cosmology. In this work, we offer a critique of different efforts at explaining the emergence of classical behavior in cosmology within the standard framework. We argue that such endeavors are generically found lacking in conceptual clarity, as they invariably rely, either u…
Zurek, Habib and Paz [W. H. Zurek, S. Habib and J. P. Paz, Phys. Rev. Lett. {\bf 70} (1993)\ 1187] have characterized the set of states of maximal stability defined as the set of states having minimum entropy increase due to interaction with an environment, and shown that coherent states are maximal for the particular environment model examined. To generalize these results, I consider entropy production within the Lindblad theory of open systems, treating environment effects perturbatively. I characterize the maximally predicitive states which emerge from several forms of effective dynamics, i…
Niels Bohr famously insisted on the indispensability of what he termed "classical concepts." In the context of the decoherence program, on the other hand, it has become fashionable to talk about the "dynamical emergence of classicality" from the quantum formalism alone. Does this mean that decoherence challenges Bohr's dictum -- for example, that classical concepts do not need to be assumed but can be derived? In this paper, we'll try to shed some light down the murky waters where formalism and philosophy mingle. To begin, we'll clarify the notion of classicality in the decoherence description…
We clarify the way in which cosmological perturbations of quantum origin, produced during inflation, assume classical properties. Two features play an important role in this process: First, the dynamics of fluctuations which are presently on large cosmological scales leads to a very peculiar state (highly squeezed) that is indistinguishable, in a precise sense, from a classical stochastic process. This holds for almost all initial quantum states. Second, the process of decoherence by interaction with the environment distinguishes the field amplitude basis as a robust pointer basis. We discuss …
A recent debate has ensued over the claim by Pikovski et al. [Nat. Phys. 11, 668 (2015)] that systems with internal degrees of freedom undergo a universal, gravity-induced, type of decoherence that explains their quantum-to-classical transition. This decoherence is supposed to arise from the different gravitational redshifts experienced by such systems when placed in a superposition of two wave packets at different heights in a gravitational field. Here we investigate some aspects of the discussion with the aid of simple examples. In particular, we first resolve an apparent conflict between th…
Any account of the emergence of classicality from quantum theory must address the fact that the quantum operators representing positions and momenta do not commute, whereas their classical counterparts suffer no such restrictions. To address this, we revive an old idea of von Neumann, and seek a pair of commuting operators $X,P$ which are, in a specific sense, "close" to the canonical non-commuting position and momentum operators, $x,p$. The construction of such operators is related to the problem of finding complete sets of orthonormal phase space localized states, a problem severely limited …
Spontaneous collapse models aim to resolve the measurement problem in quantum mechanics by considering wave-function collapse as a physical process. We analyze how these models affect a decaying flavor-oscillating system whose evolution is governed by a phenomenological non-Hermitian Hamiltonian. In turn, we apply two popular collapse models, the Quantum Mechanics with Universal Position Localization and the Continuous Spontaneous Localization models, to a neutral meson system. By using the equivalence between the approaches to the time evolution of decaying systems with a non-Hermitian Hamilt…
Correlations between spacelike separated measurements on entangled quantum systems are stronger than any classical correlations and are at the heart of numerous quantum technologies. In practice, however, spacelike separation is often not guaranteed and we typically face situations where measurements have an underlying time order. Here we aim to provide a fair comparison of classical and quantum models of temporal correlations on a single particle, as well as timelike-separated correlations on multiple particles. We use a causal modeling approach to show, in theory and experiment, that quantum…
An operational probabilistic theory where all systems are classical, and all pure states of composite systems are entangled, is constructed. The theory is endowed with a rule for composing an arbitrary number of systems, and with a nontrivial set of transformations. Hence, we demonstrate that the presence of entanglement is independent of the existence of incompatible measurements. We then study a variety of phenomena occurring in the theory -- some of them contradicting both Classical and Quantum Theories -- including: cloning, entanglement swapping, dense coding, additivity of classical capa…
It is now widely accepted that environmental entanglement and the resulting decoherence processes play a crucial role in the quantum-to-classical transition and the emergence of "classicality" from quantum mechanics. To this extent, decoherence is often understood as signifying a break with the Copenhagen interpretation, and in particular with Bohr's view of the indispensability of classical concepts. This paper analyzes the relationship between Bohr's understanding of the quantum-classical divide and his doctrine of classical concepts and the decoherence-based program of emergent classicality…
It has been claimed that decoherence of open quantum systems explains the tendency of macroscopic systems to exhibit quasiclassical behavior. We show that quasiclassicality is in fact an unremarkable property, characterizing generic subsystems of environments even in the absence of dynamical decoherence. It is suggested that decoherence is best regarded as explaining the persistence of true classicality, rather than the emergence, rather than the emergence of quasiclassicality.
We propose a new measure of non-classicality of quantum gates which is particularly suitable for probabilistic devices. This measure enables to compare, e.g., deterministic devices which prepare entangled states with low amount of entanglement with probabilistic devices which generate highly entangled states but which fail sometimes. We provide examples demonstrating advantages of this new measure over the so far employed entangling power.
