Abstract
We give a definition of uncomplexity of a mixed state without invoking any particular definitions of mixed state complexity, and argue that it gives the amount of computational power Bob has when he only has access to part of a system. We find geometric meanings of our definition in various black hole examples, and make a connection with subregion duality. We show that Bob's uncomplexity is the portion of his accessible interior spacetime inside his entanglement wedge. This solves a puzzle we encountered about the uncomplexity of thermofield double state. In this process, we identify different kinds of operations Bob can do as being responsible for the growth of different parts of spacetime.
Highlights
It was pointed out in Ref. [1] that one can do useful computations with a system away from being maximally complex
In Ref. [1], the concept of uncomplexity was introduced to characterize the amount of computational power one has with a system in some particular state
The uncomplexity of a pure state is defined as the difference of the maximal complexity and the state complexity
Summary
It was pointed out in Ref. [1] that one can do useful computations with a system away from being maximally complex. Following the simple assumption that the computational power of a mixed state does not depend on its purifications, we give a definition of the uncomplexity of a density matrix without invoking any definitions of complexity of a mixed state. In this process, we study different kinds of operations Bob can apply if he only has access to a subsystem of an entangled state. We see that the uncomplexity of a density matrix exactly corresponds to the portion of interior spacetime accessible to an observer which is inside the entanglement wedge of the density matrix (Fig. 1) In this process, we show that the different kinds of operations we studied earlier are responsible for the growth of different spacetime regions. We point out the role played by the apparent horizon [9]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
