Projective ring line of an arbitrary single qudit
نویسندگان
چکیده
منابع مشابه
Projective Ring Line of an Arbitrary Single Qudit
As a continuation of our previous work (arXiv:0708.4333) an algebraic geometrical study of a single d-dimensional qudit is made, with d being any positive integer. The study is based on an intricate relation between the symplectic module of the generalized Pauli group of the qudit and the fine structure of the projective line over the (modular) ring Zd. Explicit formulae are given for both the ...
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The projective line over the (non-commutative) ring of two-by-two matrices with coefficients in GF (2) is found to fully accommodate the algebra of 15 operators — generalized Pauli matrices — characterizing two-qubit systems. The relevant sub-configuration consists of 15 points each of which is either simultaneously distant or simultaneously neighbor to (any) two given distant points of the lin...
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Quantum algorithms are known for providing more efficient solutions to certain computational tasks than any corresponding classical algorithm. Here we show that a single qudit is sufficient to implement an oracle based quantum algorithm, which can solve a black-box problem faster than any classical algorithm. For 2d permutation functions defined on a set of d elements, deciding whether a given ...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and Theoretical
سال: 2007
ISSN: 1751-8113,1751-8121
DOI: 10.1088/1751-8113/41/1/015302