Local Unitary Invariants for N-qubit Pure State

TL;DR

This paper develops local unitary invariant polynomials for N-qubit pure states using negativity fonts, which are matrices of probability amplitudes, to understand entanglement properties.

Contribution

It introduces a novel method to derive LU invariants from first principles based on negativity fonts and their transformation properties.

Findings

Derived explicit LU invariants for N-qubit states.

Connected negativity fonts to entanglement measures.

Provided a framework for analyzing multi-qubit entanglement.

Abstract

We obtain local unitary invariant polynomials for N qubit quantum state from first principles. A basic unit of entanglement, referred to as negativity font, is defined as a two by two matrix of probability amplitudes that determines the negative eigen value of a four by four submatrix of partially transposed state operator. Transformation properties of determinants of negativity fonts under local unitary (LU) transformations are exploited to obtain multi qubit invariants written in terms of such determinants.