Real-vector-space quantum theory with a universal quantum bit

Foundations of Physics, 2015

It is shown that Quantum Mechanics is ambiguous when predicting relative frequencies for an entangled system if the measurements of both subsystems are performed in spatially separated events. This ambiguity gives way to unphysical consequences: the projection rule could be applied in one or the other temporal(?) order of measurements (being non local in any case), but symmetry of the roles of both subsystems would be broken. An alternative theory is presented in which this ambiguity does not exist. Observable relative frequencies differ from those of orthodox Quantum Mechanics, and a gendaken experiment is proposed to falsify one or the other theory. In the alternative theory, each subsystem has an individual state in its own Hilbert space, and the total system state is direct product (rank one) of both, so there is no entanglement. Correlation between subsystems appears through a hidden label that prescribes the output of arbitrary hypothetical measurements. Measurement is treated as a usual reversible interaction, and this postulate allows to determine relative frequencies when the value of a magnitude is known without in any way perturbing the system, by measurement of the correlated companion. It is predicted the existence of an accompanying system, the de Broglie wave, introduced in order to preserve the action reaction principle in indirect measurements, when there is no interaction of detector and particle. Some action on the detector, different from the one cause by a particle, should be observable.

EPL (Europhysics Letters), 2013

Recently de La Torre et al.[1] reconstructed Quantum Theory from its local structure on the basis of local discriminability and the existence of a one-parameter group of bipartite transformations containing an entangling gate. This result relies on universality of an entangling gate for quantum computation. Here we prove universality of C-NOT with local gates for Real Quantum Theory (RQT), showing that such universality would not be sufficient for the result, whereas local discriminability and the qubit structure play a crucial role. For reversible computation, generally an extra rebit is needed for RQT. As a byproduct we also provide a short proof of universality of C-NOT for CQT.

Journal of Mathematical Physics, 2008

We investigate the strengths and limitations of the Spekkens toy model, which is a local hidden variable model that replicates many important properties of quantum dynamics. First, we present a set of five axioms that fully encapsulate Spekkens' toy model. We then test whether these axioms can be extended to capture more quantum phenomena, by allowing operations on epistemic as well as ontic states. We discover that the resulting group of operations is isomorphic to the projective extended Clifford Group for two qubits. This larger group of operations results in a physically unreasonable model; consequently, we claim that a relaxed definition of valid operations in Spekkens' toy model cannot produce an equivalence with the Clifford Group for two qubits. However, the new operations do serve as tests for correlation in a two toy bit model, analogous to the well known Horodecki criterion for the separability of quantum states.

2014

In this work the usual formulation of the variational methods of Classical Mechanics is slightly modified by describing space as an interface implementing instructions: these instructions, in the form of bit strings, determine the existence and the dynamics of classical systems and are global – that is, their information content is present at every point of space. These changes are then carried over to Feynman’s path integral formulation of non-relativistic Quantum Mechanics by recurring to the quantum superposition principle. The information content of the instructions is expanded to include spin; it then follows an interpretation within this framework of the collapse of the wave function in terms of splitting and merging of information and, as an illustration, of Wheeler’s delayed choice experiment.

SSRN Electronic Journal, 2021

Speedy developments in Quantum Technologies and Computing with far reaching potential applications in non-traditional fields of finance, bio-medical, biochemistry , etc., make it imperative that fundamentals of Quantum Technologies are well explained and understood. Meanwhile, paradigms of so-called quantum non-locality, wave function (WF) "collapse", "Schrödinger cat" and some other historically popular misconceptions continue to stir controversies, feed mysteries around quantum phenomena and confuse prospective users. In this regard we argue that above misinterpretations stem essentially from classically minded and experimentally unverifiable perceptions, recasting and fitting the Principle of Superposition and key experimental details into classical terms and logic. Further, we revisit key components of general quantum measurement protocols-analyzers and detectors-and explain in this context paradoxes of WF collapse and Schrödinger cat. Then to demystify and clarify the concept of entanglement in multi-component systems (comprised of photons, electrons, atoms and even small macro-objects) and longdistance correlations, we remind that quantum measurements routinely reveal correlations mandated by conservation laws in each individual realization. Remarkably, this "correlation-by-initial conditions" (in addition to traditional "correlation-byinteractions") is by no means an exclusive quantum feature, but also has it analogiesin simplified form though-in Classical Mechanics (CM). However, an appearance and understanding of those correlations in Quantum Mechanics (QM) is governed by the wave-particle duality, forgetting of which leads to endless line of paradoxes. We keep reiterating that QM is not a dynamical theory in the same sense the CM is-it is a statistical theory, as established in 1926 by Born's postulate. That is, while QM enforces conservations laws and ensuing correlations in each individual outcome, it does not indicate how exactly a specific outcome is selected. This selection remains fundamentally random and represents true randomness of QM, the latter being a statistical paradigm with a WF standing for a complex-valued amplitude of a distribution function. We note in conclusion that, although a quantum logic is admittedly a challenge for classical imagination, mechanistically complementing quantum foundations by classically minded expectations trivializes true quantum effects to primitive classical constructions and gives rise to a mysteriously omnipresent non-locality.

