Weekly Papers on Quantum Foundations (2)

Author(s): Miao Zhang

Quantum weak measurement, measuring some observable quantities within the selected subensemble of the entire quantum ensemble, can produce many interesting results such as the superluminal phenomena. An outcome of such a measurement is the weak value which has been applied to amplify some weak signa…
[Phys. Rev. A 95, 012114] Published Fri Jan 13, 2017

Abstract

The existence of non-local correlations between outcomes of measurements in quantum entangled systems strongly suggests that we are dealing with some form of causation here. An assessment of this conjecture in the context of the collapse interpretation of quantum mechanics is the primary goal of this paper. Following the counterfactual approach to causation, I argue that the details of the underlying causal mechanism which could explain the non-local correlations in entangled states strongly depend on the adopted semantics for counterfactuals. Several relativistically-invariant interpretations of spatiotemporal counterfactual conditionals are discussed, and the corresponding causal stories describing interactions between parts of an entangled system are evaluated. It is observed that the most controversial feature of the postulated causal connections is not so much their non-local character as a peculiar type of circularity that affects them.

Okon, Elias and Sudarsky, Daniel (2017) The weight of collapse: dynamical reduction models in general relativistic contexts. [Preprint]

Author(s): Thibaut Josset, Alejandro Perez, and Daniel Sudarsky

A theoretical analysis suggests that quantum mechanical violations of energy conservation may arise in some proposed models of quantum gravity. If realized in nature, these violations could manifest on cosmological scales as an effective cosmological constant.


[Phys. Rev. Lett. 118, 021102] Published Wed Jan 11, 2017

Authors: Giulio GasbarriMarko TorošAngelo Bassi

Starting from an idea of S.L. Adler~\cite{Adler2015}, we develop a novel model of gravity-induced spontaneous wave-function collapse. The collapse is driven by complex stochastic fluctuations of the spacetime metric. After having derived the fundamental equations, we prove the collapse and amplification mechanism, the two most important features of a consistent collapse model. Under reasonable simplifying assumptions, we constrain the strength $\xi$ of the complex metric fluctuations with available experimental data. We show that $\xi\geq 10^{-26}$ in order for the model to guarantee classicality of macro-objects, and at the same time $\xi \leq 10^{-20}$ in order not to contradict experimental evidence. As a comparison, in the recent discovery of gravitational waves in the frequency range 35 to 250 Hz, the (real) metric fluctuations reached a peak $\xi \sim 10^{-21}$.

Authors: Hans-Thomas Elze

A synopsis is offered of the properties of discrete and integer-valued, hence “natural”, cellular automata (CA). A particular class comprises the “Hamiltonian CA” with discrete updating rules that resemble Hamilton’s equations. The resulting dynamics is linear like the unitary evolution described by the Schr\”odinger equation. Employing Shannon’s Sampling Theorem, we construct an invertible map between such CA and continuous quantum mechanical models which incorporate a fundamental discreteness scale $l$. Consequently, there is a one-to-one correspondence of quantum mechanical and CA conservation laws. We discuss the important issue of linearity, recalling that nonlinearities imply nonlocal effects in the continuous quantum mechanical description of intrinsically local discrete CA – requiring locality entails linearity. The admissible CA observables and the existence of solutions of the $l$-dependent dispersion relation for stationary states are mentioned, besides the construction of multipartite CA obeying the Superposition Principle. We point out problems when trying to match the deterministic CA here to those envisioned in ‘t Hooft’s CA Interpretation of Quantum Mechanics.

Authors: Cihan OkaySam RobertsStephen D. BartlettRobert Raussendorf

We provide a cohomological framework for contextuality of quantum mechanics that is suited to describing contextuality as a resource in measurement-based quantum computation. This framework applies to the parity proofs first discussed by Mermin, as well as a different type of contextuality proofs based on symmetry transformations. The topological arguments presented can be used in the state-dependent and the state-independent case.

Authors: Garrelt Quandt-Wiese

A new approach to wavefunction collapse is proposed. The so-called Dynamical Spacetime approach enhances semiclassical gravity and enables it for an explanation of wavefunction collapse by postulating that the spacetime region on which quantum fields exist and on which wavefunction’s evolution can be regarded is bounded towards future by a spacelike hypersurface, which is dynamically expanding towards future. Collapse is displayed in the way that wavefunction’s evolution becomes unstable at certain critical expansions of spacetime, at which it reconfigures via a self-reinforcing mechanism quasi abruptly to an evolution resembling a classical trajectory. Thereby, spacetime geometry changes in favour of the winning state, what causes that the path of the other state vanishes by destructive interference. This mechanism for collapse can explain the quantum correlations in EPR experiments without coming in conflict with relativity and the Free Will theorem. The Dynamical Spacetime approach is mathematically formulated on basis of the Einstein-Hilbert action and predicts for the Newtonian limit the same lifetimes of superpositions as the gravity-based approaches of Diosi and Penrose. A second important feature of the Dynamical Spacetime approach is its capability to forecast reduction probabilities. It can explain why all so-far performed experiments confirm Born’s rule, and predicts deviations from it, when solids evolve into three-state superpositions. The basics needed for the derivations in this paper are developed in Part 1 by an analysis of semiclassical gravity.

Abstract

The histories-based framework of Quantum Measure Theory assigns a generalized probability or measure μ(E) to every (suitably regular) set E of histories. Even though μ(E) cannot in general be interpreted as the expectation value of a selfadjoint operator (or POVM), we describe an arrangement which makes it possible to determine μ(E) experimentally for any desired E. Taking, for simplicity, the system in question to be a particle passing through a series of Stern-Gerlach devices or beam-splitters, we show how to couple a set of ancillas to it, and then to perform on them a suitable unitary transformation followed by a final measurement, such that the probability of a final outcome of “yes” is related to μ(E) by a known factor of proportionality. Finally, we discuss in what sense a positive outcome of the final measurement should count as a minimally disturbing verification that the microscopic event Eactually happened.

Author(s): Tao Xin, Dawei Lu, Joel Klassen, Nengkun Yu, Zhengfeng Ji, Jianxin Chen, Xian Ma, Guilu Long, Bei Zeng, and Raymond Laflamme

Quantum state tomography via local measurements is an efficient tool for characterizing quantum states. However, it requires that the original global state be uniquely determined (UD) by its local reduced density matrices (RDMs). In this work, we demonstrate for the first time a class of states that…
[Phys. Rev. Lett. 118, 020401] Published Mon Jan 09, 2017

Author(s): Fangzhou Jin, Ying Liu, Jianpei Geng, Pu Huang, Wenchao Ma, Mingjun Shi, Chang-Kui Duan, Fazhan Shi, Xing Rong, and Jiangfeng Du

As a fundamental postulate of quantum mechanics, Born’s rule assigns probabilities to the measurement outcomes of quantum systems and excludes multiorder quantum interference. Here we report an experiment on a single spin in diamond to test Born’s rule by inspecting the third-order quantum interfere…
[Phys. Rev. A 95, 012107] Published Mon Jan 09, 2017

Niestegge, Gerd (2016) Quantum teleportation and Grover’s algorithm without the wavefunction. [Published Article or Volume]

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