Entropy Guarantees for Quantum Boolean Functions

Abstract

This study demonstrates how to provide specific guarantees on the entropy produced by quantum circuits implementing Boolean functions. More specifically, we study guarantees on von Neumann entropy for subsystems in such circuits. Our findings indicate that input state initialization by rotating the target qubit around the X-axis of the Bloch sphere, combined with arbitrary but fixed individual qubit rotations of the control qubits around any axis or a combination of thereof, preserves the von Neumann entropy of reduced density matrices across subsystem traces. In contrast, similar rotations around the Y-axis cause entropy variation with rotation angle. Moreover, ceteris paribus, arbitrary qubit rotations on all qubits, including the target, result similarly in variability of subsystem entropy. We apply these findings to secure the classical communication channel in a novel multi-qubit quantum teleportation protocol. We depict a full IBM Qiskit implementation and its corresponding graphical-empirical example for the execution of a three-qubit quantum teleportation protocol. Overall, our results reveal insights into system entanglement and demonstrate that Boolean functions provide a structured approach for the purposes of controlling the dynamics of quantum entropy. This has implications beyond the secure obfuscation of classical communication in quantum teleportation and warrants additional investigation of quantum Boolean functions in the broad context of quantum information scrambling and beyond.