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Anthony Sudbery

Publications and source records attributed to Anthony Sudbery.

At least 19 recordsLinked to original sources
arXiv2024

Whose Projection Postulate?

The projection postulate is a description of the effect on a quantum system, assumed to be in a pure state, of a measurement of an observable with a discrete spectrum, in nonrelativistic quantum mechanics. It is often called "von Neumann's projection postulate" or "the L\"uders rule". This paper is an examination of the versions of this postulate due to Dirac, von Neumann and L\"uders. It is shown that Dirac, in 1930, proposed what is now generally known as the projection postulate. Von Neumann, in 1932, gave a different theory which only applies in special and rather unusual cases. L\"uders, in 1951, rejected this theory and presented one which is the same as Dirac's. Treatments of observables with continuous spectra by both Dirac and von Neumann are criticised, and the possibility of a generalised version of the projection postulate for this case is considered. The paper concludes with a discussion of the status of the projection postulate (in its various forms) as a separate postulate (independent of the other postulates of quantum mechanics) and as a separate form of time development (in addition to the time-dependent Schr\"odinger equation).

quant-ph↗
arXiv2023

The life and entangled adventures of Schrodinger's cat

In this lecture, intended for a general audience, I describe Schr\"odinger's thought experiment which was designed to show the strange results of extending the formalism of quantum theory, particularly the idea of superposition, beyond the subatomic regime. I describe a way to understand superposition in the terms of formal logic. I trace the development of Schrodinger's ideas after this thought experiment, and briefly sketch some work which realises it in actual experiments, and proposals for taking it further.

physics.pop-ph↗
arXiv2022

Is there a classical model of Wigner's friend?

"Wigner's friend" refers to a quantum process of which different observers, following the rules of quantum mechanics, give contradictory descriptions. Lostaglio and Bowles have recently claimed to describe a classical system showing the same effect. It is argued that this claim is not justified. it fails to take into account the different meanings of probability in classical and quantum mechanics.

quant-ph↗
arXiv2021

Histories without collapse

This paper is a comparison of two theories of the probability of a history in quantum mechanics. One is derived from Copenhagen quantum mechanics using the projection postulate and is the basis of the "consistent histories" interpretation; the other is based on a proposal by Bell, originally for the "pilot state" theory but here applied to pure unitary quantum mechanics. The first can be used for a wider class of histories but depends on the projection postulate, or "collapse", which is widely held to be an unsatisfactory feature of the theory; the second can be used in a theory of the universal state vector without collapse. We examine a simple model based on Wigner's friend, in which Bell's model and the projection postulate give different probabilities for the histories of a sentient system. We also examine the Frauchiger-Renner extension of this model, in which comparison of the two calculations of histories throws light on the contradiction found by Frauchiger and Renner. By extending the model to equip the observer with a memory, we reduce the probability of histories to the use of the Born rule at a single time, and show that the Born rule, with the memory, gives the same result as applying projection in the course of the history, because of entanglement with the memory: entanglement implements collapse. We discuss the implications of this for the use of histories in quantum cosmology.

quant-ph↗
arXiv2019

The hidden assumptions of Frauchiger and Renner

This note is a critical examination of the argument of Frauchiger and Renner (Nature Communications 9:3711 (2018)), in which they claim to show that three reasonable assumptions about the use of quantum mechanics jointly lead to a contradiction. It is shown that further assumptions are needed to establish the contradiction, and that each of these assumptions is invalid in some version of quantum mechanics.

quant-ph↗
arXiv2018

John Bell and the great enterprise

I outline Bell's vision of the "great enterprise" of science, and his view that conventional teachings about quantum mechanics constituted a betrayal of this enterprise. I describe a proposal of his to put the theory on a more satisfactory footing, and review the subsequent uses that have been made of one element of this proposal, namely Bell's transition probabilities regarded as fundamental physical processes.

physics.hist-ph↗
arXiv2017

Single-world theory of the extended Wigner's world experiment

Frauchiger and Renner have recently claimed to prove that "Single-world interpretations of quantum theory cannot be self-consistent". This is contradicted by a construction due to Bell, inspired by Bohmian mechanics, which shows that any quantum system can be modelled in such a way that there is only one "world" at any time, but the predictions of quantum theory are reproduced. This Bell-Bohmian theory is applied to the experiment proposed by Frauchiger and Renner, and their argument is critically examined. It is concluded that it is their version of "standard quantum theory", incorporating state vector collapse upon measurement, that is not self-consistent.

