Decoherent Histories and Realism

We reconsider the decoherent histories approach to quantum mechanics and analyze some problems related to its interpretation which we believe have not been adequately clarified by its proponents. We put forward some assumptions which, in our opinion, are necessary for a realistic interpretation of the probabilities that the formalism attaches to decoherent histories. We prove that such assumptions, unless one limits the set of the decoherent families which can be taken into account, lead to a logical contradiction. The line of reasoning we follow is conceptually different from other arguments which have been presented and which have been rejected by the supporters of the decoherent histories approach. The conclusion is that the decoherent histories approach, to be considered as an interesting realistic alternative to the orthodox interpretation of quantum mechanics, requires the identification of a mathematically precise criterion to characterize an appropriate set of decoherent families which does not give rise to any problem.     

Glafka 2004: The Decoherent Histories Approach to the Quantization of Cosmological Models

The decoherent histories approach is a particularly useful approach to quantum theory especially when time enters in a non-trivial way, or indeed, when there is no physical time coordinate at all, as is the case in quantum cosmology. Here, attempts to apply the decoherent histories approach to quantum cosmology are described.     

Spacetime Coarse Grainings and the Problem of Time in the Decoherent Histories Approach to Quantum Theory

We investigate the possibility of assigning consistent probabilities to sets of histories characterized by whether they enter a particular subspace of the Hilbert space of a closed system during a given time interval. In particular we investigate the case that this subspace is a region of the configuration space. This corresponds to a particular class of coarse grainings of spacetime regions. We consider the arrival time problem, as a warm up, to deal with the problem of time in reparametrization invariant theories (as for example in canonical quantum gravity) which subsequently we examine. Decoherence conditions and probabilities for those application are derived. The resulting decoherence condition does not depend on the explicit form of the restricted propagator that was problematic for generalizations such as application in quantum cosmology. Closely related to our results, is the problem of tunnelling time as well as the quantum Zeno effect. Some interpretational comments conclude, and we discuss the applicability of this formalism to deal with the arrival time problem and the problem of time in general.     

Quantum Cryptography in Spin Networks

In this paper we propose a new scheme of long-distance quantum cryptography based on spin networks with qubits stored in electron spins of quantum dots. By＂ conditional Faraday- rotation, single photon polarization measurement, and quantum state transfer, maximal-entangled Bell states for quantum cryptography between two long-distance parties are created. Meanwhile, efficient quantum state transfer over arbitrary＂ distances is obtained in a spin chain by＂ a proper choice of coupling strengths and using spin memory- technique improved. We also analyse the security＂ of the scheme against the cloning-based attack which can be also implemented in spin network and discover that this spin network cloning coincides with the optimal fidelity- achieved by＂ an eavesdropper for entanglement-based cryptography.     

Invariants of Spin Networks Embedded in Three-Manifolds

We study the invariants of spin networks embedded in a three-dimensional manifold which are based on the path integral for SU(2) BF-Theory. These invariants appear naturally in Loop Quantum Gravity, and have been defined as spin-foam state sums. By using the Chain-Mail technique, we give a more general definition of these invariants, and show that the state-sum definition is a special case. This provides a rigorous proof that the state-sum invariants of spin networks are topological invariants. We derive various results about the BF-Theory spin network invariants, and we find a relation with the corresponding invariants defined from Chern-Simons Theory, i.e. the Witten-Reshetikhin-Turaev invariants. We also prove that the BF-Theory spin network invariants coincide with V. Turaev’s definition of invariants of coloured graphs embedded in 3-manifolds and thick surfaces, constructed by using shadow-world evaluations. Our framework therefore provides a unified view of these invariants.     

Generation of Multi-qubit Graph States via Spin Networks

We propose an efficient scheme for preparing multi-qubit graph states via spin networks. The classical types of graph states including cluster state, Greenberger-Horne-Zeilinger state and circle-shaped states can be generated by using imaginary SWAP gate. Our method makes the generation of multipartite entangled graph states more efficient than the ones based on conventional controlled-NOT and controlled phase flip gate for solid-state devices.     

