Quantum probabilities from quantum entanglement: experimentally unpacking the Born rule

Quantum theory has nonlocal correlations, which bothered Einstein, but found to satisfy relativistic causality. Correlation for a shared quantum state manifests itself, in the standard quantum framework, by joint probability distributions that can be obtained by applying state reduction and probability assignment that is called Born rule. Quantum correlations, which show nonlocality when the shared state has an entanglement, can be changed if we apply different probability assignment rule. As a result, the amount of nonlocality in quantum correlation will be changed. The issue is whether the change of the rule of quantum probability assignment breaks relativistic causality. We have shown that Born rule on quantum measurement is derived by requiring relativistic causality condition. This shows how the relativistic causality limits the upper bound of quantum nonlocality through quantum probability assignment.

Recent high-precision measurements in a three-slit diffraction experiment [Sinha et al., Science 329, 418 (2010)] have been performed as an explicit test of the validity of Born's rule for quantum probabilities. This experiment aims to establish an upper limit to the possibility of higher-order interference, which, if observed, could support generalization of quantum probability theory. We reproduce this three-slit experiment using position-resolved detection, compare our results to a computational model, and find significant limitations to the normalization scheme proposed by Sinha et al. that influence interpretation. We further show that the dependence of the measurements on detector size and position must be taken into account for proper interpretation of results and meaningful comparison with other experimental schemes.

We present a purely wave model (based on classical random field) which reproduces quantum probabilities (given by the fundamental law of quantum mechanics, Born's rule) including probabilities for joint detection of a pair of quantum observables (e.g., spin or polarization projections). The crucial point of our approach is that the presence of detector's threshold and calibration procedure have to be treated not as simply experimental technicalities, but as the basic counteparts of the theoretical model. The presence of the background field (vacuum fluctuations) is also the key-element of our prequantum model. It is of the classical signal type and the methods of classical signal theory (including statistical radiophysics) are used for its development. We stress that our prequantum model is not objective, i.e., the values of observables (clicks of detectors) cannot be assigned in advance, i.e., before measurement. Hence, the dilemma, nonobjectivity or nonlocality, is resolved in favor of nonobjectivity (our model is local of the classical field type). In particular, we reproduce the probabilities for the EPR-experiment for photon polarization and, hence, violate CHSH inequality for classical random signals (measured by the threshold type and properly calibrated detectors acting in the presence of the background field).

Asset trading under non-classical ambiguity and heterogeneous beliefs

We propose a concept of quantum computing which incorporates an additional kind of uncertainty, i.e. vagueness (fuzziness), in a natural way by introducing new entities, obscure qudits (e.g. obscure qubits), which are characterized simultaneously by a quantum probability and by a membership function. To achieve this, a membership amplitude for quantum states is introduced alongside the quantum amplitude. The Born rule is used for the quantum probability only, while the membership function can be computed from the membership amplitudes according to a chosen model. Two different versions of this approach are given here: the “product” obscure qubit, where the resulting amplitude is a product of the quantum amplitude and the membership amplitude, and the “Kronecker” obscure qubit, where quantum and vagueness computations are to be performed independently (i.e. quantum computation alongside truth evaluation). The latter is called a double obscure-quantum computation. In this case, the measurement becomes mixed in the quantum and obscure amplitudes, while the density matrix is not idempotent. The obscure-quantum gates act not in the tensor product of spaces, but in the direct product of quantum Hilbert space and so called membership space which are of different natures and properties. The concept of double (obscure-quantum) entanglement is introduced, and vector and scalar concurrences are proposed, with some examples being given.

