Local Unitary Invariants for N-qubit Pure State

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.