Zurek’s envariance derivation of Born’s rule and measurement

Sabine Hossenfelder

Fedor Herbut

Zurek's derivation of Born's rule using envariance (invariance due to entanglement) is considered to capture the probability in full generality, but only as applied to measurement of a quantum observable. Contrariwise, textbook formulations of Born's rule begin with a pure state of a closed, undivided system. The task of this study is to show that a rearrangement of the Zurek approach is possible in which the latter is viewed as giving the probabilities for Schmidt states of an arbitrary composite state vector, and afterwards it is extended to probabilities in a closed, undivided system. This is achieved by determining simultaneously probability and measurement based on the fact that the physical meaning of probability and that of measurement are inextricably dependent on each other.

Fritiof Wallentin

Forrester, A

In recent papers on 'envariance', Zurek has objected to the decision-theoretic approach of Deutsch and Wallace to deriving the Born rule, on the grounds that it courts circularity. Zurek then derives the Born rule in the Schrodinger Picture using properties of the global Schrodinger state. In this paper a decision-theoretic approach to probability is used in the Heisenberg Picture to derive the Born rule. This derivation uses 'quantum Darwinism' - the notion that classical information is quantum information that can proliferate in the environement - following Ollivier et al. This derivation shows that envariance is not needed to derive the Born Rule and fixes the problem with the decision-theoretic approach that was pointed out by Zurek.

Detlef Dürr, Ward Struyve

Maximilian Schlosshauer, Arthur I. Fine

Recently, W. H. Zurek presented a novel derivation of the Born rule based on a mechanism termed environment-assisted invariance, or "envariance" [W. H. Zurek, Phys. Rev. Lett. 90(2), 120404 (2003)]. We review this approach and identify fundamental assumptions that have implicitly entered into it, emphasizing issues that any such derivation is likely to face.