2012

I argue for a realist interpretation of the quantum state. I begin by reviewing and critically evaluating two arguments for an antirealist interpretation of the quantum state, the first derived from the so-called 'measurement problem', and the second from the concept of local causality. I argue that existing antirealist interpretations do not solve the measurement problem. Furthermore, I argue that it is possible to construct a local, realist interpretation of quantum mechanics, using methods borrowed from quantum field theory and based on John S. Bell's concept of 'local beables'.

International Journal of Theoretical Physics, 1985

The problem of setting up quantum theory as a universal physical theory is investigated. It is shown that the existing formalism, in either the conventional or the Everett interpretation, must be supplemented by an additional structure, the "interpretation basis." This is a preferred ordered orthonormal basis in the space of states. Quantum measurement theory is developed as a tool for determining the interpretation basis. The augmented quantum theory is discussed.

Activitas Nervosa Superior, 2019

A realist view of the quantum world is given along the lines of Werner Heisenberg's Copenhagen interpretation of quantum mechanics and set in contrast to that associated with John von Neumann by Henry Stapp. This view is distinguished by, among other elements: i) the notion of quantum potentia and its actualization which results in classical recorded values of measured quantities, ii) the grounding of the existence and chancy character of individual measurement events in the plenitude principle as applied to the set of eigenvalues of observables on the space of quantum states, and iii) the identification of the individuals of the theory by a straightforward individuation principle.

2007

It is shown that a coherent understanding of all quantized phenomena, including those governed by unitary evolution equations as well as those related to irreversible quantum measurements, can be achieved in a scenario of successive nonequilibrium phase transitions, with the lowest hierarchy of these phase transitions occurring in a ``resonant cavity'' formed by the entire matter and energy content of the universe. In this formalism, the physical laws themselves are resonantly-selected and ordered in the universe cavity in a hierarchical manner, and the values of fundamental constants are determined through a Generalized Mach's Principle. The existence of a preferred reference frame in this scenario is shown to be consistent with the relational nature of the origin of physical laws. Covariant unitary evolution is shown to connect smoothly with the reduction of wavefunction in the preferred frame during quantum measurement. The superluminal nature of quantum processes in ...

2020

As one chapter, we about to begin a journey with exploring the limitation of the causality that rules the whole universe. Quantum mechanics is established on the basis of the phenomenology and the lack of ontology builds the wall which blocks the causality. It is very difficult to reconcile the probability and the causality in such a platform. A higher dimension consideration may leverage this dilemma by expanding the vision. Information may seem to be discontinuous or even so weird if only be viewed from a part of the degree of freedoms. Based on this premise, we reexamined the microscopic world within a complex space. Significantly, some knowledge beyond the empirical findings is revealed and paves the way for a more detailed exploration of the quantum world. The random quantum motion is essential for atomic particle and exhibits a wave-related property with a bulk of trajecto-ries. It seems we can break down the wall which forbids the causality entering the quantum kingdom and connect quantum mechanics with classical mechanics. The causality returns to the quantum world without any assumption in terms of the quantum random motion under the optimal guidance law in complex space. Thereby hangs a tale, we briefly introduce this new formulation from the fundamental theoretical description to the practical technology applications.