Popper's Contribution to the Philosophy of Probability

Royal Institute of Philosophy Supplement ◽

10.1017/s1358246100005452 ◽

1995 ◽

Vol 39 ◽

pp. 103-120

Author(s):

Donald Gillies

Keyword(s):

Quantum Mechanics ◽

Scientific Discovery ◽

Foundations Of Quantum Mechanics ◽

Wide Range

Popper's writings cover a remarkably wide range of subjects. The spectrum runs from Plato's theory of politics to the foundations of quantum mechanics. Yet even amidst this variety the philosophy of probability occupies a prominent place. David Miller once pointed out to me that more than half of Popper's The Logic of Scientific Discovery is taken up with discussions of probability. I checked this claim using the 1972 6th revised impression of The Logic of Scientific Discovery, and found that of the approximately 450 pages of text, approximately 250 are to do with probability. Thus Miller's claim is amply justified. It seems indeed that the philosophy of probability was one of Popper's favourite subjects, and, as we shall see, Popper certainly enriched the field with several striking innovations. In this area, as in others, Popper held very definite views, and criticized his opponents in no uncertain terms. Popper was an objectivist and anti-Bayesian, and his criticisms were directed against subjectivism and Bayesianism.

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A bonding model of entanglement for N-qubit graph states

International Journal of Quantum Information ◽

10.1142/s0219749914300058 ◽

2014 ◽

Vol 12 (06) ◽

pp. 1430005 ◽

Cited By ~ 4

Author(s):

Mordecai Waegell

Keyword(s):

Quantum Mechanics ◽

Quantum Information Processing ◽

Foundations Of Quantum Mechanics ◽

The Other ◽

Graph State ◽

Graph States ◽

Wide Range ◽

As Graph ◽

Qubit States

The class of entangled N-qubit states known as graph states, and the corresponding stabilizer groups of N-qubit Pauli observables, have found a wide range of applications in quantum information processing and the foundations of quantum mechanics. A review of the properties of graph states is given and core spaces of graph states are introduced and discussed. A bonding model of entanglement for generalized graph states is then presented, in which the presence or absence of a bond between two qubits unequivocally specifies whether or not they are entangled. A physical interpretation of these bonds is given, along with a characterization of how they can be created or destroyed by entangling unitary operations and how they can be destroyed by local Pauli measurements. It is shown that local unitary operations do not affect the bond structure of a graph state, and therefore that if two graph states have nonisomorphic bond structures, then local unitary operations and/or reordering of qubits cannot change one into the other. Color multigraphs are introduced to depict the bond structures of graph states and to make some of their properties more apparent.

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Quantum Optomechanics and Nanomechanics

10.1093/oso/9780198828143.001.0001 ◽

2020 ◽

Cited By ~ 2

Keyword(s):

Gravitational Wave ◽

Summer School ◽

Large Scale ◽

Quantum Noise ◽

Foundations Of Quantum Mechanics ◽

Wide Range ◽

Measurement Laser ◽

Quantum Limits ◽

Quantum Optomechanics ◽

Quantum Ground State

The Les Houches Summer School 2015 covered the emerging fields of cavity optomechanics and quantum nanomechanics. Optomechanics is flourishing and its concepts and techniques are now applied to a wide range of topics. Modern quantum optomechanics was born in the late 70s in the framework of gravitational wave interferometry, initially focusing on the quantum limits of displacement measurements. Carlton Caves, Vladimir Braginsky, and others realized that the sensitivity of the anticipated large-scale gravitational-wave interferometers (GWI) was fundamentally limited by the quantum fluctuations of the measurement laser beam. After tremendous experimental progress, the sensitivity of the upcoming next generation of GWI will effectively be limited by quantum noise. In this way, quantum-optomechanical effects will directly affect the operation of what is arguably the world’s most impressive precision experiment. However, optomechanics has also gained a life of its own with a focus on the quantum aspects of moving mirrors. Laser light can be used to cool mechanical resonators well below the temperature of their environment. After proof-of-principle demonstrations of this cooling in 2006, a number of systems were used as the field gradually merged with its condensed matter cousin (nanomechanical systems) to try to reach the mechanical quantum ground state, eventually demonstrated in 2010 by pure cryogenic techniques and a year later by a combination of cryogenic and radiation-pressure cooling. The book covers all aspects—historical, theoretical, experimental—of the field, with its applications to quantum measurement, foundations of quantum mechanics and quantum information. Essential reading for any researcher in the field.

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