This is a list of this week’s papers on quantum foundations published in various journals or uploaded to preprint servers such as arxiv.org and PhilSci Archive.
Quantum theory of nonlocal nonlinear Schrodinger equation. (arXiv:1511.03997v1 [quant-ph])
on 2015-11-13 9:23am GMT
Authors: Vivek M. Vyas, Zodinmawia
Nonlocal nonlinear Schrodinger model is quantised and exactly solved using the canonical framework. It is found that the usual canonical quantisation of the model leads to a theory with pathological inner product. This problem is resolved by constructing another inner product over the vector space of the theory. The resultant theory is found to be identical to that of nonrelativistic bosons with delta function interaction potential, devoid of any nonlocality. The exact eigenstates are found using the Bethe ansatz technique.
Quantum Nondemolition Measurement Enables Macroscopic Leggett-Garg Tests
PRL: General Physics: Statistical and Quantum Mechanics, Quantum Information, etc.
on 2015-11-12 3:00pm GMT
Author(s): C. Budroni, G. Vitagliano, G. Colangelo, R. J. Sewell, O. Gühne, G. Tóth, and M. W. Mitchell
We show how a test of macroscopic realism based on Leggett-Garg inequalities (LGIs) can be performed in a macroscopic system. Using a continuous-variable approach, we consider quantum nondemolition (QND) measurements applied to atomic ensembles undergoing magnetically driven coherent oscillation. We…
[Phys. Rev. Lett. 115, 200403] Published Thu Nov 12, 2015
Highlighting the Mechanism of the Quantum Speedup by Time-Symmetric and Relational Quantum Mechanics
Latest Results for Foundations of Physics
on 2015-11-12 12:00am GMT
Abstract
Bob hides a ball in one of four drawers. Alice is to locate it. Classically she has to open up to three drawers, quantally just one. The fundamental reason for this quantum speedup is not known. The usual representation of the quantum algorithm is limited to the process of solving the problem. We extend it to the process of setting the problem. The number of the drawer with the ball becomes a unitary transformation of the random outcome of the preparation measurement. This extended, time-symmetric, representation brings in relational quantum mechanics. It is with respect to Bob and any external observer and cannot be with respect to Alice. It would tell her the number of the drawer with the ball before she opens any drawer. To Alice, the projection of the quantum state due to the preparation measurement should be retarded at the end of her search; in the input state of the search, the drawer number is determined to Bob and undetermined to Alice. We show that, mathematically, one can ascribe any part of the selection of the random outcome of the preparation measurement to the final Alice’s measurement. Ascribing half of it explains the speedup of the present algorithm. This leaves the input state to Bob unaltered and projects that to Alice on a state of lower entropy where she knows half of the number of the drawer with the ball in advance. The quantum algorithm turns out to be a sum over histories in each of which Alice knows in advance that the ball is in a pair of drawers and locates it by opening one of the two. In the sample of quantum algorithms examined, the part of the random outcome of the initial measurement selected by the final measurement is one half or slightly above it. Conversely, given an oracle problem, the assumption it is one half always corresponds to an existing quantum algorithm and gives the order of magnitude of the number of oracle queries required by the optimal one.
Towards a theory of universes: structure theory and the mathematical universe hypothesis
on 2015-11-12 12:00am GMT
Abstract
The maturation of the physical image has made apparent the limits of our scientific understanding of fundamental reality. These limitations serve as motivation for a new form of metaphysical inquiry that restricts itself to broadly scientific methods. Contributing towards this goal we combine the mathematical universe hypothesis as developed by Max Tegmark with the axioms of Stewart Shapiro’s structure theory. The result is a theory we call the Theory of the Structural Multiverse (TSM). The focus is on informal theory development and constraint satisfaction. Some empirical consequences of the theory are worked out, in particular the feasibility of a predictive observer selection effect. The explanatory, unifying, and generative powers of the theory are found to substantially support the theory. The TSM is demonstrated to be an empirically significant scientific theory that is foundational to and continuous with the rest of the scientific image.
On the Brukner-Zeilinger approach
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences current issue
on 2015-11-11 1:08pm GMT
We address the problem of properly quantifying information in quantum theory. Brukner and Zeilinger proposed the concept of an operationally invariant measure based on measurement statistics. Their measure of information is calculated with probabilities generated in a complete set of mutually complementary observations. This approach was later criticized for several reasons. We show that some critical points can be overcome by means of natural extension or reformulation of the Brukner–Zeilinger approach. In particular, this approach is connected with symmetric informationally complete measurements. The ‘total information’ of Brukner and Zeilinger can further be treated in the context of mutually unbiased measurements as well as general symmetric informationally complete measurements. The Brukner–Zeilinger measure of information is also examined in the case of detection inefficiencies. It is shown to be decreasing under the action of bistochastic maps. The Brukner–Zeilinger total information can be used for estimating the map norm of quantum operations.
Dimensional reduction in causal set gravity
Classical and Quantum Gravity – latest papers
on 2015-11-09 12:00am GMT
Results from a number of different approaches to quantum gravity suggest that the effective dimension of spacetime may drop to d = 2 at small scales. I show that two different dimensional estimators in causal set theory display the same behavior, and argue that a third, the spectral dimension, may exhibit a related phenomenon of ‘asymptotic silence.’
