Nilpotent fuzz

Frydryszak, Andrzej

doi:10.1016/s0034-4877(08)80011-0

Cited by 3 publications

(4 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We think that it is something more then an ad hoc tool. The nilpotent classical mechanics [5] and nilpotent quantum mechanics as well as field theory with nilpotent commuting variables [12,9]…”

Section: Discussionmentioning

confidence: 99%

“…As it was already noted in Ref. [12,13,14,15,4,10,8,5,9] such a somehow hybrid object is not a fundamental particle, like boson or fermion and inherently carries properties of a composed object, but it can be described without any explicit reference to the constituents and the way it is composed of. The formalism we develop provides independent description of the qubit itself and gives very convenient characterization of qubit pure state entanglement.…”

Section: Canonical Qubit Relationsmentioning

confidence: 92%

“…The formalism of η-functions which later will be used to describe the nilpotent quantum mechanics was discussed in more detail in [5,8,9]. Properties of such functions allow to answer many questions related to the entanglement.…”

Section: Typementioning

confidence: 99%

See 2 more Smart Citations

Nilpotent quantum mechanics, qubits, and flavors of entanglement

Frydryszak

2008

Preprint

Self Cite

View full text Add to dashboard Cite

We address the question of description of qubit system in a formalism based on the nilpotent commuting η variables. In this formalism qubits exhibit properties of composite objects being subject of the Pauli exclusion principle, but otherwise behaving boson-like. They are not fundamental particles. In such an approach the classical limit yields the nilpotent mechanics.Using the space of η-wavefunctions, generalized Schrödinger equation etc. we study properties of pure qubit systems and also properties of some composed, hybrid models: fermion-qubit, boson-qubit. The fermion-qubit system can be truly supersymmetric, with both SUSY partners having identical spectra. It is new and very interesting that SUSY transformations relate here only nilpotent object. The η-eigenfunctions for the qubit-qubit system give the set of Bloch vectors as a natural basis.Then the η-formalism is applied to the description of the pure state entanglement. Nilpotent commuting variables were firstly used in this context in [A. Mandilara, et. al., Phys. Rev. A 74, 022331 (2006)], we generalize and extend approach presented there. Our main tool for study the entanglement or separability of states are Wronskians of ηfunctions. The known invariants and entanglement monotones for systems of n = 2, 3, 4 qubits are expressed in terms of the Wronskians. This approach gives criteria for separability of states and insight into the flavor of entanglement of the system and simplifies description.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Canonical Qubit Relationsmentioning

confidence: 92%

See 1 more Smart Citation

Nilpotent quantum mechanics, qubits, and flavors of entanglement

Frydryszak

2008

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Ref. [8][9][10]12,18,22,23,26,27, like boson or fermion and inherently carries properties of a composed object, but now it is described without any explicit reference to the constituents and the way it is composed of.…”

Section: Canonical Qubit Relationsmentioning

confidence: 99%

Pure state entanglement in terms of nilpotent variables: η-toolbox

Frydryszak

2010

Quantum Dynamics and Information

View full text Add to dashboard Cite

Entanglement is one of the most important resources in developing quantum computer technology. It might be surprising that it can be effectively described in spaces of functions of nilpotent variables η. For such functions in a natural way arise collections of invariants allowing to construct entanglement measures. Moreover various examples of nontrivial entangled states obtained using quantum physical reasoning turn out to be naturally related to the elementary functions of η-variables.

show abstract

On the Differential Equation of First and Second Order in the Zeon Algebra

Mansour

Schork²

2021

Adv. Appl. Clifford Algebras

View full text Add to dashboard Cite

Nilpotent fuzz

Cited by 3 publications

References 17 publications

Nilpotent quantum mechanics, qubits, and flavors of entanglement

Nilpotent quantum mechanics, qubits, and flavors of entanglement

Pure state entanglement in terms of nilpotent variables: η-toolbox

On the Differential Equation of First and Second Order in the Zeon Algebra

Contact Info

Product

Resources

About