Universal and distortion-free entanglement concentration of multiqubit quantum states in the W class

Abstract

We propose a multipartite extension of Matsumoto and Hayashi's distortion-free entanglement concentration protocol, which takes n copies of a general multipartite state and, via local measurements, produces a maximally-entangled multipartite state between local spaces of dimensions ∼ 2 nE i , where Ei are the local entropies of the input state. However, the extended protocol is generally not universal in the sense that for the same measurement outcomes, the output state will still depend on the input state. Our main result is that when specialized to any state in the multiqubit W class, the protocol is also universal, so that as in the biparatite version, the output is a unique, maximally-entangled state for each given set of measurement outcomes. Our analysis brings to the forefront a new and interesting family of maximally-entangled multipartite states, which we term Kronecker states. A recurrence relation to obtain the coefficients of the W-class Kronecker states is also given.

Generalization of the Tavis-Cummings model for multi-level anharmonic systems

“…, and Gram-Schmidt orthogonalization have been discussed in the literature under the name of Schur-Weyl states [40,[64][65][66], or Gelfand-Tsetlin states [67][68][69][70]. Although not necessary for the block-diagonalization of the Hamiltonian, an illustration of the explicit form of the symmetrized states in terms of the PBEs might be useful for the reader.…”

Large deviation principle for moment map estimation

“…In [24] a family of entanglement measures have been constructed based on the rate function corresponding to the standard representation of products of unitary groups. While studying a tripartite extension of the Matsumoto-Hayashi universal distortion-free entanglement concentration protocol [18], Botero and Mejía [5] found formulas for the probabilities induced by the isotypic decomposition or tensor powers of the U (2) n -representation C 2 ⊗n when the state is in the W class.…”

Phononic entanglement concentration via optomechanical interactions

“…However, the channel noise will induce decoherence and degrade the entanglement between the quantum systems. Entanglement concentration [11][12][13][14][15][16][17][18][19][20][21][22][23] is an operation which converts a partially entangled state to a more or maximally entangled state. Since the first entanglement concentration protocol (ECP), the well known Schmidt projection, was proposed by Bennett et al [11], its realization on the various physical systems has been reported.…”