A Theory of Quantum Preparation and the Corresponding Advantage of the Relative-Collapse Interpretation of Quantum Mechanics as Compared to the Conventional One
Analyzing two standard preparators, the Stern-Gerlach and the hole-in-the-screen ones, it is demonstrated that four entities are the basic ingredients of the theory: the composite-system preparator-plus-object state (coming about as a result of a suitable interaction between the subsystems), a suitable preparator observable, one of its characteristic projectors called the triggering event, and, finally, the conditional object state corresponding to the occurrence of the triggering event. The concepts of a conditional state and of retrospective apparent ideal occurrence are discussed in the conventional interpretation of quantum mechanics. In the general theory of a preparator in this interpretation first-kind and second-kind preparators are distinguished. They are described by the same entities in the same way, but in terms of different physical mechanisms. In this article the relative-collapse interpretation is extended to encompass also preparators (besides measuring apparatuses). In this interpretation also the mechanisms become the same and one has only one kind of preparators.
We study preparation of states for open quantum mechanics. For non-Markovian systems that are initially correlated with the environment, the affects of the preparation procedure are nontrivial. This is due to the indirect affects on the state of the environment induced via the correlations with the system and the act of preparation on the system. We give three concrete examples of preparation procedure to elucidate our claims.
We demonstrate that a geometric phase, generated via a sequence of four optomechanical interactions, can be used to increase, or generate nonlinearities in the unitary evolution of a mechanical resonator. Interactions of this form lead to new mechanisms for preparing mechanical squeezed states, and preparation of non-classical states with significant Wigner negativity.
According to Bohmian mechanics, we see the particle, not the pilot wave. But to make predictions we need to know the wave. How do we learn about the wave to make predictions, if we only see the particle? I show that the puzzle can be solved, but only thanks to decoherence.
For an arbitrary preparation, quantum mechanical descriptions refer to the complementary contexts set by incompatible measurements. We argue that an arbitrary preparation, therefore, should be described with respect to such a context by its degrees of disturbance (represented by real numbers) and their probability distribution (postulate 1). Measurement contexts thus provide reference frames for the preparation space of a physical system; a preparation being described by a point in this space with the aforementioned as its coordinates relative to a given measurement apparatus. However, all mea…
In the Copenhagen interpretation the Heisenberg uncertainty relation is interpreted as the mathematical expression of the concept of complementarity, quantifying the mutual disturbance necessarily taking place in a simultaneous or joint measurement of incompatible observables. This interpretation has already been criticized by Ballentine a long time ago, and has recently been challenged in an experimental way. These criticisms can be substantiated by using the generalized formalism of positive operator-valued measures, from which a new inequality can be derived, precisely illustrating the Cope…
A quantum mechanical theory with time asymmetry intrinsic to states (or observables) features the concept of an initial time of the state and thus a preparation time of the physical system represented by the state. This special time is investigated in the context of scattering theory, where, in standard quantum mechanics, the physical meaning of a preparation time has remained obscure. In an experiment, the preparation time corresponds to an ensemble of times of scattering marking the times in the laboratory when one scattering projectile interacts with one target quantum.
The measure of distinguishability between two neighboring preparations of a physical system by a measurement apparatus naturally defines the line element of the preparation space of the system. We point out that quantum mechanics can be derived from the invariance of this line element in the canonical formulation. The canonical formulation of quantum statistical mechanics is also discussed.
Macroscopic mechanical qubits are fundamental both to test the classical-quantum boundary and present suitable candidates for quantum information processing. Motivated by these, we propose a feasible probabilistic scheme to generate an on-demand mechanical qubit, as well as Schrödinger's cat and Fock number states. In order to accomplish this proposal, we study an open dispersive spin-mechanical system in the absence of any external driving. The procedure is solely based on spin post-selection in the weak coupling regime. Through this scheme we demonstrate that the achieved superposition is cl…
Entanglement had played a crucial role in developing frontier technologies as a critical resource, for instance, in quantum teleportation and quantum sensing schemes. Notably, thanks to the ability to cool down the vibrational modes of mechanical oscillators to its quantum regime, entanglement between mechanical modes and the production of nonclassical mechanical states have emerged as central resources for quantum technological applications. Thus, proposing deterministic schemes to achieve those tasks is of paramount importance. While the dominant scheme for bipartite mechanical entanglement …
The von Neumann collapse of the quantum mechanical wavefunction after a position measurement is derived by a purely probabilistic mechanism in the context of Nelson's stochastic mechanics.
