Sorting of quantum states with respect to amount of entanglement included

TL;DR

This paper discusses sorting quantum states based on their entanglement using Schmidt decomposition, introduces algorithms for this purpose, and tests their implementation in a quantum computation simulator.

Contribution

It presents new algorithms for sorting quantum states by entanglement and implements them within a quantum computation simulation framework.

Findings

Algorithms successfully sort quantum states by entanglement

Implementation tested and validated in a quantum simulator

Provides a framework for entanglement-based quantum state classification

Abstract

The canonical Schmidt decomposition of quantum states is discussed and its implementation to the Quantum Computation Simulator is outlined. In particular, the semiorder relation in the space of quantum states induced by the lexicographic semiorder of the space of the Schmidt coefficients is discussed. The appropriate sorting algorithms on the corresponding POSETs consisting from quantum states are formulated and theirs computer implementations are being tested.