We present a new application of harmonic analysis to quantum information by constructing intriguing classes of quantum channels stemming from specific representations of multiplier algebras over locally compact groups G . Beginning with a representation of the measure algebra M ( G ), we unify and elaborate on recent counter-examples to a conjecture on the structure of fixed point subalgebras in infinite dimensions, as well as present an application to the noiseless subsystems method of quantum error correction. Using a representation of the completely bounded Fourier multiplier algebra M cb A ( G ), we provide a new class of counter-examples to the recently solved asymptotic quantum Birkhoff conjecture, along with a systematic method of producing the examples using a geometric representation of Schur maps. Further properties of our channels including duality, quantum capacity, and entanglement preservation are discussed along with potential applications to additivity conjectures.We present a new application of harmonic analysis to quantum information by constructing intriguing classes of quantum channels stemming from specific representations of multiplier algebras over locally compact groups G . Beginning with a representation of the measure algebra M ( G ), we unify and elaborate on recent counter-examples to a conjecture on the structure of fixed point subalgebras in infinite dimensions, as well as present an application to the noiseless subsystems method of quantum error correction. Using a representation of the completely bounded Fourier multiplier algebra M cb A ( G ), we provide a new class of counter-examples to the recently solved asymptotic quantum Birkhoff conjecture, along with a systematic method of producing the examples using a geometric representation of Schur maps. Further properties of our channels including duality, quantum capacity, and entanglement preservation are discussed along with potential applications to additivity conjectures.

arXiv:1210.2738Journal of Physics A Mathematical and TheoreticalJan 10, 201311 citations

The Structure of Quantum States

Gary E. Bowman

Oxford University Press eBooksNov 1, 20070 citations

Tighter monogamy and polygamy relations based on the generalized W-class states

LI Bo, XIE Bing, ZHANG ZhanJun

Entanglement monogamy and polygamy are indispensable features of multipartite quantum systems that describe the entanglement distribution characteristics in these systems. Under the arbitrary partition of superposition of generalized W-class and vacuum states, we investigate a class of monogamy and polygamy inequality based on Tsallis-q and Rényi-q entropy entanglements. We show with concrete examples that parameter selection reduces these inequalities to some existing inequalities; that is, the existing inequalities can be considered a special case of this new class of inequality. Otherwise, these inequalities are tighter than existing ones and are finer representations of entanglement distributions in tripartite and multipartite quantum systems. The inequality of monogamy and polygamy established in this paper has wider applicability.Entanglement monogamy and polygamy are indispensable features of multipartite quantum systems that describe the entanglement distribution characteristics in these systems. Under the arbitrary partition of superposition of generalized W-class and vacuum states, we investigate a class of monogamy and polygamy inequality based on Tsallis-q and Rényi-q entropy entanglements. We show with concrete examples that parameter selection reduces these inequalities to some existing inequalities; that is, the existing inequalities can be considered a special case of this new class of inequality. Otherwise, these inequalities are tighter than existing ones and are finer representations of entanglement distributions in tripartite and multipartite quantum systems. The inequality of monogamy and polygamy established in this paper has wider applicability.

Zhongguo kexue. Wulixue Lixue TianwenxueOct 31, 20230 citations

Quasifree and Classical Quantum States

WORLD SCIENTIFIC eBooksApr 27, 20150 citations

Scale perturbation in valence bond ground states

E. Rico

A simple and efficient method for calculating the ground state for a class of antiferromagnet systems is presented. It combines the valence bond structure of the ground state for this class of systems and real space renormalization group. As an example, the entire Haldane phase for a spin-1 chain is described, from the AKLT model through to the Heisenberg model, ending at the critical WZNW $SU_2(2)$ model. The picture that emerges from this new method leads us to consider the relationship between the hidden topological order that characterizes the Haldane phase and potential applications in quantum communication technology.A simple and efficient method for calculating the ground state for a class of antiferromagnet systems is presented. It combines the valence bond structure of the ground state for this class of systems and real space renormalization group. As an example, the entire Haldane phase for a spin-1 chain is described, from the AKLT model through to the Heisenberg model, ending at the critical WZNW $SU_2(2)$ model. The picture that emerges from this new method leads us to consider the relationship between the hidden topological order that characterizes the Haldane phase and potential applications in quantum communication technology.

arXiv:cond-mat/0601254Jan 12, 20060 citations

SU_2(2)

model. The picture that emerges from this new method leads us to consider the relationship between the hidden topological order that characterizes the Haldane phase and potential applications in quantum communication technology.