Quantum information technology mainly includes quantum communication, quantum radar, quantum computer these three aspects, in recent years, rapid development, many countries invested heavily in development. The awarding of the Nobel Prize in Physics in 2022 to three scientists for their work in quantum informatics has further stimulated people's interest in quantum theory, which has been studied and discussed. This paper not only reviews the historical situation, but also thinks and innovates in theory. The main contents of this paper are as follows: It is pointed out that there are fundamental contradictions between relativity and quantum mechanics; The wave function, quantum statistics and uncertainty principle are discussed in detail. The hidden variable theory is reviewed and the Bell inequality is discussed. The Aspect two-photon experiment was analyzed. The rationality of Bohm experiment scheme is discussed. The development of Bell type experiment is discussed. It is pointed out that the entangled state is not acting at a distance but propagating faster than the speed of light. Reviews the Copenhagen interpretation of quantum mechanics; Quantum communication and Wootters theorem are discussed. etc. This paper holds that quantum mechanics has been finalized from 1926 to 1928, and its basic content has not changed much. But for some of the accusations, it is necessary to answer them theoretically. For example, we believe that the Copenhagen interpretation fundamentally changes our understanding of nature and marks a profound revolution in physics. And no other theory has since emerged that has such a profound understanding and wide application of microscopic phenomena as this interpretation. Another example is Bohm's two-particle correlation spin scheme in quantum entanglement experiments, which has been proved to be effective in a series of experiments, which is an important contribution in Bohm's life. This paper holds that the so-called quantum field theory is a failure, and the original quantum mechanics should still be advocated today. Current theoretical research should pay great attention to quantum entangled states, because its nature is still unclear. Understanding this "first mystery of the physical world" not only has scientific significance, but also has great philosophical significance for understanding the universe.

UndiscoveredSection:ChooseTop of pageUndiscovered <<Breakfast with Einstein: ...Scientifically Thinking: ...The Formula: The Universa...The Tectonic Plates Are M... Undiscovered, Elah Feder and Annie Minoff, Science Friday, 2018 (2nd season) Producers Elah Feder and Annie Minoff host this lively and informative podcast that explores the human side of scientific research, including priority disputes, unexpected results, and public clashes over scientific findings. The pair investigates everything from a psychology experiment about empathy for robots to the ethics of artificial hearts to controversies over dinosaur extinction. The hosts of Undiscovered have a sharp eye for fascinating stories and don’t shy away from the complexities and contradictions that emerge in reporting them. The second season is now available for download on iTunes, Google Play, and other podcast platforms. —mb Breakfast with Einstein: The Exotic Physics of Everyday ObjectsSection:ChooseTop of pageUndiscoveredBreakfast with Einstein: ... <<Scientifically Thinking: ...The Formula: The Universa...The Tectonic Plates Are M... Breakfast with Einstein: The Exotic Physics of Everyday Objects, Chad Orzel, BenBella Books, 2018, $16.95 (paper) To many people, quantum physics is strange and intimidating and evokes such mysterious and mind-boggling phenomena as spinning electrons, particles passing through multiple slits at once, and “spooky action at a distance.” To counter that preconception, physicist Chad Orzel uses his mundane morning routine to show how quantum principles are integral to everyday life, from the force required to hoist himself out of bed, to the red glow when he turns on his electric stove, to the savory aroma of his morning tea. Each activity or observation launches an extensive discussion of the physics involved and the history and scientists behind it. Orzel’s goal, he says, is to showcase the wonder to be found in the world around us. —cc Scientifically Thinking: How to Liberate Your Mind, Solve the World’s Problems, and Embrace the Beauty of ScienceSection:ChooseTop of pageUndiscoveredBreakfast with Einstein: ...Scientifically Thinking: ... <<The Formula: The Universa...The Tectonic Plates Are M... Scientifically Thinking: How to Liberate Your Mind, Solve the World’s Problems, and Embrace the Beauty of Science, Stanley A. Rice, Prometheus Books, 2018, $25.00 Believing fake news, denying climate change, and trying out fad diets are just a few examples of the ways humans fall victim to illusions and bias. It is human nature to mistake correlation for causation and to rationalize rather than to reason. However, people can use the scientific method to overcome those tendencies, writes biology professor Stanley Rice in his new book, Scientifically Thinking. Rice addresses common human biases and argues that the scientific method—forming hypotheses and putting them to the test—is really just organized common sense. Most important of all, he points out that one doesn’t need to be a scientist to use it. —cc The Formula: The Universal Laws of SuccessSection:ChooseTop of pageUndiscoveredBreakfast with Einstein: ...Scientifically Thinking: ...The Formula: The Universa... <<The Tectonic Plates Are M... The Formula: The Universal Laws of Success, Albert-László Barabási, Little, Brown and Co, 2018, $29.00 What is the link between performance and success? In his new book, physicist and network theorist Albert-László Barabási uses scientific tools to explore what success means and to identify some of the variables involved, such as hard work, talent, timing, and persistence. With stories of people who achieved real-world success—golfer Tiger Woods, ice cream moguls Ben Cohen and Jerry Greenfield, and musical-theater duo Richard Rodgers and Oscar Hammerstein, to name a few—Barabási lays out the principles that underlie their personal achievements and discusses how to implement those principles. —cc The Tectonic Plates Are Moving!Section:ChooseTop of pageUndiscoveredBreakfast with Einstein: ...Scientifically Thinking: ...The Formula: The Universa...The Tectonic Plates Are M... << The Tectonic Plates Are Moving!, Roy Livermore, Oxford U. Press, 2018, $33.95 Based on a remark made by a politician, the title The Tectonic Plates Are Moving! serves as a reminder of how little the general public understands about the revolutionary theory of plate tectonics. Author Roy Livermore, a retired marine geophysicist, has written a nontechnical discussion of the history and science of plate tectonics and the many researchers whose work contributed to the theory. Livermore attempts to lighten his rather weighty subject by including such playful chapter headings as “Plate Tectonics by Jerks,” “Scum of the Earth,” and “Chilling Out.” —cc © 2018 American Institute of Physics.

