Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Uncertain Decisions and the Many-Minds Interpretation of Quantum Mechanics

David Papineau

Published Jan 16, 2003• 1 citation
Publisher

Abstract

Abstract Imagine you are faced with a quantum-mechanical device which will display either H or T (‘heads’, ‘tails’) when it is operated (‘spun’). You know that the single-case probability, or chance, of H is 0.8, and the chance of T is 0.2. (I could have taken a biased coin, but I wanted to make it clear that we are dealing with chances.)

DOI
10.1093/oso/9780199243846.003.0007

Related papers

Uncertain Decisions and the Many-Minds Interpretation of Quantum Mechanics

David Papineau

David Papineau; Uncertain Decisions and The Many-Minds Interpretation of Quantum Mechanics, The Monist, Volume 80, Issue 1, 1 January 1997, Pages 97–117, https:

The Monist•Jan 1, 1997•1 citation

Shadows and Mirrors: Reconstructing Quantum States of Atom Motion

Dietrich G. Leibfried, Tilman Pfau, Christopher R. Monroe

Imagine that a pair of coins are tossed in a black box. The box reports only one of the following three results at random: (1) the outcome of the first coin (heads or tails), (2) the outcome of the second coin (heads or tails), or (3) whether the outcomes of the two coins matched or were different. Our task is to construct a joint probability distribution of the four possible outcomes of the coins (HH, TT, HT, TH) based on many observations of the black box outputs. Now suppose that after many trials, the black box reports that each coin comes up heads two-thirds of the time when measured individually, yet the coins never match when they are compared. (Clearly the results of the coin tosses have been correlated—perhaps a joker in the black box flips the coins and then changes the outcomes appropriately). We seek a distribution that both reflects this correlation and obeys the marginal distributions of each coin as two-thirds heads, one-third tails (see the three tables on page 23). The only way to satisfy both requirements is to force the joint probability P(TT) of getting two tails to be negative! Mathematically, this is because P(HH)+P(TT) is observed to be zero, yet we expect P(HH)to be greater than P(TT), because the individual coins are weighted toward heads.

Physics Today•Apr 1, 1998•92 citations

Introduction to Quantum Computing

Santanu Pattanayak

Present-day computers work on the principles of classical mechanics. Imagine a coin in the classical regime. When we toss the coin, it can take up either of these two states: “head” (H) or “tail” (T). However, in a quantum world, a coin, or rather a quantum one, can exist in both the states “head” and “tail” simultaneously. This property of quantum mechanical objects—existing in multiple states simultaneously—is known as superposition . Similarly, quantum mechanical objects can exhibit a much stronger correlation than their classical counterparts through the phenomenon of entanglement . Using entanglement, two or more quantum particles can be linked in perfect unison, even when they are placed at opposite ends of the universe. Quantum computing harnesses and exploits the laws of quantum mechanics, especially superposition, entanglement, and interference, to process information. An important idea in quantum computing is to collapse a probability distribution toward specific measurement states. Quantum interference is a by-product of quantum superposition, and it helps bias quantum measurement toward specific quantum states.

Apress eBooks•Jan 1, 2021•4 citations

Probability in the Many-Worlds Interpretation of Quantum Mechanics

Lev Vaidman A

The frontiers collection•Aug 13, 2011•60 citations

Is quantum mechanics compatible with a deterministic universe? Two interpretations of quantum probabilities

László E. Szabó

arXiv:gr-qc/9412005•Foundations of Physics Letters•Oct 1, 1995•21 citations

A Fair Deal for Everettians

David Papineau

Abstract Those who criticize the Everett interpretation on the grounds that it makes no sense of probability apply a double-standard, for no other physical theory of probability does any better in explaining probability or in deriving its link with decision theory. In fact, others do worse, for in any one world theory it is a mystery as to why, given that only a single outcome of a chance process occurs, we should nevertheless act so as to maximize expected utilities, which involves all possible outcomes of a chance process. This difficulty does not apply to the Everett interpretation, in which all outcomes happen.

•Jun 24, 2010•32 citations
Abstract Imagine you are faced with a quantum-mechanical device which will display either H or T (‘heads’, ‘tails’) when it is operated (‘spun’). You know that the single-case probability, or chance, of H is 0.8, and the chance of T is 0.2. (I could have taken a biased coin, but I wanted to make it clear that we are dealing with chances.)
Imagine that a pair of coins are tossed in a black box. The box reports only one of the following three results at random: (1) the outcome of the first coin (heads or tails), (2) the outcome of the second coin (heads or tails), or (3) whether the outcomes of the two coins matched or were different. Our task is to construct a joint probability distribution of the four possible outcomes of the coins (HH, TT, HT, TH) based on many observations of the black box outputs. Now suppose that after many trials, the black box reports that each coin comes up heads two-thirds of the time when measured individually, yet the coins never match when they are compared. (Clearly the results of the coin tosses have been correlated—perhaps a joker in the black box flips the coins and then changes the outcomes appropriately). We seek a distribution that both reflects this correlation and obeys the marginal distributions of each coin as two-thirds heads, one-third tails (see the three tables on page 23). The only way to satisfy both requirements is to force the joint probability P(TT) of getting two tails to be negative! Mathematically, this is because P(HH)+P(TT) is observed to be zero, yet we expect P(HH)to be greater than P(TT), because the individual coins are weighted toward heads.
Present-day computers work on the principles of classical mechanics. Imagine a coin in the classical regime. When we toss the coin, it can take up either of these two states: “head” (H) or “tail” (T). However, in a quantum world, a coin, or rather a quantum one, can exist in both the states “head” and “tail” simultaneously. This property of quantum mechanical objects—existing in multiple states simultaneously—is known as superposition . Similarly, quantum mechanical objects can exhibit a much stronger correlation than their classical counterparts through the phenomenon of entanglement . Using entanglement, two or more quantum particles can be linked in perfect unison, even when they are placed at opposite ends of the universe. Quantum computing harnesses and exploits the laws of quantum mechanics, especially superposition, entanglement, and interference, to process information. An important idea in quantum computing is to collapse a probability distribution toward specific measurement states. Quantum interference is a by-product of quantum superposition, and it helps bias quantum measurement toward specific quantum states.
Abstract Those who criticize the Everett interpretation on the grounds that it makes no sense of probability apply a double-standard, for no other physical theory of probability does any better in explaining probability or in deriving its link with decision theory. In fact, others do worse, for in any one world theory it is a mystery as to why, given that only a single outcome of a chance process occurs, we should nevertheless act so as to maximize expected utilities, which involves all possible outcomes of a chance process. This difficulty does not apply to the Everett interpretation, in which all outcomes happen.