Collapse models describe the breakdown of the quantum superposition principle when moving from microscopic to macroscopic scales. They are among the possible solutions to the quantum measurement problem and thus describe the emergence of classical mechanics from the quantum one. Testing collapse models is equivalent to test the limits of quantum mechanics. I will provide an overview on how one can test collapse models, and which are the future theoretical and experimental challenges ahead.
The wave function transformation of the quantum particle considered as a continuous medium was described by the evolution operator with the kernel in the form of path integral. It is shown that this approach allows considering not only Schrodinger evolution, but and the collapse phenomenon. The collapse entity is the nonlocal transformation of the quantum particle internal structure and it is not connected with its mechanical motion. Probably this fact allows the instantaneous signalling using the collapse without violating relativistic requirements.
We perform the probabilistic analysis of the pilot wave formalism. From the probabilistic point of view it is not so natural to follow D. Bohm and to consider nonlocal interactions between parts of (e.g.) a two-particle system. It is more natural to consider dependence of corresponding preparation procedures and the propagation of the initial correlations between preparation procedures. In the pilot wave formalism it is more natural to speak about correlations of the initial pilot waves which propagate with time.
Why microscopic objects exhibit wave properties (are delocalized), but macroscopic do not (are localized)? Traditional quantum mechanics attributes wave properties to all objects. When complemented with a deterministic collapse model (Quantum Stud.: Math. Found. 3, 279 (2016)) quantum mechanics can dissolve the discrepancy. Collapse in this model means contraction and occurs when the object gets in touch with other objects and satisfies a certain criterion. One single collapse usually does not suffice for localization. But the object rapidly gets in touch with other objects in a short time, le…
The collapse challenge for interpretations of quantum mechanics is to build from first principles and your preferred interpretation a complete, observer-free quantum model of the described experiment (involving a photon and two screens), together with a formal analysis that completely explains the experimental result. The challenge is explained in detail, and discussed in the light of the Copenhagen interpretation and the decoherence setting.
We show that a continuous quantum non-demolition measurement of the energy of a nanomechanical resonator can be achieved by monitoring the resonator with a quantum point contact via a Cooper-pair box. This technique can further be used to prepare highly non-classical states of two resonators, such as canonical phase-reference states, and so-called "noon" states.
Quantum mechanics gives many versions of reality but we perceive only one. One potential explanation for this, the one considered here, is that the wave function collapses down to just one version. The experimental situation is briefly reviewed, with no evidence found for collapse. The theoretical position is also reviewed and found wanting. Collapse-by-observation schemes are logically untenable. A mathematical theory of collapse must be nonlinear, a significant departure from current quantum theory. In addition, the primary candidate theory, the GRW-Pearle model, requires instantaneous, non-…
We show that the Bub-Clifton uniqueness theorem for 'no collapse' interpretations of quantum mechanics (Studies in the History and Philosophy of Modern Physics 27, 181-219 (1996)) can be proved without the 'weak separability' assumption.
Collapse models implement a progressive loss of quantum coherence when the mass and the complexity of quantum systems increase. We will review such models and the current attempts to test their predicted loss of quantum coherence.
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…
It is argued that the three assumptions of quantum collapse, one photon-one count, and relativity of simultaneity cannot hold together: Nonlocal correlations can depend on the referential frames of the beam-splitters but not of the detectors. New experiments using interferometers in series are proposed which make it possible to test Quantum Mechanics vs Multisimultaneity.
Cramer's transactional interpretation of quantum mechanics is reviewed, and a number of issues related to advanced interactions and state vector collapse are analyzed. Where some have suggested that Cramer's predictions may not be correct or definite, I argue that they are, but I point out that the classical-quantum distinction problem in the Copenhagen interpretation has its parallel in the transactional interpretation.