Inflammation as a biological concept has been around a long time and derives from the Latin “to set on fire” and refers to the redness and heat, and usually swelling, which accompanies injury and infection. Chronic inflammation is also associated with ageing and is described by the term “inflammaging”. Likewise, the biological concept of hormesis, in the guise of what “does not kill you, makes you stronger”, has long been recognized, but in contrast, seems to have anti-inflammatory and age-slowing characteristics. As both phenomena act to restore homeostasis, they may share some common underlying principles. Thermodynamics describes the relationship between heat and energy, but is also intimately related to quantum mechanics. Life can be viewed as a series of self-renewing dissipative structures existing far from equilibrium as vortexes of “negentropy” that ages and dies; but, through reproduction and speciation, new robust structures are created, enabling life to adapt and continue in response to ever changing environments. In short, life can be viewed as a natural consequence of thermodynamics to dissipate energy to restore equilibrium; each component of this system is replaceable. However, at the molecular level, there is perhaps a deeper question: is life dependent on, or has it enhanced, quantum effects in space and time beyond those normally expected at the atomistic scale and temperatures that life operates at? There is some evidence it has. Certainly, the dissipative adaptive mechanism described by thermodynamics is now being extended into the quantum realm. Fascinating though this topic is, does exploring the relationship between quantum mechanics, thermodynamics, and biology give us a greater insight into ageing and, thus, medicine? It could be said that hormesis and inflammation are expressions of thermodynamic and quantum principles that control ageing via natural selection that could operate at all scales of life. Inflammation could be viewed as a mechanism to remove inefficient systems in response to stress to enable rebuilding of more functional dissipative structures, and hormesis as the process describing the ability to adapt; underlying this is the manipulation of fundamental quantum principles. Defining what “quantum biological normality” is has been a long-term problem, but perhaps we do not need to, as it is simply an expression of one end of the normal quantum mechanical spectrum, implying that biology could inform us as to how we can define the quantum world.

We present a simple classical (random) signal model reproducing Born's rule. The crucial point of our approach is that the presence of detector's threshold and calibration procedure have to be treated not as simply experimental technicalities, but as the basic counterparts of the theoretical model. We call this approach threshold signal detection model (TSD). The experiment on coincidence detection which was done by Grangier in 1986 [22] played a crucial role in rejection of (semi-)classical field models in favour of quantum mechanics (QM): impossibility to resolve the wave-particle duality in favour of a purely wave model. QM predicts that the relative probability of coincidence detection, the coefficient g(2) (0), is zero (for one photon states), but in (semi-)classical models g(2)(0) ≥ 1. In TSD the coefficient g(2)(0) decreases as 1/ε2d, where εd > 0 is the detection threshold. Hence, by increasing this threshold an experimenter can make the coefficient g(2) (0) essentially less than 1. The TSD-prediction can be tested experimentally in new Grangier type experiments presenting a detailed monitoring of dependence of the coefficient g(2)(0) on the detection threshold. Structurally our model has some similarity with the prequantum model of Grossing et al. Subquantum stochasticity is composed of the two counterparts: a stationary process in the space of internal degrees of freedom and the random walk type motion describing the temporal dynamics.

