We develop a general theory of the time distribution quantum events, applicable to large class problems such as arrival time, dwell and tunneling time. A stopwatch ticks until an awaited event is detected, at which stops. The represented by projection operator $\pi$, while ideal modeled series projective measurements state gets projected with either $\bar{\pi}=1-\pi$ (when does not happen) or $...

It is shown that the quarks and leptons of the standard model, including a right-handed neutrino, can be obtained by gauging the holonomy groups of complex projective spaces of complex dimensions two and three. The spectrum emerges as chiral zero modes of the Dirac operator coupled to gauge fields and the demonstration involves an index theorem analysis on a general complex projective space in ...

We realize indirect partial measurement of a transmon qubit in circuit quantum electrodynamics by interaction with an ancilla qubit and projective ancilla measurement with a dedicated readout resonator. Accurate control of the interaction and ancilla measurement basis allows tailoring the measurement strength and operator. The tradeoff between measurement strength and qubit backaction is charac...

We introduce the notion of the projective linking number LinkP(Γ, Z) of a compact oriented real submanifold Γ of dimension 2p − 1 in complex projective n-space P with an algebraic subvariety Z ⊂ P − Γ of codimension p. This notion is related to projective winding numbers and quasi-plurisubharmonic functions, and it generalizes directly from P to any projective manifold. Part 1 of this paper est...

let $g$ be a locally compact group, $h$ be a compact subgroup of $g$ and $varpi$ be a representation of the homogeneous space $g/h$ on a hilbert space $mathcal h$. for $psi in l^p(g/h), 1leq p leqinfty$, and an admissible wavelet $zeta$ for $varpi$, we define the localization operator $l_{psi,zeta} $ on $mathcal h$ and we show that it is a bounded operator. moreover, we prove that the localizat...

A C++ library, named ZKCM, has been developed for the purpose of multiprecision matrix calculations, which is based on the GNU MP and MPFR libraries. It is especially convenient for writing programs involving tensorproduct operations, tracing-out operations, and singular-value decompositions. Its extension library, ZKCM QC, for simulating quantum computing has been developed using the time-depe...

Finite element derivative superconvergent points for harmonic functions under local rectangular mesh are investigated. All superconvergent points for the finite element space of any order that is contained in the tensorproduct space and contains the intermediate family can be predicted. In the case of the serendipity family, results are given for finite element spaces of order below 6. The resu...

Let P be the n-dimensional projective space over C. Denote by G(1,P) the grassmannian of the all projective lines in P. By the Plücker embedding G(1,P) →֒ P( n+1 2 )−1 the grassmannian is an algebraic subset of P( n+1 2 ). For any projective line L ⊂ P we will denote by [L] the corresponding point of G(1,P) and for any P,Q ∈ P, P 6= Q, we will denote by PQ the unique projective line in P spanned...

Let M be a left module over a ring R and I an ideal of R. We call (P,f ) a projective I -cover of M if f is an epimorphism from P to M , P is projective, Kerf ⊆ IP , and whenever P = Kerf + X, then there exists a summand Y of P in Kerf such that P = Y +X. This definition generalizes projective covers and projective δ-covers. Similar to semiregular and semiperfect rings, we characterize I -semir...

Unitary evolution and projective measurement are fundamental axioms of quantum mechanics. Even though projective measurement yields one of the eigenstates of the measured operator as the outcome, there is no theory that predicts which eigenstate will be observed in which experimental run. There exists only an ensemble description, which predicts probabilities of various outcomes over many exper...