The $\ell_{1}$-norm in quantum information via the approach of Yang-Baxter Equation - INSPIRE

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The $\ell_{1}$ -norm in quantum information via the approach of Yang-Baxter Equation

Kai Niu
(
- Nankai, CIM
)
,
Kang Xue
(
- Changchun, Northeast Normal U.
)
,
Qing Zhao
(
- Beijing, Inst. Tech.
)
,
Mo-Lin Ge
(
- Nankai, CIM
)

Jan, 2010

17 pages

e-Print:

1001.3465 [quant-ph]

View in:

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Abstract: (arXiv)

The role of

\ell_{1}

-norm in Quantum Mechanics (QM) has been studied through Wigner's D-functions where

\ell_{1}

-norm means

\sum_{i}\left|C_{i}\right|

for

\left|\Psi\right\rangle =\sum_{i}C_{i}\left|\psi_{i}\right\rangle

if

\left|\psi_{i}\right\rangle

are uni-orthogonal and normalized basis. It was shown that the present two types of transformation matrix acting on the natural basis in physics consist in an unified braiding matrix, which can be viewed as a particular solution of the Yang-Baxter equation (YBE). The maximum of the

\ell_{1}

-norm is connected with the maximally entangled states and topological quantum field theory (TQFT) with two-component anyons while the minimum leads to the permutation for fermions or bosons.

Note:

17 pages, 5 figures

03.67.Lx
05.30.Pr
03.65.Fd
field theory: topological
spin: wave function
entanglement
Yang-Baxter equation
rotation
braid group

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Figures(5)

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