**PLAYING WITH QUBITS**

**A Challenge to Quantum Physicists**

**Tom Leonard**

*Retired Professor of Statistics*

**Universities of Wisconsin-Madison and Edinburgh****CHAPTER 1: GETTING STARTED**

**1.1. My Grand Scheme (13**^{th}September 2019)
This
morning I gave a brief ministry to South Edinburgh Quakers on
Morningside Road
on
the other side of Edinburgh, to
a meeting in
the plush
basement of the more
basic
Open Door CafÃ©
which I
have attended for almost three years (though
I am not a Quaker myself and
struggle with the concept of a
Creator
God as
well as the
apparent irrationality of consensus
decision making).
I
was
responding
to three previous ministries during our hour of, otherwise
silent, contemplation. As I remember, I suddenly
leapt
to my feet with the help of my bright
blue walking
frame
Freddie, and, sounding
holier than thou,
blethered
something like:

*Before 2017, I spent a couple of years driving around the Scottish countryside with Thomas, enjoying all the sorts of views of coastlines and sunsets which you have described. Now I no longer have a car, and I plan to spend the remainder of my old age studying the mathematics of Quantum theory, so that I can escape from reality. My flatmate has just given me a beginner's book, and I intend to research and generalise its contents, in the hope of also discovering more about nature, genetics, evolution, and so on and so forth.*

Everybody
had a good, silent, chuckle at that!
As
with all such ministries, my
utterances were
interpreted by
the members present
as the spontaneous' Word of the Living God'. What I said, out of my
sub-conscious,
might sound over-ambitious, but I am proudly
Attention
Deficit and neurodiverse, a
highly
eccentric
septuagenarian, and
eclectic enough to firmly believe that I will be able to use my
old-fashioned
skills in probability and
frequentist
and Bayesian
statistics
to discover mathematical methodologies
which
turn out to be earth shattering generalisations of quantum mechanics.

The
book I am referring to
is
entitled

*Quantum Mechanics: The Theoretical Minimum*, and it was written in quite amiable style by Leonard Sussman and Art Friedman (2014). I will mainly focus on this book for a while, and check any extensions for originality later
Along
the way I will doubtlessly derive lots
of
things which are already well-known e.g. to the
courageous
quantum
Bayesians who
follow
in the foot steps of my sadly deceased friend Ed Jaynes [It
was Ed who
encouraged me to use the idea of

*maximum entropy*when representing incomplete information. These is one of the various themes discussed in my book*Bayesian Methods*(with John Hsu, 1999)]. At the very least I will learn a bit about the diverse approaches to quantum mechanics and provide my readership with a easy way of surveying them. Concepts like quantum cognition particularly appeal to me. Maybe this will produce ways of describing how we people on the spectrum of neurodiversity actually think.
What
are my skills in Mathematical Physics? Pretty slim! While I obtained
a grade one in Physics at G.C.E.
ordinary
level, and a grade B at advanced level, I scarcely remember any of
the Physics I studied at High School, and wouldn't even be able to
operate
a Bunsen burner or
describe a Wheatstone Bridge. However, my A grades at advanced level
in Pure and Applied Mathematics helped me obtain lowly

*Gamma*grades in my first and (repeated) second year Applied Maths courses at Imperial College London in 1967 and 1969. Fortunately I did better in Statistics, after a monumental disaster in 1968, and quickly progressed, after graduating with a very lucky first class honours degree, to obtain my M.Sc. and Ph.D. from University College London (supervised by Dennis V. Lindley) during 1971 and 1973.
The
title of my Ph.D. thesis was

*Bayesian Methods for the Simultaneous Estimation of Several Parameters*. I, for example, derived alternatives to the shrinkage estimators for multinomial probabilities which had been used by I.J. Good and Alan Turing, when developing cryptanalysis techniques to solve the Nazi Codes during the Second World War. My entertaining correspondences with Jack Good (who also published 25 papers entitled*Partly Baked Ideas*) helped to stimulate this and further research.
Maybe
I'll be able to use some of my ideas from my Ph.D, thesis and my
follow up articles to extend the
quantum mechanics literature, for example by developing further
probabilistic representations for a collection of entangled Qubits.
This might be used to
imply
spatial correlations between electrons in different states of spin.