We show that the interaction of a pulsed laser light with a mechanical oscillator through the radiation pressure results in an opto-mechanical entangled state in which the photon number is correlated with the oscillator position. Interestingly, the mechanical oscillator can be delocalized over a large range of positions when driven by an intense laser light. This provides a simple yet sensitive method to probe hypothetic post-quantum theories including an explicit wave function collapse model, like the Diosi and Penrose model. We propose an entanglement witness to reveal the quantum nature of …
We propose an efficient scheme for generating spin-squeezed states at steady state in a spin-mechanical hybrid system, where an ensemble of SiV centers are coupled to a strongly damped nanomechanical resonator. We show that,there exists a collective steady state in the system, which is exactly formed by the collective spin states plus the zero excitation state of the mechanical mode. The generation of the steady spin-squeezed state is based on a dissipative quantum dynamical process in which the mechanical dissipation plays a positive role but without destroying the target state. We demonstrat…
In the framework of an interference setup in which only two outcomes are possible (such as in the case of a Mach-Zehnder interferometer), we discuss in a simple and pedagogical way the difference between a standard, unitary quantum mechanical evolution and the existence of a real collapse of the wave function. Moreover, we also present the Elitzur-Vaidman bomb, the delayed choice experiment, and the effect of decoherence. In the end, we propose two simple experiments to visualize decoherence and to test the role of an entagled particle.
The measurement problem is to explain why a system which is in a linear combination of states appears, upon measurement, to be in just one of those states. The solution given here is to first show that if one assumes linear, unitary, no collapse, no particle quantum mechanics, the different versions of reality are completely isolated from each other. This then implies only the eigenstates appropriate to the measurement setup will be perceived. In a Stern-Gerlach experiment, for example, only spin up or spin down will be perceived, but never a combination of the two.
The conventional postulate for the probabilistic interpretation of quantum mechanics is asymmetric in preparation and measurement, making retrodiction reliant on inference by use of Bayes' theorem. Here, a more fundamental symmetric postulate is presented, from which both predictive and retrodictive probabilities emerge immediately, even where measurement devices more general than those usually considered are involved. It is shown that the new postulate is perfectly consistent with the conventional postulate.
Reservoir engineering enables the robust preparation of pure quantum states in noisy environments. We show how a new family of quantum states of a mechanical oscillator can be stabilized in a cavity that is parametrically coupled to both the mechanical displacement and the displacement squared. The cavity is driven with three tones, on the red sideband, on the cavity resonance and on the second blue sideband. The states so stabilized are (squeezed and displaced) superpositions of a finite number of phonons. They show the unique feature of encompassing two prototypes of nonclassicality for boso…
Precisely engineered mechanical oscillators keep time, filter signals, and sense motion, making them an indispensable part of today's technological landscape. These unique capabilities motivate bringing mechanical devices into the quantum domain by interfacing them with engineered quantum circuits. Proposals to combine microwave-frequency mechanical resonators with superconducting devices suggest the possibility of powerful quantum acoustic processors. Meanwhile, experiments in several mechanical systems have demonstrated quantum state control and readout, phonon number resolution, and phonon-…
The quantum field of a single particle is expressed as the sum of the particle's ordinary wave function and the vacuum fluctuations. An exact quantum-field calculation shows that the squared amplitude of this field sums, at any time, to a delta function representing a discrete corpuscle at one point and zero everywhere else. The peak of the delta function is located at the point where the vacuum fluctuations interfere constructively with the ordinary wave function. Similarly, the collapsed wave function after a measurement of an observable is determined by interference between the initial wave…
Spontaneous collapse models and Bohmian mechanics are two different solutions to the measurement problem plaguing orthodox quantum mechanics. They have, a priori nothing in common. At a formal level, collapse models add a non-linear noise term to the Schrödinger equation, and extract definite measurement outcomes either from the wave function (e.g. mass density ontology) or the noise itself (flash ontology). Bohmian mechanics keeps the Schrödinger equation intact but uses the wave function to guide particles (or fields), which comprise the primitive ontology. Collapse models modify the predict…
Long-baseline laser-interferometer gravitational-wave detectors are operating at a factor of 10 (in amplitude) above the standard quantum limit (SQL) within a broad frequency band. Such a low classical noise budget has already allowed the creation of a controlled 2.7 kg macroscopic oscillator with an effective eigenfrequency of 150 Hz and an occupation number of 200. This result, along with the prospect for further improvements, heralds the new possibility of experimentally probing macroscopic quantum mechanics (MQM) - quantum mechanical behavior of objects in the realm of everyday experience …
Among several possibilities for what reality could be like in view of the empirical facts of quantum mechanics, one is provided by theories of spontaneous wave function collapse, the best known of which is the Ghirardi-Rimini-Weber (GRW) theory. We show mathematically that in GRW theory (and similar theories) there are limitations to knowledge, that is, inhabitants of a GRW universe cannot find out all the facts true about their universe. As a specific example, they cannot accurately measure the number of collapses that a given physical system undergoes during a given time interval; in fact, t…
