In recent years two fundamental aspects of quantum mechanics have attracted a great deal of interest, namely the investigation on the irreducible nonlocal properties of Nature implied by quantum entanglement and the physical realization of the 'Schroedinger Cat'. In the present work a macro - state consisting of about 3.5 x 10^4 photons in a quantum superposition and entangled with a far apart single - photon state is generated. Then, the non-separability of the overall micro-macro system is demonstrated and the corresponding Bell's inequalities are found to be violated. Precisely, an entangled photon pair is created by a nonlinear optical process, then one photon of the pair is injected into an optical parametric amplifier operating for any input polarization state, i.e. into a phase-covariant cloning machine. Such transformation establishes a connection between the single photon and the multi particle fields. We then demonstrate the non-separability of the bipartite system by adopting a local filtering technique within a positive operator valued measurement.
The author cannot grant that Quantum Mechanics satisfies the axioms described here when repeated measurements are at stake. This does not compromise the validity of the conclusions of the previous article "A glance beyond the quantum model", Proc. Roy. Soc. Lond. A 466, 881-890 (2009).
We propose a method to generate analytical quantum Bell inequalities based on the principle of Macroscopic Locality. By imposing locality over binary processings of virtual macroscopic intensities, we establish a correspondence between Bell inequalities and quantum Bell inequalities in bipartite scenarios with dichotomic observables. We discuss how to improve the latter approximation and how to extend our ideas to scenarios with more than two outcomes per setting.
The categorization of quantum states for composite systems as either separable or entangled, or alternatively as Bell local or Bell non-local states based on local hidden variable theory is reviewed in Sections 1 and 2, focusing on simple bipartite systems. The significance of states demonstrating Bell non-locality for settling the long standing controversy between the Copenhagen interpretation of the quantum measurement process involving the collapse of the wave-function and the alternative interpretation based on pre-existing hidden variables is emphasized. Although experiments demonstrating…
In a Bell test, the set of observed probability distributions complying with the principle of local realism is fully characterized by Bell inequalities. Quantum theory allows for a violation of these inequalities, which is famously regarded as Bell nonlocality. However, finding the maximal degree of this violation is, in general, an undecidable problem. Consequently, no algorithm can be used to derive quantum analogs of Bell inequalities, which would characterize the set of probability distributions allowed by quantum theory. Here we present a family of inequalities, which approximate the set …
Two physical principles, Macroscopic Locality (ML) and Information Causality (IC), so far, have been most successful in distinguishing quantum correlations from post-quantum correlations. However, there are also some post-quantum probability distributions which cannot be distinguished with the help of these principles. Thus, it is interesting to see whether consideration of these two principles, separately, along with some additional physically plausible constraints, can explain some interesting quantum features which are otherwise hard to reproduce. In this paper we show that, in a Bell-CHSH …
It is usually believed that coarse-graining of quantum correlations leads to classical correlations in the macroscopic limit. Such a principle, known as macroscopic locality, has been proved for correlations arising from independent and identically distributed (IID) entangled pairs. In this letter we consider the generic (non-IID) scenario. We find that the Hilbert space structure of quantum theory can be preserved in the macroscopic limit. This leads directly to a Bell violation for coarse-grained collective measurements, thus breaking the principle of macroscopic locality.
