scholarly journals The Independence Condition in the Variety-of-Evidence Thesis

2013 ◽  
Vol 80 (1) ◽  
pp. 94-118 ◽  
Author(s):  
François Claveau
Keyword(s):  
Independence Condition

Can quantum cryptography imply quantum mechanics? -- reply to Smolin

2005 ◽  
Vol 5 (2) ◽  
pp. 170-175
Author(s):  
H. Halvorson ◽  
J. Bub
Keyword(s):  
Quantum Mechanics ◽  
Quantum Cryptography ◽  
Physical Theory ◽  
Information Theoretic ◽  
Independence Condition

Clifton, Bub, and Halvorson (CBH) have argued that quantum mechanics can be derived from three cryptographic, or broadly information-theoretic, axioms. But Smolin disagrees, and he has given a toy theory that he claims is a counterexample. Here we show that Smolin's toy theory violates an independence condition for spacelike separated systems that was assumed in the CBH argument. We then argue that any acceptable physical theory should satisfy this independence condition.

Causal Non-Symmetry

2020 ◽  
pp. 344-381
Author(s):  
Paul Noordhof
Keyword(s):  
Transition Period ◽  
Proper Understanding ◽  
Independence Condition ◽  
Asymmetric Relation ◽  
The Asymmetry ◽  
Priority Ordering ◽  
The Way

Causation is a non-symmetric rather than asymmetric relation. Different bases of causal non-symmetry include an asymmetry of overdetermination, the independence condition, and agency. Causal non-symmetry can be rooted in one or more of these three while also recognizing a fourth non-symmetry appealing to a primitive non-symmetric chance-raising. Each counts as an appropriate basis for causal non-symmetry because it is a (partial) realization of non-symmetric chance-raising. Key moves involve a refinement of how to understand the way in which the asymmetry of overdetermination works, and how it interacts with the revised similarity weighting, the contribution of the independence condition to a proper understanding of the transition period, the role that appeals to primitive non-symmetric chance-raising should play in the treatment of problem cases, the circumstances in which an appeal to an interlevel non-symmetry of agency may be appropriate, and the priority ordering of these various realizations of causal non-symmetry.

scholarly journals On an independence condition for consensus n-trees

1989 ◽  
Vol 2 (1) ◽  
pp. 75-78 ◽  
Author(s):  
Jean-Pierre Barthelemy ◽  
F.R. McMorris
Keyword(s):  
Independence Condition

A counterpart of the Borel-Cantelli lemma

1980 ◽  
Vol 17 (4) ◽  
pp. 1094-1101 ◽  
Author(s):  
F. Thomas Bruss
Keyword(s):  
Random Walk ◽  
Probability Space ◽  
Branching Processes ◽  
Simple Random Walk ◽  
Cantelli Lemma ◽  
Sequence Of Events ◽  
Independence Condition ◽  
General Part

The general part of the Borel-Cantelli lemma says that for any sequence of events (An) defined on a probability space (Ω, Σ, P), the divergence of ΣnP(An) is necessary for P(An i.o.) to be one (see e.g. [1]). The sufficient direction is confined to the case where the An are independent. This paper provides a simple counterpart of this lemma in the sense that the independence condition is replaced by for some . We will see that this property of (An) may frequently be assumed without loss of generality. We also disclose a useful duality which allows straightforward conclusions without selecting independent sequences. A simple random walk example and a new result in the theory of ϕ -branching processes will show the tractability of the method.

scholarly journals SECURITY OF QUANTUM KEY DISTRIBUTION

2008 ◽  
Vol 06 (01) ◽  
pp. 1-127 ◽  
Author(s):  
RENATO RENNER
Keyword(s):  
Representation Theorem ◽  
Physical System ◽  
Quantum Channel ◽  
Quantum Key Distribution ◽  
Key Distribution ◽  
Symmetry Condition ◽  
Secret Key ◽  
Independence Condition ◽  
Security Proof ◽  
Joint State

Quantum Information Theory is an area of physics which studies both fundamental and applied issues in quantum mechanics from an information-theoretical viewpoint. The underlying techniques are, however, often restricted to the analysis of systems which satisfy a certain independence condition. For example, it is assumed that an experiment can be repeated independently many times or that a large physical system consists of many virtually independent parts. Unfortunately, such assumptions are not always justified. This is particularly the case for practical applications — e.g. in quantum cryptography — where parts of a system might have an arbitrary and unknown behavior. We propose an approach which allows us to study general physical systems for which the above mentioned independence condition does not necessarily hold. It is based on an extension of various information-theoretical notions. For example, we introduce new uncertainty measures, called smooth min- and max-entropy, which are generalizations of the von Neumann entropy. Furthermore, we develop a quantum version of de Finetti's representation theorem, as described below. Consider a physical system consisting of n parts. These might, for instance, be the outcomes of n runs of a physical experiment. Moreover, we assume that the joint state of this n-partite system can be extended to an (n + k)-partite state which is symmetric under permutations of its parts (for some k ≫ 1). The de Finetti representation theorem then says that the original n-partite state is, in a certain sense, close to a mixture of product states. Independence thus follows (approximatively) from a symmetry condition. This symmetry condition can easily be met in many natural situations. For example, it holds for the joint state of n parts, which are chosen at random from an arbitrary (n + k)-partite system. As an application of these techniques, we prove the security of quantum key distribution (QKD), i.e. secret key agreement by communication over a quantum channel. In particular, we show that, in order to analyze QKD protocols, it is generally sufficient to consider so-called collective attacks, where the adversary is restricted to applying the same operation to each particle sent over the quantum channel separately. The proof is generic and thus applies to known protocols such as BB84 and B92 (where better bounds on the secret-key rate and on the the maximum tolerated noise level of the quantum channel are obtained) as well as to continuous variable schemes (where no full security proof has been known). Furthermore, the security holds with respect to a strong so-called universally composable definition. This implies that the keys generated by a QKD protocol can safely be used in any application, e.g. for one-time pad encryption — which, remarkably, is not the case for most standard definitions.

scholarly journals The Invention of the Independence Condition for Preferences

1995 ◽  
Vol 41 (7) ◽  
pp. 1130-1144 ◽  
Author(s):  
Peter Fishburn ◽  
Peter Wakker
Keyword(s):  
Independence Condition
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