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Daniel I. Fivel

Publications and source records attributed to Daniel I. Fivel.

12 recordsLinked to original sources
arXiv2010

Derivation of the Rules of Quantum Mechanics from Information-Theoretic Axioms

Conventional quantum mechanics with a complex Hilbert space and the Born Rule is derived from five axioms describing properties of probability distributions for the outcome of measurements. Axioms I,II,III are common to quantum mechanics and hidden variable theories. Axiom IV recognizes a phenomenon, first noted by Turing and von Neumann, in which the increase in entropy resulting from a measurement is reduced by a suitable intermediate measurement. This is shown to be impossible for local hidden variable theories. Axiom IV, together with the first three, almost suffice to deduce the conventional rules but allow some exotic, alternatives such as real or quaternionic quantum mechanics. Axiom V recognizes a property of the distribution of outcomes of random measurements on qubits which holds only in the complex Hilbert space model. It is then shown that the five axioms also imply the conventional rules for all dimensions.

quant-ph↗
arXiv2003

Disappearance of the Measurement Paradox in a Metaplectic Extension of Quantum Dynamics

It is shown that Schrodinger dynamics can be embedded in a larger dynamical theory which extends its symmetry group from the unitary group to the full metaplectic group, i.e. the group of linear canonical transformations. Among the newly admitted non-unitary processes are analogues of the classical measurement process which makes it possible to treat the wave-function as an objective property of the quantum mechanical system on the same footing as the phase-space coordinates of a classical system. The notion of "observables" that in general have values only when measured can then be dispensed with, and the measurement paradox disappears.

quant-ph↗
arXiv2002

Quantum Surveying: How Entangled Pairs Act as Measuring Rods on Manifolds of Generalized Coherent States

Generalized coherent states arise from reference states by the action of locally compact transformation groups and thereby form manifolds on which there is an invariant measure. It is shown that this implies the existence of canonically associated Bell states that serve as measuring rods by relating the metric geometry of the manifold to the observed EPR correlations. It is further shown that these correlations can be accounted for by a hidden variable theory which is non-local but invariant under the stability group of the reference state.

quant-ph↗
arXiv2001

How a Quantum Theory Based on Generalized Coherent States Resolves the EPR and Measurement Problems

It is shown that the quantum theory can be formulated on homogeneous spaces of generalized coherent states in a manner that accounts for interference, entanglement, and the linearity of dynamics without using the superposition principle. The coherent state labels, which are essentially instructions for preparing states, make it unnecessary to identify properties with projectors in Hilbert space. This eliminates the so called "eigenvalue-eigenstate" link, and the theory thereby escapes the measurement problem. What the theory allows us to predict is the distribution in the outcomes of tests of relations between coherent states. It is shown that quantum non-determinism can be attributed to a hidden variable (noise) in the space of relations without violating the no-go theorems (e.g. Kochen-Specker). It is shown that the coherent state vacuum is distorted when entangled states are generated. The non-locality of the vacuum permits this distortion to be felt everywhere without the transmission of a signal and thereby accounts for EPR correlations in a manifestly covariant way.

quant-ph↗
arXiv1997

An Indication From the Magnitude of CP Violations that Gravitation is a Possible Cause of Wave-Function Collapse

We consider experimental evidence for the hypothesis that the Planck energy, $E_p \approx 10^{19}GeV$, sets the scale $ε$ at which wave function collapse causes deviations from linear Schrödinger evolution. With a few plausible assumptions about the collapse process, we first show that the observed CP violation in $K_L$ decay implies a lower bound on $ε$ remarkably close to $E_p$. If the bound is saturated, the entire CP violation is due to collapse and a prediction made that the branching ratio for CP violation in the B meson decay will be $γ\approx 10^{-5}$. We then show that the assumptions are consequences of a simple non-linear, stochastic modification of the Schrödinger equation with $ε$ setting the scale of the non-linearity.

quant-ph↗
arXiv1997

How to Probe for Dynamical Structure in the Collapse of Entangled States Using Nuclear Magnetic Resonance

