Efficient quantum compression for identically prepared states with arbitrary dimensio

Abstract

Identical preparation creates permutation symmetry that can be used for lossless quantum compression. For $n$ copies of an unknown $d$-dimensional pure state, the tensor-power input lies in the fully symmetric subspace, whose dimension is polynomial in $n$ for fixed local dimension. Schur--Weyl duality isolates this subspace coherently, allowing the fixed representation labels to be discarded while retaining all information needed for recovery. The resulting encoder and decoder are exact on the input family. Because tensor-power states span the symmetric subspace, the achieved memory dimension is also necessary for reversible coherent compression, so the scheme is space-optimal. The encoder is implemented recursively with Clebsch--Gordan transforms, and only the branches reached by symmetric inputs need to be reproduced. Standard efficient synthesis of these transforms yields polynomial-size circuits for fixed local dimension and arbitrary target accuracy. Thus identically prepared pure states in arbitrary dimension admit lossless, space-optimal compression with an efficient circuit implementation.