quant-ph↗
arXiv2016

The logic of the future in quantum theory

According to quantum mechanics, statements about the future made by sentient beings like us are, in general, neither true nor false; they must satisfy a many-valued logic. I propose that the truth value of such a statement should be identified with the probability that the event it describes will occur. After reviewing the history of related ideas in logic, I argue that it gives an understanding of probability which is particularly satisfactory for use in quantum mechanics. I construct a lattice of future-tense propositions, with truth values in the interval $[0,1]$, and derive logical properties of these truth values given by the usual quantum-mechanical formula for the probability of a history.

quant-ph↗
arXiv2016

The future's not ours to see

An account of determinism and indeterminism in physics, addressed to non-physicist readers, leading up to proposals for how to understand statements about the future and single-event probability, motivated by quantum mechanics.

physics.hist-ph↗
arXiv2016

Time, chance and quantum theory

I propose an understanding of Everett and Wheeler's relative-state interpretation of quantum mechanics, which restores the feature of indeterminism to the theory. This incorporates a theory of probability as truth values in a many-valued logic for future statements, and a contextual theory of truth which gives objective and subjective perspectives equal validity.

quant-ph↗
arXiv2011

Global asymmetry of many-qubit correlations: A lattice gauge theory approach

We introduce a novel bridge between the familiar gauge field theory approaches used in many areas of modern physics such as quantum field theory and the SLOCC protocols familiar in quantum information. Although the mathematical methods are the same the meaning of the gauge group will be different. The measure we introduce, `twist', is constructed as a Wilson loop from a correlation induced holonomy. The measure can be understood as the global asymmetry of the bipartite correlations in a loop of three or more qubits; if the holonomy is trivial (the identity matrix), the bipartite correlations can be globally untwisted using general local qubit operations, the gauge group of our theory, which turns out to be the group of Lorentz transformations familiar from special relativity. If it is not possible to globally untwist the bipartite correlations in a state globally using local operations, the twistedness is given by a non-trivial element of the Lorentz group, the correlation induced holonomy. We provide several analytical examples of twisted and untwisted states for three qubits, the most elementary non-trivial loop one can imagine.

quant-ph↗
arXiv2011

Geometric local invariants and pure three-qubit states

We explore a geometric approach to generating local SU(2) and $SL(2,\mathbb{C})$ invariants for a collection of qubits inspired by lattice gauge theory. Each local invariant or 'gauge' invariant is associated to a distinct closed path (or plaquette) joining some or all of the qubits. In lattice gauge theory, the lattice points are the discrete space-time points, the transformations between the points of the lattice are defined by parallel transporters and the gauge invariant observable associated to a particular closed path is given by the Wilson loop. In our approach the points of the lattice are qubits, the link-transformations between the qubits are defined by the correlations between them and the gauge invariant observable, the local invariants associated to a particular closed path are also given by a Wilson loop-like construction. The link transformations share many of the properties of parallel transporters although they are not undone when one retraces one's steps through the lattice. This feature is used to generate many of the invariants. We consider a pure three qubit state as a test case and find we can generate a complete set of algebraically independent local invariants in this way, however the framework given here is applicable to mixed states composed of any number of $d$ level quantum systems. We give an operational interpretation of these invariants in terms of observables.

quant-ph↗
arXiv2011

Philosophical lessons of entanglement

The quantum-mechanical description of the world, including human observers, makes substantial use of entanglement. In order to understand this, we need to adopt concepts of truth, probability and time which are unfamiliar in modern scientific thought. There are two kinds of statements about the world: those made from inside the world, and those from outside. The conflict between contradictory statements which both appear to be true can be resolved by recognising that they are made in different perspectives. Probability, in an objective sense, belongs in the internal perspective, and to statements in the future tense. Such statements obey a many-valued logic, in which the truth values are identified as probabilities.

quant-ph↗
arXiv2010

The Everett-Wheeler interpretation and the open future

I discuss the meaning of probability in the Everett-Wheeler interpretation of quantum mechanics, together with the problem of defining histories. To resolve these, I propose an understanding of probability arising from a form of temporal logic: the probability of a future-tense proposition is identified with its truth value in a many-valued and context-dependent logic. In short, probability is degree of truth. These ideas appear to be new (though I expect correction on this), but they are natural and intuitive, and relate to traditional naive ideas of time and chance. Indeed, I argue that Everettian quantum mechanics is the only form of scientific theory that truly incorporates the perception that the future is open.

quant-ph↗
arXiv2010

Duality and the geometric measure of entanglement of general multiqubit W states

We find the nearest product states for arbitrary generalized W states of n qubits, and show that the nearest product state is essentially unique if the W state is highly entangled. It is specified by a unit vector in Euclidean n-dimensional space. We use this duality between unit vectors and highly entangled W states to find the geometric measure of entanglement of such states.

quant-ph↗