Nanomechanical resonators are a key tool for future quantum technologies such as quantum force sensors and interfaces, and for studies of macroscopic quantum physics. The ability to prepare room temperature non-classical states is a major outstanding challenge. Here, we explore the use of measurement-based state conditioning to achieve this. We demonstrate conditional cooling of a nanomechanical resonator that has non-Markovian decoherence, and show theoretically that the non-Markovianity makes quantum squeezing significantly easier to achieve. We further show that collective measurement of mu…
We analyse the wave function collapse as seem by two distinct observers (with identical detectors) in relative motion. Imposing that the measurement process demands information transfer from the system to the detectors, we note that although different observers will acquire different amount of information from their measurements due to correlations between spin and momentum variables, all of them will agree about the orthogonality of the outcomes, as defined by their own reference frame. So, in this sense, such a quantum mechanical postulate is observer invariant, however the effective efficie…
The postulate of the collapse of the wave function stands between the microscopic, quantum world, and the macroscopic world. Because of this intermediate position, the collapse process cannot be examined with the formalism of the quantum mechanics (QM), neither with that of classical mechanics. This fact makes some physicists to propose interpretations of QM, which avoid this postulate. However, the common procedure used in that, is making assumptions incompatible with the QM formalism. The present work discusses the most popular interpretations. It is shown that because of such assumptions th…
Heisenberg in 1929 introduced the "collapse of the wavepacket" into quantum theory. We review here an experiment at Berkeley which demonstrated several aspects of this idea. In this experiment, a pair of daughter photons was produced in an entangled state, in which the sum of their two energies was equal to the sharp energy of their parent photon, in the nonlinear optical process of spontaneous parametric down-conversion. The wavepacket of one daughter photon collapsed upon a measurement-at-a-distance of the other daughter's energy, in such a way that the total energy of the two-photon system …
Based on the modelling of quantum systems with the aid of (classical) non-equilibrium thermodynamics, both the emergence and the collapse of the superposition principle are understood within one and the same framework. Both are shown to depend in crucial ways on whether or not an average orthogonality is maintained between reversible Schroedinger dynamics and irreversible processes of diffusion. Moreover, said orthogonality is already in full operation when dealing with a single free Gaussian wave packet. In an application, the quantum mechanical "decay of the wave packet" is shown to simply r…
We study the following problem: Is it possible to explain the quantum interference of probabilities in the purely corpuscular model for elementary particles? We demonstrate that (by taking into account perturbation effects of measurement and preparation procedures) we can obtain $\cosθ$-perturbation (interference term) in probabilistic rule connecting preparation procedures for purely corpuscular objects. On one hand, our investigation demonstrated that there is nothing special in so called `quantum probabilities': the right choice of statistical ensembles gives the possibility to escape all `…
We analyze three important experimental domains (SQUIDs, molecular interferometry, and Bose-Einstein condensation) as well as quantum-biophysical studies of the neuronal apparatus to argue that (i) the universal validity of unitary dynamics and the superposition principle has been confirmed far into the mesoscopic and macroscopic realm in all experiments conducted thus far; (ii) all observed "restrictions" can be correctly and completely accounted for by taking into account environmental decoherence effects; (iii) no positive experimental evidence exists for physical state-vector collapse; (iv…
In addition to being a very interesting quantum phenomenon, Schrödinger cat swapping has the potential for application in the preparation of quantum states that could be used in metrology and other quantum processing. We study in detail the effects of field decoherence on a cat-swapping system comprising a set of identical qubits, or spins, all coupled to a field mode. We demonstrate that increasing the number of spins actually mitigates the effects of field decoherence on the collapse and revival of a spin Schrödinger cat, which could be of significant utility in quantum metrology and other q…
The possibility of consistency between the basic quantum principles of quantum mechanics and wave function collapse is reexamined. A specific interpretation of environment is proposed for this aim and applied to decoherence. When the organization of a measuring apparatus is taken into account, this approach leads also to an interpretation of wave function collapse, which would result in principle from the same interactions with environment as decoherence. This proposal is shown consistent with the non-separable character of quantum mechanics.
The transition from quantum to classical physics remains an intensely debated question even though it has been investigated for more than a century. Further clarifications could be obtained by preparing macroscopic objects in spatial quantum superpositions and proposals for generating such states for nano-mechanical devices either in a transient or a probabilistic fashion have been put forward. Here we introduce a method to deterministically obtain spatial superpositions of arbitrary lifetime via dissipative state preparation. In our approach, we engineer a double-well potential for the motion…
The dynamical equation of hybrid systems, being the combination of Schrödinger and Liouville equations, produces noncausal evolution when the initial state of interacting quantum and classical mechanical systems is as it is demanded in discussions regarding the problem of measurement. It is found that state of quantum mechanical system instantaneously collapses due to the non-negativity of probabilities.