Some years ago Aerts et al. presented a macroscopic model in which the amount of non-locality and indeterminism could be continuously varied, and used it to show that by increasing non-locality one increases, as expected, the degree of violation of Bell's inequality (BI), whereas, more surprisingly, by increasing indeterminism one decreases the degree of the violation of BI. In this note we propose a different macroscopic model in which the amount of non-locality and indeterminism can also be parameterized, and therefore varied, and we find that, in accordance with the model of Aerts et al., a…
Entanglement of a macroscopic system with a microscopic one is shown to begin by a topological property of histories in the Feynman formulation of quantum mechanics. This property can also be expressed algebraically on the Schrödinger equation through a convenient extension of the Hilbert space formalism. Entanglement shows then properties of growth and transport, the corresponding local and temporary character of entanglement being called here "intricacy" when it occurs. When applied to the continuous interaction of a macroscopic system with a random environment, intricacy implies a "predecoh…
We propose a new test of local realism based on correlation measurements of continuum valued functions of positions and momenta, known as modular variables. The Wigner representation of these observables are bounded in phase space, and therefore, the associated inequality holds for any state described by a non-negative Wigner function. This agrees with Bell's remark that positive Wigner functions, serving as a valid probability distribution over local (hidden) phase space coordinates, do not reveal non-locality. We construct a class of entangled states resulting in a violation of the inequalit…
We explore a connection between monogamy of non-locality and a weak macroscopic locality condition: the locality of the average behaviour. These are revealed by our analysis as being two sides of the same coin. Moreover, we exhibit a structural reason for both in the case of Bell-type multipartite scenarios, shedding light on but also generalising the results in the literature [Ramanathan et al., Phys. Rev. Lett. 107, 060405 (2001); Pawlowski & Brukner, Phys. Rev. Lett. 102, 030403 (2009)]. More specifically, we show that, provided the number of particles in each site is large enough compared …
Quantum mechanics allows only certain sets of experimental results (or "probabilistic models") for Bell-type quantum non-locality experiments. A derivation of this set from simple physical or information theoretic principles would represent an important step forward in our understanding of quantum mechanics, and this problem has been intensely investigated in recent years. "Macroscopic locality," which requires the recovery of locality in the limit of large numbers of trials, is one of several principles discussed in the literature that place a bound on the set of quantum probabilistic models.…
We study multipartite correlations and non-locality in an isotropic Ising ring under transverse magnetic field at both zero and finite temperature. We highlight parity-induced differences between the multipartite Bell-like functions used in order to quantify the degree of non-locality within a ring state and reveal a mechanism for the passive protection of multipartite quantum correlations against thermal spoiling effects that is clearly related to the macroscopic properties of the ring model.
I argue that conventional estimates of the criterion for classical behavior of a macroscopic body are incorrect, because they do not take into account the locality of interactions, which characterizes the behavior of all systems described approximately by local quantum field theory. Black holes are the only localized objects which do not have such a description. The deviations from classical behavior of a macroscopic body, except for those which can be described as classical uncertainties in the initial values of macroscopic variables,are {\it exponentially} small as a function of the volume o…
The EPR argument points to the existence of additional variables that are necessary to complete standard quantum theory. It was dismissed by Bohr because it attributes physical reality to isolated microscopic systems, independently of the macroscopic measurement apparatus. Here, we transpose the EPR argument to macroscopic systems, assuming that they are in spatially extended Fock spin states and subject to spin measurements in remote regions of space. Bohr's refutation of the EPR argument does not seem to apply in this case, since the difference of scale between the microscopic measured syste…
In quantum systems of a macroscopic size V, such as interacting many particles and quantum computers with many qubits, there exist pure states such that fluctuations of some intensive operator A is anomalously large, <δA^2> = O(V^0), which is much larger than that assumed in thermodynamics, <δA^2> = O(1/V). By making full use of the locality, we show, starting from Hamiltonians of macroscopic degrees of freedom, that such states decohere at anomalously fast rates when they are weakly perturbed from environments.
