Information transfer in generalized probabilistic theories

• We generalize Zurek's derivation in standard quantum mechanics to generalized probabilistic theories.
• The definition and properties of fidelity between states in GPT is used in our derivation in GPT.
• We considered a series of invertible transformations instead of unitary evolutions.
• We do not need to call on the Born's rule for probabilities in deriving the collapse postulate in GPT.

The tension between unitarity and wave-packet collapse is an annoying problem in quantum mechanics, while a breakthrough was made by Zurek recently from the point of view of information transfer. In this paper, we reconsider Zurek's derivation in the setting of generalized probabilistic theories (GPT), and establish that actionable information about a system can be repeatedly passed on to other systems only when the chosen states of the system have mutual zero fidelity. This may be interpreted as an extension of Zurek's result to GPT.