Quantum entanglement via nilpotent polynomials
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Date
2006
Authors
Mandilara, Aikaterini
Akulin, Vladimir M.
Smilga, Andrei V.
Viola, Lorenza
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Abstract
We propose a general method for introducing extensive characteristics of quantum entanglement. The
method relies on polynomials of nilpotent raising operators that create entangled states acting on a reference
vacuum state. By introducing the notion of tanglemeter, the logarithm of the state vector represented in a
special canonical form and expressed via polynomials of nilpotent variables, we show how this description
provides a simple criterion for entanglement as well as a universal method for constructing the invariants
characterizing entanglement. We compare the existing measures and classes of entanglement with those emerging
from our approach. We derive the equation of motion for the tanglemeter and, in representative examples
of up to four-qubit systems, show how the known classes appear in a natural way within our framework. We
extend our approach to qutrits and higher-dimensional systems, and make contact with the recently introduced
idea of generalized entanglement. Possible future developments and applications of the method are discussed.
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Keywords
Research Subject Categories::NATURAL SCIENCES::Physics, quantum entanglement
Citation
Aikaterini Mandilara, Vladimir M. Akulin, Andrei V. Smilga, Lorenza Viola; 2006; Quantum entanglement via nilpotent polynomials; PHYSICAL REVIEW A