Patrick Coles, Carnegie Mellon University
Abstract
... why these three fields of quantum research are intimately connected
I will tell the story of my research journey over the past two years that ultimately led to the title of this talk. It began with my attempts to find a simple proof of the uncertainty principle with quantum memory, which was first proven with lengthy and highly technical arguments [1]. A key finding that allowed us to simplify the proof [2,3] was a quantitative connection between two different views of decoherence: information flow to the environment and loss of off-diagonal elements of the system’s density matrix. I thought it was worth pointing out this connection to the decoherence community, since in some sense it unified seemingly different ideas of decoherence [4]. This unification of different decoherence views also allowed me to give a new perspective on quantum discord, as a measure of information missing from the environment [4]. To fully complete the circle and bring us back to the beginning, I realized that one of the decoherence connections gave a new perspective on uncertainty: an observable's uncertainty is actually a measure of how much entanglement is created upon measuring that observable. This last point has the fascinating consequence that uncertainty relations can be interpreted in a completely new way: as lower bounds on the entanglement created when incompatible observables are measured [5]. Hence, researchers have (unknowingly) been deriving strong bounds on entanglement creation for a few decades now, even though they thought they were bounding uncertainty.
[1] M. Berta, M. Christandl, R. Colbeck, J. M. Renes, and R. Renner. Nature Physics 6, 659 (2010).
[2] P. J. Coles, L. Yu, V. Gheorghiu, and R. B. Griffiths. Phys. Rev. A 83, 062338 (2011).
[3] P. J. Coles, R. Colbeck, L. Yu, and M. Zwolak. eprint arXiv:1112.0543 (2011).
[4] P. J. Coles. Phys. Rev. A 85, 042103 (2012).
[5] P. J. Coles. eprint arXiv:1203.3153 (2012).