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Entanglement and Weak Values: A Quantum Miracle Cookbook

  • Alonso BoteroEmail author
Conference paper

Abstract

The concept of the weak value has proved to be a powerful and operationally grounded framework for the assignment of physical properties to a quantum system at any given time. More importantly, this framework has allowed us to identify a whole range of surprising quantum effects, or “miracles”, which are readily testable but which lie buried “under the noise” when the results of measurements are not post-selected. In all cases, these miracles have to do with the fact that weak values can take values lying outside the conventional ranges of quantum expectation values. We explore the extent to which such miracles are possible within the weak value framework. As we show, given appropriate initial and final states, it is generally possible to produce any set of weak values that is consistent with the linearity of weak values, provided that the states are entangled states of the system with some external ancillary system. Through a simple constructive proof, we obtain a recipe for arbitrary quantum miracles, and give examples of some interesting applications. In particular, we show how the classical description of an infinitely-localized point in phase-space is contained in the weak-value framework augmented by quantum entanglement. [Editor’s note: for a video of the talk given by Prof. Botero at the Aharonov-80 conference in 2012 at Chapman University, see quantum.chapman.edu/talk-27.]

Keywords

Entangle State Entanglement Entropy Canonical Variable Wigner Function Weak Measurement 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Italia 2014

Authors and Affiliations

  1. 1.Physics DepartmentUniversidad de los AndesBogotáColombia

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