Weekly Papers on Quantum Foundations (17)

Authors: Hemza Azri

Here we concisely review the nonminimal coupling dynamics of a single scalar field in the context of purely affine gravity and extend the study to multifield dynamics. The coupling is performed via an affine connection and its associated curvature without referring to any metric tensor. The latter arises a posteriori and it may gain an emergent character like the scale of gravity. What is remarkable in affine gravity is the transition from nonminimal to minimal couplings which is realized by only field redefinition of the scalar fields. Consequently, the inflationary models gain a unique description in this context where the observed parameters, like the scalar tilt and the tensor-to-scalar ratio, are invariant under field reparametrization. Overall, gravity in its affine approach is expected to reveal interesting and rich phenomenology in cosmology and astroparticle physics.

Authors: Kazuo FujikawaKoichiro Umetsu

A classical limit of Grover’s algorithm is discussed by assuming a very rapid decoherence (or dephasing) between consecutive Grover’s unitary operations, which leads pure quantum states to completely decohered mixed states. One can identify a specific element among $N$ unsorted elements by a probability of the order of unity after $k\sim N/4$ steps of classical amplification defined by the decohered mixed states, in contrast to Grover’s $k\sim \pi \sqrt{N}/4$ steps in quantum mechanical amplification. This difference is caused by the loss of quantum coherence with or without the loss of entanglement depending on each case.

Authors: Kohtaro Tadaki

The notion of probability plays a crucial role in quantum mechanics. It appears in quantum mechanics as the Born rule. In modern mathematics which describes quantum mechanics, however, probability theory means nothing other than measure theory, and therefore any operational characterization of the notion of probability is still missing in quantum mechanics. In this paper, based on the toolkit of algorithmic randomness, we present a refinement of the Born rule, as an alternative rule to it, for specifying the property of the results of quantum measurements in an operational way. Algorithmic randomness is a field of mathematics which enables us to consider the randomness of an individual infinite sequence. We then present an operational refinement of the Born rule for mixed states, as an alternative rule to it, based on algorithmic randomness. In particular, we give a precise definition for the notion of mixed state. We then show that all of the refined rules of the Born rule for both pure states and mixed states can be derived from a single postulate, called the principle of typicality, in a unified manner. We do this from the point of view of the many-worlds interpretation of quantum mechanics. Finally, we make an application of our framework to the BB84 quantum key distribution protocol in order to demonstrate how properly our framework works in practical problems in quantum mechanics, based on the principle of typicality.

Authors: Tsubasa Ichikawa

Logical inference leads to one of the major interpretations of probability theory called logical interpretation, in which the probability is seen as a measure of the plausibility of a logical statement under incomplete information. In this paper, assuming that our usual inference procedure makes sense for every set of logical propositions represented in terms of commuting projectors on a given Hilbert space, we extend the logical interpretation to quantum mechanics and derive the Born rule. Our result implies that, from the epistemological viewpoints, we can regard quantum mechanics as a natural extension of the classical probability.

Authors: Karl Svozil

A remark by Gleason about the ad hoc construction of probability measures in Hilbert spaces as a result of the Pythagorean property of vector components is interpreted platonically. Unless there is a total match between preparation and measurement contexts, information about the former from the latter is not ontic but epistemic. This is corroborated by configurations of observables and contexts which a truth-implies-value indefiniteness property.

Authors: V. A. De LorenciL.H. Ford

Subvacuum effects arise in quantum field theory when a classically positive quantity, such as the local energy density, acquires a negative renormalized expectation value. Here we investigate the case of states of the quantized electromagnetic field with negative mean squared electric field, and their effects on the propagation of light pulses in a nonlinear dielectric material with a nonzero third order susceptibility. We identify two distinct signature of the subvacuum effect in this situation. The first is an increase in the speed of the pulse, which is analogous to the superluminal light propagation in gravity which can arise from negative energy density. This increase in speed leads to a phase shift which might be large enough to observe. The second effect is a change in the frequency spectrum of the pulse. We identify a specific measure of the modified spectrum which can signal the presence of a negative mean squared electric field.

Authors: Kenny ChooCurt W. von KeyserlingkNicolas RegnaultTitus Neupert

Entanglement properties are routinely used to characterize phases of quantum matter in theoretical computations. For example the spectrum of the reduced density matrix, or so-called “entanglement spectrum”, has become a widely used diagnostic for universal topological properties of quantum phases. However, while being convenient to calculate theoretically, it is notoriously hard to measure in experiments. Here we use the IBM quantum computer to make the first ever measurement of the entanglement spectrum of a symmetry-protected topological state. We are able to distinguish its entanglement spectrum from those we measure for trivial and long-range ordered states.

Authors: A. Y. KamenshchikA. TronconiT. VardanyanG. Venturi

In the context of Quantum Cosmology and the Wheeler-DeWitt equation we investigate the possible effects of a non semiclassical wave-function of the universe on the evolution of the inflationary perturbations. These are associated with the quantum behaviour of the homogenous degrees of freedom (in particular the radius of the universe) in the early stages of the inflationary expansion, which in turn can affect the dynamics of the trans-Planckian modes of the fields present. The existence of a bounce for the homogeneous gravitational wave-function is studied. This can lead to an interference between a contracting and an expanding universe and, as a consequence, to the above quantum gravitational effects on the primordial spectra. In the traditional study of the inflationary fluctuations such effects are neglected and a quasi-classical behaviour for the homogeneous inflaton-gravity system is taken.

Kryukov, Alexey (2018) On observation of position in quantum theory. [Preprint]
Thebault, Karim P Y (2018) The Problem of Time. [Preprint]
Quantum mechanics, gravity, dark matter, the end of the universe and more, all explained at New Scientist Live 2018 from 19 to 23 September at London’s ExCeL centre
Roy, Sudipto and Nandi, Dipika and Ghosh, Sumana and Das, Apashanka (2018) Time Evolution of Energy Density, EoS Parameter and the Density Parameters for Matter and Dark Energy in Brans-Dicke Gravity. [Preprint]
Brown, Harvey R. and Read, James (2018) The dynamical approach to spacetime theories. [Preprint]
Fraser, Doreen (2018) The development of renormalization group methods for particle physics: Formal analogies between classical statistical mechanics and quantum field theory. [Preprint]
Vaidman, Lev (2018) Ontology of the wave function and the many-worlds interpretation. [Preprint]
Read, James and Brown, Harvey R. and Lehmkuhl, Dennis (2018) Two Miracles of General Relativity. [Preprint]

Author(s): Calvin Leung, Amy Brown, Hien Nguyen, Andrew S. Friedman, David I. Kaiser, and Jason Gallicchio

To help test quantum physics, a new method generates random numbers using light from distant stars and quasars that presumably have no correlation with experiments on Earth.


[Phys. Rev. A 97, 042120] Published Tue Apr 24, 2018

Quantum supremacy, here we come

Quantum supremacy, here we come, Published online: 23 April 2018; doi:10.1038/s41567-018-0131-y

It’s still unclear which problems can be solved by near-term quantum computers that are beyond the reach of their classical counterparts. A new analysis makes a practical assessment of how sampling the output of a quantum circuit leaves supercomputers in the dust.

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