We examine the emergence of objectivity for quantum many-body systems in a setting without an environment to decohere the system's state, but where observers can only access small fragments of the whole system. We extend the result of Reidel (2017) to the case where the system is in a mixed state, measurements are performed through POVMs, and imprints of the outcomes are imperfect. We introduce a new condition on states and measurements to recover full classicality for any number of observers. We further show that evolutions of quantum many-body systems can be expected to yield states that sat…
We investigate the entanglement of a quantum field in the expanding universe. By introducing a bipartite system using a coarse-grained scalar field, we apply the separability criterion based on the partial transpose operation and numerically calculate the bipartite entanglement between separate spatial regions. We find that the initial entangled state becomes separable or dis-entangled after the spatial separation of two points exceed the Hubble horizon. This provides the necessary condition for the appearance of classicality of the quantum fluctuation. We also investigate the condition of cla…
We apply estimation theory to a system formed by two interacting trapped ions. By using the Fisher matrix formalism, we introduce a simple scheme for estimation of the temperature of the longitudinal vibrational modes of the ions. We use the ions interaction to effectively infer the temperature of the individual ions, by optimising the interaction time evolution and by measuring only over one of the ions. We also investigate the effect of a non-thermal reservoir over the inference approach. The non-classicality of one of the ions vibrational modes, introduced due to a squeezed thermal reservoi…
We investigate theoretically the emergence of classical statistical physics in a finite quantum system that is either totally isolated or otherwise subjected to a quantum measurement process. We show via a random matrix theory approach to nonintegrable quantum systems that the set of outcomes of the measurement of a macroscopic observable evolve in time like stochastic variables, whose variance satisfies the celebrated Einstein relation for Brownian diffusion. Our results show how to extend the framework of eigenstate thermalization to the prediction of properties of quantum measurements on an…
We investigate the influence of environmental noise on polarization entangled light generated by parametric emission in a cavity. By adopting a recently developed separability criterion, we show that: i) self-stimulation may suppress the detrimental influence of noise on entanglement; ii) when self-stimulation becomes effective, a classical model of parametric emission incorporating noise provides the same results of quantum theory for the expectation values involved in the separability criterion. Moreover we show that, in the macroscopic limit, it is impossible to observe violations of local …
Quantum measurements are crucial for quantum technologies and give rise to some of the most classically counter-intuitive quantum phenomena. As such, the ability to certify the presence of genuinely non-classical joint measurements in a device-independent fashion is vital. However, previous work has either been non-device-independent, or has relied on post-selection---the ability to discard all runs of an experiment in which a specific event did not occur. In the case of entanglement, the post-selection approach applies an entangled measurement to independent states and post-selects the outcom…
According to the so-called Quantum Darwinist approach, the emergence of "classical islands" from a quantum background is assumed to obey a (selection) principle of maximal information. We illustrate this idea by considering the coupling of two oscillators (modes). As our approach suggests that the classical limit could have emerged throughout a long and progressive Evolution mechanism, it is likely that primitive living organisms behave in a "more quantum", "less classical" way than more evolved ones. This brings us to seriously consider the possibility to measure departures from classicality …
The connection between coarse-graining of measurement and emergence of classicality has been investigated for some time, if not well understood. Recently in (PRL $\textbf{112}$, 010402, (2014)) it was pointed out that coarse-graining measurements can lead to non-violation of Bell-type inequalities by a state which would violate it under sharp measurements. We study here the effects of coarse-grained measurements on bipartite cat states. We show that while it is true that coarse-graining does indeed lead to non-violation of a Bell-type inequality, this is not reflected at the state level. Under…
Quantum physics allows for entanglement between microscopic and macroscopic objects, described by discrete and continuous variables, respectively. As in Schrödinger's famous cat gedanken experiment, a box enclosing the objects can keep the entanglement alive. For applications in quantum information processing, however, it is essential to access the objects and manipulate them with suitable quantum tools. Here we reach this goal and deterministically generate entangled light-matter states by reflecting a coherent light pulse with up to four photons on average from an optical cavity containing o…
With the exception of superselection rules, there are no known explicit violations of the Principle of quantum Superposition. However, quantum measurement and the emergence of classicality seem to imply that the Principle of Superposition is not universal, so perhaps new superselection rules or something similar wait to be found. This invites us to search for explicit violations of superposition, even in places where we expect it to hold. Given that many quantum measurement devices rely on atoms absorbing photons, these processes are natural places for a first search for such violations. We pr…
Quantum Darwinism explains the emergence of classical reality from the underlying quantum reality by the fact that a quantum system is observed indirectly, by looking at parts of its environment, so that only specific information about the system that is redundantly proliferated to many parts of the environment becomes accessible and objective. However it is not clear under what conditions this mechanism holds true. Here we rigorously prove that the emergence of classicality is a general feature of any quantum dynamics: observers who acquire information about a quantum system indirectly have a…
Quantum Darwinism proposes that the proliferation of redundant information plays a major role in the emergence of objectivity out of the quantum world. Is this kind of objectivity necessarily classical? We show that if one takes Spekkens' notion of noncontextuality as the notion of classicality and the approach of Brandão, Piani and Horodecki to quantum Darwinism, the answer to the above question is `yes', if the environment encodes sufficiently well the proliferated information. Moreover, we propose a threshold on this encoding, above which one can unambiguously say that classical objectivity…
