Properties of the (Un)Complexity of Subsystems

TL;DR

This paper explores the properties of subsystem complexity and uncomplexity in quantum states, highlighting their dependence on density matrix degeneracy and investigating superadditivity of uncomplexity.

Contribution

It introduces new insights into how subsystem complexity scales with degeneracy and advances understanding of uncomplexity superadditivity in quantum systems.

Findings

Subsystem complexity scaling varies with degeneracy, showing linear vs. exponential behavior.

Uncomplexity of quantum states can be superadditive under certain conditions.

Progress in proving superadditivity of uncomplexity in general cases.

Abstract

I investigate some properties of proposed definitions for subsystem/mixed state complexity and uncomplexity. A very strong dependence arises on the density matrix's degeneracy which gives a large separation in the scaling of maximum subsystem complexity with number of qubits (linear compared to exponential). I also investigate several cases where the uncomplexity of quantum states are superadditive and present some challenges and progress in showing that the relation holds in complete generality.