For an isolated macrosystem classical state parameters $ζ(t)$ are introduced inside a quantum mechanical treatment. By a suitable mathematical representation of the actual preparation procedure in the time interval $[T,t_0]$ a statistical operator is constructed as a solution of the Liouville von Neumann equation, exhibiting at time $t$ the state parameters $ζ(t')$, $t_0\leq t' \leq t$, and {\it preparation parameters} related to times $T \leq t'\leq t_0$. Relation with Zubarev's non-equilibrium statistical operator is discussed. A mechanism for memory loss is investigated and time evolution b…
In this short communication, I gave a generalization of measurement postulate in quantum mechanics. It is regarding the case with partial measurement, namely, measurement on only part of a wave function. Upon a partial measurement, the wavefunction will either collapse in one of the eigenstate covered by the measured partial wavefunction; or collapses out of the measured part and shifts to the unmeasured part. An explanation in the WISE (Wavefunction Is System Entity) interpretation is given.
Recently I proposed the linguistic interpretation of quantum mechanics, which is characterized as the linguistic turn of the Copenhagen interpretation of quantum mechanics. This turn from physics to language does not only extend quantum theory to classical theory but also yield the quantum mechanical world view. Although the wave function collapse is prohibited in the linguistic interpretation, in this paper I show that the phenomenon like wave function collapse can be realized in the linguistic interpretation. And furthermore, I propose the justification of the von Neumann-Lüders projection p…
The gap between the predictions of collapse models and those of standard quantum mechanics widens with the complexity of the involved systems. Addressing the way such gap scales with the mass or size of the system being investigated paves the way to testing the validity of the collapse theory and identify the values of the parameters that characterize it. Here, we review the recently proposed non-interferometric approach to the testing of collapse models, focusing on the opto-mechanical platform.
I propose to resolve the controversy over the speed of collapse of quantum-mechanical wavefunctions by means of an experimental test with a modified symmetric Mach-Zehnder atom interferometer, with non-intersecting, parallel, widely separated final beams. According to the conventional collapse scenario, the coherent twin-peak atomic wavefunction in the beams of the interferometer suffers an instantaneous collapse, at infinite speed, when the atom is captured by one of the two detectors at the ends of the beams, but it remains coherent until that instant. In contrast, according to the Hellwig-K…
We present a scheme to deterministically prepare non-classical quantum states of a massive mirror including highly non-Gaussian states exhibiting sizeable negativity of the Wigner function. This is achieved by exploiting the non-linear light-matter interaction in an optomechanical cavity by driving the system with optimally designed frequency patterns. Our scheme reveals to be resilient against mechanical and optical damping, as well as mechanical thermal noise and imperfections in the driving scheme. Our proposal thus opens a promising route for table-top experiments to explore and exploit ma…
Based on an analysis of two conventional preparators, the Stern-Gerlach and the hole-in-the-screen ones, it is argued that four entities can be taken as the basic ingredients of a rather general theory of a quantum preparator. These are the composite-system (object plus preparator) state coming about as a result of a suitable interaction between the subsystems, a suitable preparator projector called the triggering event, the conditional quantum state (density operator) of the quantum object coming about as a consequence of the occurrence of the triggering event on the preparator, and, finally,…
Recalling the state of the art in the interpretation of quantum physics, this paper emphasizes that one cannot simply add a collapse parameter to the Schrödinger equation in order to solve the measurement problem. If one does so, one is also committed to a primitive ontology of a configuration of matter in physical space in order to have something in the ontology that constitutes the determinate measurement outcomes. The paper then argues that in the light of this consequence, the collapse postulate loses its attractiveness in comparison to an ontology of persisting particles moving on contin…
The main distinction between classical mechanics and quantum mechanics is the lack in the latter of a full mechanical determinism: different final states can arise from the same physical state, after the measurement. No hidden variable is supposed to exist, nothing can discriminate two apparently identical states even if they give a different result. In this paper we try to put the basis for a more fundamental theory that (approximately) coincides with quantum mechanics when comparing statistics, but it is more fundamental, since it mathematically describes measurement processes giving an expl…