I
must say that I'm extremely impressed by the
superb
theoretical level of
mathematical physics,
which epitomizes
the amazing heights of human accomplishment. I
have only come close to this level in three of my published papers,
by Leonard (1978), Leonard and Hsu (1992), and Chiu, Leonard and
Tsui(1996), and all of these utilised theory developed by the great
applied mathematician Richard E. Bellman.

*Richard E. Bellman (1920-84)*

I
have more recently been impressed to learn that Roger Penrose thinks
that an older Universe could have existed before the 'Big Bang', and
that it might be possible to use Quantum Theory to explain human
consciousness.

My
flat
is packed with books which my much more diversely
intellectual
flatmate orders on the Internet, and they come crashing through the
door several times a week. We've
recently discussed the amazing complexity of biochemistry, epigenetics,
the human
genome,
and
our biological, neurological and reproductive systems, and we'
ve
wondered how all of this has
been produced so
speedily by
our
evolutionary
process,
and
how
the geological systems, which affect the weather on the surface of
our planets and
thereby
create
a propensity for Life, could
have
existed
before intelligent
life forms came into being.

I
also live in hope that a joint 'afterlife' can be predicted in some
convincing scientific way.
So immense mysteries remain, and these certainly shouldn't
be blamed on some mythical
divinity
or other. How
far Science will progress before our planet is destroyed by the
return of the dinosaurs, or
whatever, is
another question.

In
the morning, I will return to first principles and examine the
properties of Qubits
in greater detail. Maybe they will ultimately explain everything!

https://en.wikipedia.org/wiki/Probability_amplitude

ReplyDeletehttps://en.wikipedia.org/wiki/Max_Born#Early_life

https://en.wikipedia.org/wiki/Quantum_logic

https://en.wikipedia.org/wiki/Hidden-variable_theory#Early_attempts_at_hidden-variable_theories

https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation

ReplyDeletehttps://en.wikipedia.org/wiki/Mathematical_formulation_of_quantum_mechanics#The_%22old_quantum_theory%22_and_the_need_for_new_mathematics

https://plato.stanford.edu/entries/qt-quantlog/

https://en.wikipedia.org/wiki/Gleason%27s_theorem

https://en.wikipedia.org/wiki/Born_rule

ReplyDeletePhysics maths Symbols keyboard

ReplyDeletehttps://physics.info/symbols/ requires copy and pasting

or https://math.typeit.org/

easier to use but less symbols.

https://en.wikipedia.org/wiki/Quantum_Bayesianism

ReplyDeletehttps://en.wikipedia.org/wiki/Quantum_Markov_chain

ReplyDeletehttps://en.wikipedia.org/wiki/Quantum_probability

https://en.wikipedia.org/wiki/Exotic_probability

https://en.wikipedia.org/wiki/Belavkin_equation

https://uwaterloo.ca/institute-for-quantum-computing/sites/ca.institute-for-quantum-computing/files/uploads/files/Big%20QBism.pdf

ReplyDelete"This article summarizes the Quantum Bayesian [1–7] point

of view of quantum mechanics, with special emphasis on the

view’s outer edges—dubbed QBism.1 QBism has its roots

in personalist Bayesian probability theory, is crucially dependent upon the tools of quantum information theory, and most

recently, has set out to investigate whether the physical world

might be of a type sketched by some false-started philosophies

of 100 years ago (pragmatism, pluralism, nonreductionism,

and meliorism). Beyond conceptual issues, work at Perimeter

Institute is focussed on the hard technical problem of finding

a good representation of quantum mechanics purely in terms

of probabilities, without amplitudes or Hilbert-space operators. The best candidate representation involves a mysterious

entity called a symmetric informationally complete quantum

measurement. Contemplation of it gives a way of thinking

of the Born Rule as an addition to the rules of probability theory, applicable when an agent considers gambling on

the consequences of his interactions with a newly recognized

universal capacity: Hilbert-space dimension. (The word “capacity” should conjure up an image of something like gravitational mass—a body’s mass measures its capacity to attract

other bodies when nothing impedes. With hindsight one can

say that the founders of quantum mechanics discovered another universal capacity, “dimension.”) The article ends by

showing that the egocentric elements in QBism represent no

impediment to pursuing quantum cosmology and outlining

some directions for future work."

https://digitalcommons.chapman.edu/cgi/viewcontent.cgi?article=1559&context=scs_articles

ReplyDelete2017

Review ofQBism: The Future of Quantum Physics

Matthew S. Leifer

"Is it all in my head?

