Quantum Deep Learning Triuniverse

An original quantum foundations concept of a deep learning computational Universe is introduced. The fundamental information of the Universe (or Triuniverse) is postulated to evolve about itself in a Red, Green and Blue (RGB) tricoloured stable self-mutuality in three information processing loops. The colour is a non-optical information label. The information processing loops form a feedback-reinforced deep learning macrocycle with trefoil knot topology. Fundamental information processing is driven by ψ-Epistemic Drive, the Natural appetite for information selected for advantageous knowledge. From its substrate of Mathematics, the knotted information processing loops determine emergent Physics and thence the evolution of super-emergent Life (biological and artificial intelligence). RGB-tricoloured information is processed in sequence in an Elemental feedback loop (R), then an Operational feedback loop (G), then a Structural feedback loop (B) and back to an Elemental feedback loop (R), and so on around the trefoil in deep learning macrocycles. It is postulated that hierarchical information correspondence from Mathematics through Physics to Life is mapped and conserved within each colour. The substrate of Mathematics has RGB-tricoloured feedback loops which are respectively Algebra (R), Algorithms (G) and Geometry (B). In Mathematics, the trefoil macrocycle is Algebraic Algorithmic Geometry and its correlation system is a Tensor Neural Knot Network enabling Qutrit Entanglement. Emergent Physics has corresponding RGB-tricoloured feedback loops of Quantum Mechanics (R), Quantum Deep Learning (G) and Quantum Geometrodynamics (B). In Physics, the trefoil macrocycle is Quantum Intelligent Geometrodynamics and its correlation system is Quantum Darwinism. Super-emergent Life has corresponding RGB-tricoloured loops of Variation (R), Selection (G) and Heredity (B). In the evolution of Life, the trefoil macrocycle is Variational Selective Heredity and its correlation ecosystem is Darwin’s ecologically “Entangled Bank”.

Conceptual Problems in Bell’s Inequality and Quantum Entanglement

The description of the microscopic world in quantum mechanics is very different from that in classical physics, and there are some points of view that are contrary to intuition and logic. The first is the problem of reality;quantum mechanics believes the behavior of micro particles is random and jumping. The second is the loss of certainty;the conjugate physical variables of a system cannot be determined synchronously, they satisfy the Heisenberg uncertainty principle. The third is the non-local correlation. The measurement of one particle in the quantum entanglement pair will influence the state of the other entangled particle simultaneously. In this paper, some concepts related to quantum entanglement, such as EPR correlation, quantum entanglement correlation function, Bell’s inequality and so on, are analyzed in detail. Analysis shows that the mystery and confusion in quantum theory may be caused by the logical problems in its basic framework. Bell’s inequality is only a mathematical theorem, but its physical meaning is actually unclear. The Bell state of quantum entangled pair may not satisfy the dynamic equation of quantum theory, so it cannot describe the true state of microscopic particles. In this paper, the correct correlation functions of spin entanglement pair and photonic entanglement pair are strictly derived according to normal logic. Quantum theory is a more fundamental theory than classical mechanics, and they are not equal relation in logic. However, there are still some unreasonable contents in the framework of quantum theory, which need to be improved. In order to disclose the real relationship between quantum theory and classical mechanics, we propose some experiments which provide intuitionistic teaching materials for the new interpretation of quantum theory.

Optimal phase estimation with photon-number difference measurement using twin-Fock states of light

Quantum phase measurement with multiphoton twin-Fock states has been shown to be optimal for detecting equal numbers of photons at the output ports of a Mach–Zehnder interferometer(i.e., the so-called single-fringe detection), since the phase sensitivity can saturate the quantum Cramér–Rao lower bound at certain values of phase shift. Here we report a further step to achieve a global phase estimation at the Heisenberg limit by detecting the particle-number difference(i.e., the ?_z measurement). We show the role of experimental imperfections on the ultimate estimation precision with the six-photon twin-Fock state of light. Our results show that both the precision and the sensing region of the ?_z measurement are better than those of the single-fringe detection, due to combined contributions of the measurement outcomes. We numerically simulate the phase estimation protocol using an asymptotically unbiased maximum likelihood estimator.

