Measurement-induced asymmetry in bipartite networks

Adam Lowe, E. Medina-Guerra

Adam Lowe, E. Medina-Guerra

We consider an interacting bipartite network through a Bayesian game-theoretic framework and demonstrate that weak measurements introduce an inherent asymmetry that is not present when using standard projective measurements. These asymmetries are revealed in the expected payoff for a Bayesian version of Prisoner's dilemma, demonstrating that certain advantages can be found for given subsystems depending on the measurements performed in the network. We demonstrate that this setup allows measurement-induced control for one of the respective parties.

Gerardo A. Paz-Silva, John Henry Reina

Mark S. Williamson, Marie Ericsson, Markus Johansson +3 more

We introduce a bridge between the familiar gauge field theory approaches used in many areas of modern physics such as quantum field theory and the stochastic local operations and classical communication protocols familiar in quantum information. Although the mathematical methods are the same, the meaning of the gauge group is different. The measure we introduce, ``twist,'' is constructed as a Wilson loop from a correlation-induced holonomy. The measure can be understood as the global asymmetry of the bipartite correlations in a loop of three or more qubits; if the holonomy is trivial (the identity matrix), the bipartite correlations can be globally untwisted using general local qubit operations, the gauge group of our theory, which turns out to be the group of Lorentz transformations familiar from special relativity. If it is not possible to globally untwist the bipartite correlations in a state using local operations, the twistedness is given by a nontrivial element of the Lorentz group, the correlation-induced holonomy. We provide several analytical examples of twisted and untwisted states for three qubits, the most elementary nontrivial loop one can imagine.

Jonas Maziero

M. Martinelli