This is an improved remake of a previous work submitted with the same title. An epistemologicalphysical, strictly qualitative discipline, IQM (infra-quantum mechanics), is constructed independently of the mathematical formalism of QM. IQM emerges under exclusively the constraints imposed by: the cognitive situation of a human being who decides to construct communicable and consensual knowledge on microstates; general requirements of human conceptualization. IMQ brings into evidence how the mathematical formalism of QM manages to signify. It explicates an integrated expression of a radically ne…
I argue that conventional estimates of the criterion for classical behavior of a macroscopic body are incorrect in most circumstances,because they do not take into account the locality of interactions, which characterizes the behavior of all systems described approximately by local quantum field theory. The deviations from classical behavior of a macroscopic body, except for those that can be described as classical uncertainties in the initial values of macroscopic variables,are {\it exponentially} small as a function of the volume of the macro-system in microscopic units. Conventional estimat…
The action reaction principle is violated in the standard formulation of Quantum Mechanics, so that its phase space is incomplete. Moreover, projection of state of a quantum system under indirect measurement, when there are alternative virtual paths and one of them is discarded by negative detection implies, according to the action reaction principle, a reaction on the detector, although its macroscopic state does not change. If all interactions are local, mediated by fields with relativistically causal evolution, some system, different from the particle which follows another path, must locall…
The question whether Quantum Mechanics describes all aspects of both the micro-world of elementary particles and living organisms adequately is still open. A Bell inequality test without locality and detection loopholes will deliver the answer when applied to macroscopic systems. Here we show that an experimentally feasible loophole-free Bell test is possible using only multi-photon polarization entanglement and linear optics. We apply a preselection protocol which produces genuine macroscopic superpositions and entanglement, thus eliminating postselection and dark counts. Such superpositions …
Neutron interference measurements with macroscopic beam separation allow to study the influence of magnetic fields on spin properties. By calculating the interaction energy with a dynamic and deterministic model, we are able to establish that the phase shift on one component of the neutron beam is linear with magnetic intensity, and equally, that interaction energy as well as phase shifts do not depend on the orientation of the magnetic field. The theoretical treatment allows the conclusion that the non-local properties of particle spin derive from the classical equation for interaction energy…
There is an ongoing search for a physical or operational definition for quantum mechanics. Several informational principles have been proposed which are satisfied by a theory less restrictive than quantum mechanics. Here, we introduce the principle of "many-box locality", which is a refined version of the previously proposed "macroscopic locality". These principles are based on coarse-graining the statistics of several copies of a given box. The set of behaviors satisfying many-box locality for $N$ boxes is denoted $MBL_N$. We study these sets in the bipartite scenario with two binary measurem…
In the Schrödinger-cat gedanken experiment a cat is in a quantum superposition of two macroscopically distinct states, alive and dead.The paradoxical interpretation of quantum mechanics is that the cat is not in one state or the other, alive or dead, immediately prior to its measurement. Because of this apparent defiance of macroscopic reality, quantum superpositions of states macroscopically distinct have generated much interest. Here we address the issue of proving a contradiction with macroscopic reality objectively, through the testable predictions of quantum mechanics. We consider the pre…
Quantum physics has intrigued scientists and philosophers alike, because it challenges our notions of reality and locality--concepts that we have grown to rely on in our macroscopic world. It is an intriguing open question whether the linearity of quantum mechanics extends into the macroscopic domain. Scientific progress over the last decades inspires hope that this debate may be decided by table-top experiments.
Quantum correlations may violate the Bell inequalities. Most of the experimental schemes confirming this prediction have been realized in all-optical Bell tests suffering from the detection loophole. Experiment which closes this loophole and the locality loophole simultaneously is highly desirable and remains challenging. A novel approach to a loophole-free Bell tests is based on amplification of the entangled photons, i.e.\@ on macroscopic entanglement, which optical signal should be easy to detect. However, the macroscopic states are partially indistinguishable by the classical detectors. An…
We consider finite macroscopic systems, i.e., systems of large but finite degrees of freedom, which we believe are poorly understood as compared with small systems and infinite systems. We focus on pure states that do not have the `cluster property.' Such a pure state is entangled macroscopically, and is quite anomalous in view of many-body physics because it does not approach any pure state in the infinite-size limit. However, we often encounter such anomalous states when studying finite macroscopic systems, such as quantum computers with many qubits and finite systems that will exhibit symme…
We argue that the quantum probability law follows, in the large N limit, from the compatibility of quantum mechanics with classical-like properties of macroscopic objects. For a finite sample, we find that likely and unlikely measurement outcomes are associated with distinct interference effects in a sample weakly coupled to an environment.
We formulate a theory for entangled imaging, which includes also the case of a large number of photons in the two entangled beams. We show that the results for imaging and for the wave-particle duality features, which have been demonstrated in the microscopic case, persist in the macroscopic domain. We show that the quantum character of the imaging phenomena is guaranteed by the simultaneous spatial entanglement in the near and in the far field.