Counterfactual Definiteness and Bell’s Inequality

Counterfactual definiteness must be used as at least one of the postulates or axioms that are necessary to derive Bell-type inequalities. It is considered by many to be a postulate that not only is commensurate with classical physics (as for example Einstein’s special relativity), but also separates and distinguishes classical physics from quantum mechanics. It is the purpose of this paper to show that Bell’s choice of mathematical functions and independent variables implicitly includes counterfactual definiteness. However, his particular choice of variables reduces the generality of his theory, as well as the physics of all Bell-type theories, so significantly that no meaningful comparison of these theories with actual Einstein-Podolsky-Rosen experiments can be made.

Experimental demonstration of tight duality relation in three-path interferometer

Bohr’s principle of complementarity has a long history and it is an important topic in quantum theory,among which the famous example is the duality relation.The relation between visibilityC and distinguishability D,C2+D2≤1,has long been recognized as the only representative of the duality relation.However,recent researches have shown that this inequality is not good enough because it is not tight for multipath interferometers.Meanwhile,a tight bound for the multipath interferometer has been put forward.Here we design and experimentally implement a three-path interferometer coupling with path indicator states.The wave property of photons is characterized by l1-norm coherence measure,and the particle property is based on distinguishability of the indicator states.The new duality relation of the three-path interferometer is demonstrated in our experiment,which bounds the union of a right triangle and a part of elliptical area inside the quadrant of a unit circle.Data analysis confirms that the new bound is tight for photons in three-path interferometers.

Time Operator in Relativistic Quantum Mechanics

It is first shown that the Dirac＇s equation in a relativistic frame could be modified to allow discrete time, in agreement to a recently published upper bound. Next, an exact self-adjoint 4 x 4 relativistic time operator for spin-l/2 particles is found and the time eigenstates for the non-relativistic case are obtained and discussed. Results confirm the quantum mechanical speculation that particles can indeed occupy negative energy levels with vanishingly sma/l but non- zero probablity, contrary to the general expectation from classical physics. Hence, Wolfgang Pauli＇s objection regarding the existence of a self-adjoint time operator is fully resolved. It is shown that using the time operator, a bosonic field referred here to as energons may be created, whose number state representations in non-relativistic momentum space can be explicitly found.

Quantum state tomography for generic pure states

We examine the problem of whether a multipartite pure quantum state can be uniquely determined by its reduced density matrices.We show that a generic pure state in three party Hilbert space HA■HB■HC, where dim(HA) = 2 and dim(HB) = dim(HC), can be uniquely determined by its reduced states on subsystems HA■HB and HA■HC. Then, we generalize the conclusion to the case that dim(H_1) > 2. As a corollary, we show that a generic N-qudit pure quantum state is uniquely determined by only two of its[(N+1)/2]-particle reduced density matrices. Furthermore,our results indicate a method to uniquely determine a generic N-qudit pure state of dimension D = d^N with only O(D) local measurements, which is an improvement compared to the previous known approach that uses O(D log^2 D) or O(D log D) local measurements.

Consequences of a two-time relativistic Bohmian model

Effects of a Bohmian type quantum-relativistic theory are explored.The model is obtained by introducing a new and independent time parameter whose relative motions are not directly observable and cause quantum uncertainties of the physical observables.Unlike the usual de Broglie-Bohm theories,the Quantum Potential does not directly affect the observable motion,but determines the one that is relative to the new time variable.It turns out that the Zitterbewegung of a free particle,of which a more general law is obtained,is the key example of these hidden motions and,through it,it seems possible to give physical reality to the Feynman's paths.A relativistic revision of the uncertainty principle is also derived from the theory.

Photons can hide where they have been

Recently,the nested Mach–Zehnder interferometer[Phys.Rev.Lett.111,240402(2013)]was modified by adding Dove prisms in a paper[Quantum Stud.:Math.Found.2,255(2015)],and an interesting result is that,after the Dove prisms were inserted,a signal at the first mirror of the nested interferometer was obtained.But,according to the former original paper,the photons have never been present near that mirror.In this work,we interpret this result naturally by resorting to the three-path interference method.Moreover,we find that even though the photons have been somewhere,they can hide the trace of being there.