The spin state of two magnetically inequivalent protons in contiguous atoms of a molecule becomes entangeled by the indirect spin-spin interaction (j-coupling). The degree of entanglement oscillates at the beat frequency resulting from the splitting of a degeneracy. This beating is manifest in NMR spectroscopy as an envelope of the transverse magnetization and should be visible in the free induction decay signal. The period (approximately 1 sec) is long enough for interference between the linear dynamics and collapse of the wave-function induced by a Stern-Gerlach inhomogeneity to significantly alter the shape of that envelope. Various dynamical collapse theories can be distinguished by their observably different predictions with respect to this alteration. Adverse effects of detuning due to the Stern-Gerlach inhomogeneity can be reduced to an acceptable level by having a sufficiently thin sample or a strong rf field.

quant-ph↗
arXiv1996

A Dynamical Reduction Theory of Einstein-Podolsky-Rosen Correlations and a Possible Origin of CP Violations

We show that there is essentially only one way to construct a stochastic Schrodinger equation that gives a dynamical account of the transformation of entangled into factorized states and is consistent both with quantum mechanics and required symmetries. The noisy, non-linear term is a unimodular scalar multiple of the time reversal operator that must be present whenever a Hamiltonian term in the Schrodinger equation can distinguish the factorized constituents of an entangled state. The dynamical mechanism involved in the transformation of entangled into factorized states provides an explanation for the fact that Einstein-Podolsky-Rosen correlations appear in a time determined by the response of the measuring device and independent of the distance between the particles. The dependence on the response time of the measuring device may be testable through a delay in observing the collapse of mesoscopic ``Schrodinger cat" states in ion traps. It is further shown that there are situations where a two-particle interaction can induce a non-linear term by virtue of coupling to decay modes that distinguish factorized constituents of an entangled state. We show that this should happen in the neutral K-meson system where the entangled $K_L$ state is pushed slightly in the direction of a factorized constituent ($K_o$ or $\overline{K_o}$) as a consequence of the fact that these can be distinguished via the sign of the charged lepton in a semi-leptonic decay mode. The result is a CP violation that is within 20% of the experimental value.

quant-ph↗
arXiv1994

The prime factorization property of entangled quantum states

Completely entangled quantum states are shown to factorize into tensor products of entangled states whose dimensions are powers of prime numbers. The entangled states of each prime-power dimension transform among themselves under a finite Heisenberg group. We are thus led to examine processes in which factors are exchanged between entangled states and so consider canonical ensembles in which these processes occur. It is shown that the Riemann zeta function is the appropriate partition function and that the Riemann hypothesis makes a prediction about the high temperature contribution of modes of large dimension.

hep-th↗
arXiv1994

The Lattice Dynamics of Completely Entangled States and its Application to Communication Schemes

(Presented at conference on Fundamental Problems in Physics - UMBC - June 1994) It is shown that among the orthogonal sets of EPR (completely entangled) states there is a unique basis (up to equivalence) that is a also a perfectly resolved set of coherent states with respect to a pair of complementary observables. This basis defines a lattice phase space in which quadratic Hamiltonians constructed from the observables induce site-to-site hopping at discrete time intervals. When recently suggested communication schemes\cite{BENa} are adapted to the lattice they are greatly enhanced, because the finite Heisenberg group structure allows dynamic generation of signal sequences using the quadratic Hamiltonians. We anticipate the possibility of interferometry by determining the relative phases between successive signals produced by the simplest Hamiltonians of this type, and we show that they exhibit a remarkable pattern determined by the number-theoretic Legendre symbol.

hep-th↗
arXiv1994

How Interference Effects in Mixtures Determine the Rules of Quantum Mechanics

It is shown that elementary indistinguishability properties of partially polarized mixtures are consistent only with the conventional Hilbert space model of quantum mechanics and a few exotic alternatives. This applies even in low dimensions where quantum logic and Gleason's theorem give either weak or no constraints. Experimental methods for eliminating the exotic cases (which include quaternionic and octonionic variants of quantum mechanics) are described.

hep-th↗
arXiv1994

Implications of an Ambiguity in J.S. Bell's Analysis of the Einstein-Podolsky-Rosen Problem

An ambiguity is pointed out in J.S. Bell's argument that the distinction between quantum mechanics and hidden variable theories cannot be found in the behavior of single-particle beams. Within the context of theories for which states are unambiguously defined it is shown that the question of whether quantum mechanics or a locally realistic theory is valid may indeed be answered by single-particle beam measurements. It is argued that two-particle correlation experiments are required to answer the more fundamental question of whether or not the notion of a state can be unambiguously defined. As a byproduct of the discussion the general form of completely entangled states is deduced.

hep-th↗