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Maximally entangled numerical range

Definition

Maximally entangled numerical range Went(A) of a square matrix A of size d=d1×d2 is a subset of the complex plane defined as

Went(A)={zC:z=ψ|A|ψ,|ψCentd1×d2}.

Centd1×d2={|ψ:=(U1U2)i=1dmin1dmin|ψi1|ψi2}, where

  • dmin=min(d1,d2),
  • |ψi1, |ψi2 form orthonormal bases in Cd1 and Cd2 respectively,
  • U1SU(d1) and U2SU(d2).