ReplyDeleteAccording to the Bayesian approach, quantum theory is not a law of Nature that

physical systems ‘must obey.’ Rather, it is a theory that advises you about how

you should decide your degree of confidence in predicting outcomes of future

experiments, based on your prior knowledge and your latest observations of

these systems.

The Bayesian approach seems to be a consistent way to view quantum theory,

and it will never make a prediction that contradicts any other valid ways of

interpreting the theory. Independent of which philosophy might be preferred by

users of quantum theory, they calculate and use the same probabilities. Yet many

physicists are not comfortable with the Bayesian approach when taken to its

limits, wherein quantum theory represents beliefs rather than representing the

physical world. One of its proponents, Ruediger Schack, acknowledges that the

philosophy of Quantum Bayesianism, also called QBism for short, can be a hard

pill to swallow for many physicists. He said, “When QBism holds that science is

as much about the scientist as it is about the world external to the scientist, it

challenges one of the most deeply held prejudices that most physicists subscribe

to.”

12

Some physicists have criticized the Bayesian approach by claiming it equates

a person’s degree of confidence with a mere arbitrary belief. A counter to such

criticism is to point out that, of course, this theory should reflect deeply Nature’s

ways of behaving so your degree of confidence is based on sound reasoning.

This is where the detailed physics comes in, constraining what a person

following the Bayesian approach will choose to believe. In other words, a careful

use of the Bayesian approach will not lead one to predict one thousand fairies

dancing on the head of a pin. Yet there is still a lingering awkwardness in

Quantum Bayesianism, according to many physicists. Physicist Steven van Enk

says, “Quantum Bayesians simply assume quantum mechanics does not describe

the world, just what we know about it. But of course, then they still have to

answer the question what the world is like.”

13 That is, what is it about the

physical world that makes it this way? Brukner writes about the problem in

understanding how measurements happen:

One possibility to address these questions would be to dismiss the measurement problem as a pseudoissue. … It seems to me that this path is taken by some proponents of … Quantum Bayesianism

(QBists), for example when Fuchs and Schack write, “a measurement is an action an agent takes to

elicit an experience. The measurement outcome is the experience so elicited.” Such a view is

consistent and self-contained, but in my opinion, it is not the whole story. It is silent about the

question: what makes a photon counter a better device for detecting photons than a beam splitter? Yet

the question is scientifically well posed and has an unambiguous answer (which manufacturers of

photo-detectors do know!)."

(P.250-251, Quantum Physics What everyone should know, Michael Raymer).

https://www.quantamagazine.org/the-born-rule-has-been-derived-from-simple-physical-principles-20190213/

ReplyDeletehttps://www.quantamagazine.org/quantum-theory-rebuilt-from-simple-physical-principles-20170830/

https://arxiv.org/abs/1003.5209

https://www.quantamagazine.org/how-randomness-can-arise-from-determinism-20191014/

https://en.wikipedia.org/wiki/Wave_function

https://en.wikipedia.org/wiki/Born_rule

"Within the Quantum Bayesianism interpretation of quantum theory, the Born rule is seen as an extension of the standard Law of Total Probability, which takes into account the Hilbert space dimension of the physical system involved.[5] In the ambit of the so-called Hidden-Measurements Interpretation of quantum mechanics the Born rule can be derived by averaging over all possible measurement-interactions that can take place between the quantum entity and the measuring system.[6][7] It has been claimed that Pilot wave theory can also statistically derive Born's law.[8] While it has been claimed that Born's law can be derived from the many-worlds interpretation, the existing proofs have been criticized as circular.[9] Kastner claims that the transactional interpretation is unique in giving a physical explanation for the Born rule.[10]"

https://en.wikipedia.org/wiki/Law_of_total_probability

ReplyDelete