Weekly Papers on Quantum Foundations (1)

The first superconductor was discovered in 1911, when elemental mercury was cooled below the helium liquefaction temperature. Suddenly, it ceased to show any resistance to the flow of electricity. Soon after, it became clear that some metals become superconducting upon cooling, and some do not. Half a century or so later, a quantum-mechanical theory of superconductivity was conceived by Bardeen, Cooper, and Schrieffer (BCS). On page 52 of this issue, Prakash et al. (1) report the surprise discovery of superconductivity at extremely low temperatures in bismuth, a familiar and extensively documented metal (2). The results mark a new episode in the history of superconductivity. Author: Kamran Behnia

Authors: Adam R. BrownLeonard Susskind

We give arguments for the existence of a thermodynamics of quantum complexity that includes a “Second Law of Complexity”. To guide us, we derive a correspondence between the computational (circuit) complexity of a quantum system of $K$ qubits, and the positional entropy of a related classical system with $2^K$ degrees of freedom. We also argue that the kinetic entropy of the classical system is equivalent to the Kolmogorov complexity of the quantum Hamiltonian. We observe that the expected pattern of growth of the complexity of the quantum system parallels the growth of entropy of the classical system. We argue that the property of having less-than-maximal complexity (uncomplexity) is a resource that can be expended to perform directed quantum computation.

Although this paper is not primarily about black holes, we find a surprising interpretation of the uncomplexity-resource as the accessible volume of spacetime behind a black hole horizon.

Authors: Kevin VansletteAriel Caticha

The problem of measurement in quantum mechanics is studied within the Entropic Dynamics framework. We discuss von Neumann and Weak measurements, wavefunction collapse, and Weak Values as examples of bayesian and entropic inference.

Authors: Qiu-Cheng SongJun-Li LiGuang-Xiong PengCong-Feng Qiao

Uncertainty relation lies at the heart of quantum mechanics, characterizing the incompatibility of non-commuting observables in the preparation of quantum states. An important question is how to improve the lower bound of uncertainty relation. Here we present a variance-based sum uncertainty relation for $N$ incompatible observables stronger than the simple generalization of the uncertainty relation for two observables derived by Maccone and Pati [Phys. Rev. Lett. {\bf113}, 260401 (2014)]. Further comparisons of our uncertainty relation with other related ones for spin-$\frac{1}{2}$ and spin-$1$ particles indicate that the obtained uncertainty relation gives a better lower bound.

Authors: Kevin M. ShortMatthew M. Morena

We consider the quantum-classical correspondence from a classical perspective by discussing the potential for chaotic systems to support behaviors normally associated with quantum mechanical systems. Our main analytical tool is a chaotic system’s set of cupolets, which are essentially highly-accurate stabilizations of its unstable periodic orbits. The discussion is motivated by the bound or entangled states that we have recently detected between interacting chaotic systems, wherein pairs of cupolets are induced into a state of mutually-sustaining stabilization that can be maintained without external intervention. This state is known as chaotic entanglement as it has been shown to exhibit several properties consistent with quantum entanglement. For instance, should the interaction be disturbed, then the chaotic entanglement would be broken. In this paper, we further describe chaotic entanglement and go on to discuss the capacity for chaotic systems to exhibit other characteristics that are conventionally associated with quantum mechanics, namely analogs to wave function collapse, the measurement problem, the superposition of states, and to quantum entropy definitions. In doing so, we argue that these characteristics need not be regarded exclusively as quantum mechanical.

Tales of the Quantum


on 2017-1-05 12:00am GMT

Author: Art Hobson
ISBN: 9780190679637
Binding: Hardcover
Publication Date: 05 January 2017
Price: $29.95

Quantum computers ready to leap out of the lab in 2017

Nature 541, 7635 (2017). http://www.nature.com/doifinder/10.1038/541009a

Author: Davide Castelvecchi

Google, Microsoft and a host of labs and start-ups are racing to turn scientific curiosities into working machines.

Kim, Bryce (2016) PBR theorem and sub-ensemble of quantum state. [Preprint]
Kim, Bryce (2016) Can Everettian Interpretation Survive Continuous Spectrum? [Preprint]
Kim, Bryce (2016) What if we have only one universe and closed timelike curves exist? [Preprint]

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