The unreasonable success of quantum probability I: Quantum measurements as uniform fluctuations

We consider a variation of the multi-party communication complexity scenario where the parties are supplied with an extra resource: particles&lt;br /&gt;in an entangled quantum state. We show that, although a prior&lt;br /&gt;quantum entanglement cannot be used to simulate a communication channel, it can reduce the communication complexity of functions in&lt;br /&gt;some cases. Specifically, we show that, for a particular function among three parties (each of which possesses part of the function's input), a prior quantum entanglement enables them to learn the value of the&lt;br /&gt;function with only three bits of communication occurring among the parties, whereas, without quantum entanglement, four bits of communication are necessary. We also show that, for a particular two-party probabilistic communication complexity problem, quantum entanglement&lt;br /&gt;results in less communication than is required with only classical&lt;br /&gt;random correlations (instead of quantum entanglement). These results are a noteworthy contrast to the well-known fact that quantum entanglement cannot be used to actually simulate communication among&lt;br /&gt;remote parties.

We theoretically study the reversible process of quantum entanglement state by means of weak measurement and corresponding reversible operation. We present a protocol of the reversion operation in two bodies based on the theory of reversion of single photon and then expend it in quantum communication channels. The theoretical results demonstrate that the protocol does not break the information transmission after a weak measurement and a reversible measurement with the subsequent process in the transmission path. It can reverse the perturbed entanglement intensity evolution to its original state. Under the condition of different weak measurement intensity the protocol can reverse the perturbed quantum entanglement system perfectly. In the process we can get the classical information described by information gain from the quantum system through weak measurement operation. On the other hand, in order to realize complete reversibility, the classical information of the quantum entanglement system must obey a limited range we present in this paper in the reverse process.

In this work, we study the impact of quantum entanglement on the two-point correlation function and the associated primordial power spectrum of mean square vacuum fluctuation in a bipartite quantum field theoretic system. The field theory that we consider is the effective theorry of axion field arising from Type IIB string theory compactified to four dimensions. We compute the expression for the power spectrum of vacuum fluctuation in three different approaches, namely (1) field operator expansion (FOE) technique with the quantum entangled state, (2) reduced density matrix (RDM) formalism with mixed quantum state and (3) the method of non-entangled state (NES). For massless axion field, in all these three formalism, we reproduce, at the leading order, the exact scale invariant power spectrum which is well known in the literature. We observe that due to quantum entanglement, the sub-leading terms for these thee formalisms are different. Thus, such correction terms break the degeneracy among the analysis of the FOE, RDM and NES formalisms in the super-horizon limit. On the other hand, for massive axion field we get a slight deviation from scale invariance and exactly quantify the spectral tilt of the power spectrum in small scales. Apart from that, for massless and massive axion field, we find distinguishable features of the power spectrum for the FOE, RDM, and NES on the large scales, which is the result of quantum entanglement. We also find that such large-scale effects are comparable to or greater than the curvature radius of the de Sitter space. Most importantly, in near future if experiments probe for early universe phenomena, one can detect such small quantum effects. In such a scenario, it is possible to test the implications of quantum entanglement in primordial cosmology.

Bohm's quantum potential as an internal energy

The standard Bloch sphere representation has been recently generalized to describe not only systems of arbitrary dimension, but also their measurements, in what has been called the extended Bloch representation of quantum mechanics. This model, which offers a solution to the longstanding measurement problem, is based on the hidden-measurement interpretation of quantum mechanics, according to which the Born rule results from our lack of knowledge of the measurement interaction that each time is actualized between the measuring apparatus and the measured entity. In this article, we present the extended Bloch model and use it to investigate, more specifically, the nature of the quantum spin entities and of their relation to our three-dimensional Euclidean theater. Our analysis shows that spin eigenstates cannot generally be associated with directions in the Euclidean space, but only with generalized directions in the Blochean space, which apart from the special case of spin one-half entities, is a space of higher dimensionality. Accordingly, spin entities have to be considered as genuine non-spatial entities. We also show, however, that specific vectors can be identified in the Blochean theater that are isomorphic to the Euclidean space directions, and therefore representative of them, and that spin eigenstates always have a predetermined orientation with respect to them. We use the details of our results to put forward a new view of realism, that we call multiplex realism, providing a specific framework with which to interpret the human observations and understanding of the component parts of the world. Elements of reality can be represented in different theaters, one being our customary Euclidean space, and another one the quantum realm, revealed to us through our sophisticated experiments, whose elements of reality, in the quantum jargon, are the eigenvalues and eigenstates. Our understanding of the component parts of the world can then be guided by looking for the possible connections, in the form of partial morphisms, between the different representations, which is precisely what we do in this article with regard to spin entities.