In many experiments on microscopic quantum systems, it is implicitly assumed that when a macroscopic procedure or "instruction" is repeated many times -- perhaps in different contexts -- each application results in the same microscopic quantum operation. But in practice, the microscopic effect of a single macroscopic instruction can easily depend on its context. If undetected, this can lead to unexpected behavior and unreliable results. Here, we design and analyze several tests to detect context-dependence. They are based on invariants of matrix products, and while they can be as data intensiv…
Using different optical setups based on squeezed state and photon subtraction we show how optical entanglement between a macroscopic and a microscopic state - the so-called Schrodinger cat state or micro-macro state - can be generated. The entangled state is heralded and is thus produced a priori in contrast to previous proposals. We define the macroscopicity of the macroscopic part of the state as their mean distance in phase space and the success rate in discriminating them with homodyne detection, and subsequently, based on these measures we investigate the macroscopicity of different state…
The question has been solved whether Bell's inequalities cover all possible kinds of hidden-variable theories. It has been shown that the given nequalities can be hardly derived when the changing space position of photon-pair source together with the microscopic space structure of measuring devices are taken into account; and when corresponding impact parameters (i.e., exact impact points) of photons in individual measuring devices (polarizers) influence measured values, in addition to usually considered characteristics.
Environment induced decoherence entails the absence of quantum interference phenomena from the macroworld. The loss of coherence between superposed wave packets depends on their separation. The precise temporal course depends on the relative size of the time scales for decoherence and other processes taking place in the open system and its environment. We use the exactly solvable model of an harmonic oscillator coupled to a bath of oscillators to illustrate various decoherence scenarios: These range from exponential golden-rule decay for microscopic superpositions, system-specific decay for la…
Quantum non-locality has been an extremely fruitful subject of research, leading the scientific revolution towards quantum information science, in particular to device-independent quantum information processing. We argue that time is ripe to work on another basic problem in the foundations of quantum physics, the quantum measurement problem, that should produce good physics both in theoretical, mathematical, experimental and applied physics. We briefly review how quantum non-locality contributed to physics (including some outstanding open problems) and suggest ways in which questions around Ma…
We report the observation of quantum jumps between macroscopic quantum states in a superconducting phase qubit coupled to the two-level systems in the Josephson tunnel junction, and all key features of quantum jumps are confirmed in the experiments. Moreover, quantum jumps can be used to calibrate such two-level systems, which are believed to be one of the main decoherence sources in Josephson devices.
A qualitative but formalized representation of microstates is first established quite independently of the quantum mechanical mathematical formalism, exclusively under epistemological-operational-methodological constraints. Then, using this representation as a reference-and-imbedding-structure, the foundations of an intelligible reconstruction of the Hilbert-Dirac formulation of Quantum Mechanics is developed. Inside this reconstruction the measurement problem as well as the other major problems raised by the quantum mechanical formalism, dissolve.
We present several examples where prominent quantum properties are transferred from a microscopic superposition to thermal states at high temperatures. Our work is motivated by an analogy of Schrodinger's cat paradox, where the state corresponding to the virtual cat is a mixed thermal state with a large average photon number. Remarkably, quantum entanglement can be produced between thermal states with nearly the maximum Bell-inequality violation even when the temperatures of both modes approach infinity.
