We propose a generalization of the Bloch sphere representation for arbitrary spin states. It provides a compact and elegant representation of spin density matrices in terms of tensors that share the most important properties of Bloch vectors. Our representation, based on covariant matrices introduced by Weinberg in the context of quantum field theory, allows for a simple parametrization of coherent spin states, and a straightforward transformation of density matrices under local unitary and partial tracing operations. It enables us to provide a criterion for anticoherence, relevant in a broader context such as quantum polarization of light.We propose a generalization of the Bloch sphere representation for arbitrary spin states. It provides a compact and elegant representation of spin density matrices in terms of tensors that share the most important properties of Bloch vectors. Our representation, based on covariant matrices introduced by Weinberg in the context of quantum field theory, allows for a simple parametrization of coherent spin states, and a straightforward transformation of density matrices under local unitary and partial tracing operations. It enables us to provide a criterion for anticoherence, relevant in a broader context such as quantum polarization of light.

arXiv:1409.1106Physical Review LettersFeb 25, 201557 citations

COVARIANT DENSITY MATRICES FOR ARBITRARY SPINS

Arif-Uz Zaman, Yibo Liu

Il Nuovo CimentoAug 21, 19660 citations

Quantum Fisher Information for Density Matrices with Arbitrary Ranks

刘京, 井晓辛, 钟伟 +1 more

理论物理通讯：英文版Jan 1, 20140 citations

Nonlocal Parameters for Multiparticle Density Matrices

Noah Linden, Sandu Popescu, Anthony Sudbery

As far as entanglement is concerned, two density matrices of $n$ particles are completely equivalent if one can be transformed into the other by local unitary transformations. We present two methods to find whether or not two generic density matrices of arbitrary numbers of spin-1/2 particles are equivalent. Both methods describe density matrices in terms of a finite number of invariant parameters.As far as entanglement is concerned, two density matrices of $n$ particles are completely equivalent if one can be transformed into the other by local unitary transformations. We present two methods to find whether or not two generic density matrices of arbitrary numbers of spin-1/2 particles are equivalent. Both methods describe density matrices in terms of a finite number of invariant parameters.

arXiv:quant-ph/9801076Physical Review LettersJul 12, 1999146 citations

Spin Density Matrices

Alan McLachlan

NatureDec 5, 19700 citations

Permutation-Algebraic Formulation of Spin-Free Transition Density Matrices

R. D. Poshusta, F. A. Matsen

Spin-free transition density matrices are derived from spin-free kets which are symmetry-adapted to the symmetric group and its algebra. The Dirac identity establishes that these spin-free density matrices are identical to those obtained by integrating the spin from the full-spin density martices. Derivations are first given for arbitrary primitive kets which may be geminals of higher polymals, after which we consider products of orbitals, either orthonormal or nonorthonormal. Correlation in the spin-free space is discussed and we show the influence of permutational symmetry on the probability of coincidence of pairs. A special case of this correlation is the well-known Fermi hole.Spin-free transition density matrices are derived from spin-free kets which are symmetry-adapted to the symmetric group and its algebra. The Dirac identity establishes that these spin-free density matrices are identical to those obtained by integrating the spin from the full-spin density martices. Derivations are first given for arbitrary primitive kets which may be geminals of higher polymals, after which we consider products of orbitals, either orthonormal or nonorthonormal. Correlation in the spin-free space is discussed and we show the influence of permutational symmetry on the probability of coincidence of pairs. A special case of this correlation is the well-known Fermi hole.

Journal of Mathematical PhysicsApr 1, 196618 citations

As far as entanglement is concerned, two density matrices of

n

particles are completely equivalent if one can be transformed into the other by local unitary transformations. We present two methods to find whether or not two generic density matrices of arbitrary numbers of spin-1/2 particles are equivalent. Both methods describe density matrices in terms of a finite number of invariant parameters.