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Universal realizability in low dimension [PDF]

open access: yesLinear Algebra and Its Applications, 2021
This paper deals with the nonnegative inverse eigenvalue problem (NIEP) for matrices of size \(n \times n\), \(n \leq 5\). The aim is to find necessary and sufficient conditions for a list \(\Lambda=\{\lambda_1,\dots,\lambda_n\}\) of complex numbers to be the spectrum of a nonnegative matrix \(A\).
Miriam Pisonero   +2 more
exaly   +4 more sources
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On the universal realizability problem

Linear Algebra and Its Applications, 2020
A multi-set \(\Lambda = \{\lambda_1, \lambda_2,\dots, \lambda_n\}\) of complex numbers is said to be realizable if it is the spectrum of a (entrywise) nonnegative matrix A. The problem of finding necessary and sufficient conditions for \(\Lambda\) being realizable is known as the nonnegative inverse eigenvalue problem (NIEP).
Ricardo L Soto, Ana Isabel Julio
exaly   +3 more sources

On universal realizability of spectra [PDF]

open access: yesLinear Algebra and Its Applications, 2019
22 pages, 2 ...
Miriam Pisonero   +2 more
exaly   +3 more sources

Realization of the universal‐NOT gate and of the universal quantum cloning

Fortschritte der Physik, 2003
AbstractAn arbitrary quantum state cannot be “cloned” perfectly, i.e. reproduced with “fidelity” F = 1 into M > 1 states identical to the original by any conceivable physical device. The main root of this impossibility resides in the linearity of quantum mechanics.
C. Sias   +2 more
openaire   +4 more sources

Realizable Universal Quantum Logic Gates

Physical Review Letters, 1995
We identify a 2-bit quantum gate that is sufficient to build any quantum logic network. The existence of such a 2-bit universal gate considerably simplifies the search for physical realizations of quantum computational networks. We propose an explicit construction of this gate, which is based on cavity QED techniques and may be realizable with current ...
Sleator, Tycho, Weinfurter, Harald
openaire   +2 more sources

Realization is universal

Mathematical Systems Theory, 1972
Behavior is left adjoint to minimal realization, as functors between certain categories of machines and behaviors. This gives a succinct characterization of minimal realization valid for discrete as well as linear machines, with or without finiteness condition. Realization theory is therefore expressed in contemporary algebra in a way which reveals its
openaire   +2 more sources

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