arXiv subjects

I. Pitowsky

Publications and source records attributed to I. Pitowsky.

3 recordsLinked to original sources

arXiv2002

Probability and Nonlocality in Many Minds Interpretations of Quantum Mechanics

We argue that a certain type of many minds (and many worlds) interpretations of quantum mechanics due to Lockwood (and Deutsch) do not provide a coherent interpretation of the quantum mechanical probabilistic algorithm. By contrast, in Albert and Loewer's version of the many minds interpretation there is a coherent interpretation of the quantum mechanical probabilities. We consider Albert and Loewer's probability interpretation in the context of Bell-type and GHZ-type states and argue that it exhibits a certain form of nonlocality which is, however, much weaker than Bell's nonlocality.

quant-ph↗

arXiv2002

Betting on the Outcomes of Measurements: A Bayesian Theory of Quantum Probability

We develop a systematic approach to quantum probability as a theory of rational betting in quantum gambles. In these games of chance the agent is betting in advance on the outcomes of several (finitely many) incompatible measurements. One of the measurements is subsequently chosen and performed and the money placed on the other measurements is returned to the agent. We show how the rules of rational betting imply all the interesting features of quantum probability, even in such finite gambles. These include the uncertainty principle and the violation of Bell's inequality among others. Quantum gambles are closely related to quantum logic and provide a new semantics to it. We conclude with a philosophical discussion on the interpretation of quantum mechanics.

quant-ph↗

arXiv2001

Range Theorems for Quantum Probability and Entanglement

We consider the set of all matrices of the form $p_{ij}=tr[W(E_{i}\otimes F_{j})]$ where $E_{i}$, $F_{j}$ are projections on a Hilbert space $H$, and $W$ is some state on $H\otimes H$. We derive the basic properties of this set, compare it with the classical range of probability, and note how its properties may be related to geometric measures of entanglement.

quant-ph↗