Overcoming Decoherent Effects from Squeezed Vacuum Reservoir

A strategy is investigated to overcome the decoherence for open quantum system by controlling external parameters. The results show that output state may be a pure state in some critical magnetic field parameters which depend on the decay rates so that one may perfectly preserve memory of initial single-qubit states at the finial state under some conditions. The way is applied to two-level atomic systems interacting with squeezed vacuum reservoir.     

Decoherent quantum walks driven by a generic coin operation

We consider the effect of different unitary noise mechanisms on the evolution of a quantum walk (QW) on a linear chain with a generic coin operation: (i) bit-flip channel noise, restricted to the coin subspace of the QW and (ii) topological noise caused by randomly broken links in the linear chain. Similarities and differences in the respective decoherent dynamics of the walker as a function of the probability per unit time of a decoherent event taking place are discussed.     

Duality Between Spin Networks and the 2D Ising Model

The goal of this paper is to exhibit a deep relation between the partition function of the Ising model on a planar trivalent graph and the generating series of the spin network evaluations on the same graph. We provide respectively a fermionic and a bosonic Gaussian integral formulation for each of these functions and we show that they are the inverse of each other (up to some explicit constants) by exhibiting a supersymmetry relating the two formulations. We investigate three aspects and applications of this duality. First, we propose higher order supersymmetric theories that couple the geometry of the spin networks to the Ising model and for which supersymmetric localization still holds. Secondly, after interpreting the generating function of spin network evaluations as the projection of a coherent state of loop quantum gravity onto the flat connection state, we find the probability distribution induced by that coherent state on the edge spins and study its stationary phase approximation. It is found that the stationary points correspond to the critical values of the couplings of the 2D Ising model, at least for isoradial graphs. Third, we analyze the mapping of the correlations of the Ising model to spin network observables, and describe the phase transition on those observables on the hexagonal lattice. This opens the door to many new possibilities, especially for the study of the coarse-graining and continuum limit of spin networks in the context of quantum gravity.     

Histories Without Collapse

International Journal of Theoretical Physics - In this paper, we introduce the concept of non-deterministic tree automata based on quantum-valued logic whose underlying structure is a complete...     

Consistent Histories in Quantum Cosmology

We illustrate the crucial role played by decoherence (consistency of quantum histories) in extracting consistent quantum probabilities for alternative histories in quantum cosmology. Specifically, within a Wheeler-DeWitt quantization of a flat Friedmann-Robertson-Walker cosmological model sourced with a free massless scalar field, we calculate the probability that the universe is singular in the sense that it assumes zero volume. Classical solutions of this model are a disjoint set of expanding and contracting singular branches. A naive assessment of the behavior of quantum states which are superpositions of expanding and contracting universes suggests that a “quantum bounce” is possible i.e. that the wave function of the universe may remain peaked on a non-singular classical solution throughout its history. However, a more careful consistent histories analysis shows that for arbitrary states in the physical Hilbert space the probability of this Wheeler-DeWitt quantum universe encountering the big bang/crunch singularity is equal to unity. A quantum Wheeler-DeWitt universe is inevitably singular, and a “quantum bounce” is thus not possible in these models.     

Spin q , Twistor and Spin c

Spin ^q structures induce (Spin ^q style) twistor spaces, which possess canonical Spin ^c structures. Such structures produce Dirac operators. Their indices for the even dimensional case, and the adiabatic limit of their reduced η-invariants for the odd dimensional case, are discussed. Received: 3 October 1995 / Accepted: 2 March 1997     

Consistency Conditions for Probabilities of Quantum Histories

In the framework of the histories approach to quantum mechanics developed by Griffiths and Omnès, we consider the question of the uniqueness of the probability assigned to the histories; the question was solved by Omnès only in special cases. We find conditions which ensure uniqueness of such probability in the general case.