We identify a class of quantum states, each consisting of a microscopic and a macroscopic section, that are effectively decoherence-free when each particle is locally passed through a quantum channel. In particular, and in contrast to other macroscopic quantum states like the Greenberger-Horne-Zeilinger state, the content of entanglement and other quantum correlations in the microscopic to macroscopic partition of this class of states is independent of the number of particles in their macroscopic sectors, when all the particles suffer passage through local amplitude and phase damping channels.…
The violation of Bell inequalities by quantum physical experiments disproves all relativistic micro causal, classically real models, short Local Realistic Models (LRM). Non-locality, the infamous "spooky interaction at a distance" (A. Einstein), is already sufficiently 'unreal' to motivate modifying the "realistic" in "local realistic". This has led to many worlds and finally many minds interpretations. We introduce a simple many world model that resolves the Einstein Podolsky Rosen paradox. The model starts out as a classical LRM, thus clarifying that the many worlds concept alone does not im…
We present a technique for addressing single NV$^{-}$ center spins in diamond over macroscopic distances using a tunable dielectric microwave cavity. We demonstrate optically detected magnetic resonance (ODMR) for a single NV$^{-}$ center in a nanodiamond (ND) located directly under the macroscopic microwave cavity. By moving the cavity relative to the ND, we record the ODMR signal as a function of position, mapping out the distribution of the cavity magnetic field along one axis. In addition, we argue that our system could be used to determine the orientation of the NV$^{-}$ major axis in a s…
We demonstrate experimentally the creation and measurement of an entangled state between a microscopic two level system and a macroscopic superconducting resonator where their indirect interaction is mediated by an artificial atom, a superconducting persistent current qubit (PCQB). We show that the microscopic two level system, formed by a defect in an oxide layer, exhibits an order of magnitude longer dephasing time than the PCQB, while the dephasing time of the entangled states between the microscopic two level system and macroscopic superconducting resonator is significantly longer than the…
We propose a hybrid approach to the experimental assessment of the genuine quantum features of a general system consisting of microscopic and macroscopic parts. We infer entanglement by combining dichotomic measurements on a bidimensional system and phase-space inference through the Wigner distribution associated with the macroscopic component of the state. As a benchmark, we investigate the feasibility of our proposal in a bipartite-entangled state composed of a single-photon and a multiphoton field. Our analysis shows that, under ideal conditions, maximal violation of a Clauser-Horne-Shimony…
We study the nature of and approach to thermal equilibrium in isolated quantum systems. An individual isolated macroscopic quantum system in a pure or mixed state is regarded as being in thermal equilibrium if all macroscopic observables assume rather sharply the values obtained from thermodynamics. Of such a system (or state) we say that it is in macroscopic thermal equilibrium (MATE). A stronger requirement than MATE is that even microscopic observables (i.e., ones referring to a small subsystem) have a probability distribution in agreement with that obtained from the micro-canonical, or equ…
In the microscopic world, multipartite entanglement has been achieved with various types of nanometer sized two-level systems such as trapped ions, atoms and photons. On the macroscopic scale ranging from micrometers to millimeters, recent experiments have demonstrated bipartite and tripartite entanglement for electronic quantum circuits with superconducting Josephson junctions. It remains challenging to bridge these largely different length scales by constructing hybrid quantum systems. Doing this may allow for manipulating the entanglement of individual microscopic objects separated by macro…
Collapse models possibly suggest the need for a better understanding of the structure of space-time. We argue that physical space, and space-time, are emergent features of the Universe, which arise as a result of dynamical collapse of the wave function. The starting point for this argument is the observation that classical time is external to quantum theory, and there ought to exist an equivalent reformulation which does not refer to classical time. We propose such a reformulation, based on a non-commutative special relativity. In the spirit of Trace Dynamics, the reformulation is arrived at, …
Structured Non-Locality and Emergent Locality in Cavity-QED Many-Body Dynamics
ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology（ICFO-光子科学研究所，巴塞罗那科学技术研究院）；ICREA-Institució Catalana de Recerca i Estudis Avançats（ICREA-加泰罗尼亚高级研究学院）
Macroscopic quantum vacuum and modern theories of gravitation share the strong interplay between geometry and physical phenomena. We review selected issues related to the accuracy of the measurement of Casimir forces with particular emphasis on the implications for the search of non-Newtonian gravitational forces in the micrometer range. We then discuss the interplay of the Higgs particle with gravitation, arguing that spectroscopic shifts in atomic transitions due to the modifications of the vacuum expectation value of the Higgs field in regions with strong curvature of space-time may be of c…
We present a scheme to entangle two magnon modes in two macroscopic yttrium-iron-garnet spheres. The two spheres are placed inside two microwave cavities, which are driven by a two-mode squeezed microwave field. By using the linear state-swap interaction between the cavity and the magnon mode in each cavity, the quantum correlation of the two driving fields is with high efficiency transferred to the two magnon modes. Considerable entanglement could be achieved under experimentally achievable conditions $g \gg κ_a \gg κ_m$, where $g$ is the cavity-magnon coupling rate and $κ_a$, $κ_m$ are the d…
