اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدThe Uncertainty Way of Generalization of Coherent States
157
0
0.0
(
0
)
تأليف
D.A. Trifonov
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
The three ways of generalization of canonical coherent states are briefly reviewed and compared with the emphasis laid on the (minimum) uncertainty way. The characteristic uncertainty relations, which include the Schroedinger and Robertson inequalities, are extended to the case of several states. It is shown that the standard SU(1,1) and SU(2) coherent states are the unique states which minimize the second order characteristic inequality for the three generators. A set of states which minimize the Schroedinger inequality for the Hermitian components of the su_q(1,1) ladder operator is also constructed. It is noted that the characteristic uncertainty relations can be written in the alternative complementary form.
قيم البحث
اقرأ أيضاً
In this paper we treat coherent-squeezed states of Fock space once more and study some basic properties of them from a geometrical point of view. Since the set of coherent-squeezed states ${ket{alpha, beta} | alpha, beta in fukuso}$ makes a real 4-
dimensional surface in the Fock space ${cal F}$ (which is of course not flat), we can calculate its metric. On the other hand, we know that coherent-squeezed states satisfy the minimal uncertainty of Heisenberg under some condition imposed on the parameter space ${alpha, beta}$, so that we can study the metric from the view point of uncertainty principle. Then we obtain a surprising simple form (at least to us). We also make a brief review on Holonomic Quantum Computation by use of a simple model based on nonlinear Kerr effect and coherent-squeezed operators.
We study truncated Bose operators in finite dimensional Hilbert spaces. Spin coherent states for the truncated Bose operators and canonical coherent states for Bose operators are compared. The Lie algebra structure and the spectrum of the truncated Bose operators are discussed.
It is well known that the majorization condition is the necessary and sufficient condition for the deterministic transformations of both pure bipartite entangled states by local operations and coherent states under incoherent operations. In this pape
r, we present two explicit protocols for these transformations. We first present a permutation-based protocol which provides a method for the single-step transformation of $d$-dimensional coherent states. We also obtain generalized solutions of this protocol for some special cases of $d$-level systems. Then, we present an alternative protocol where we use $d$-level ($d$ $<$ $d$) subspace solutions of the permutation-based protocol to achieve the complete transformation as a sequence of coherent-state transformations. We show that these two protocols also provide solutions for deterministic transformations of pure bipartite entangled states.
Nonlinear fermions of degree $n$ ($n$-fermions) are introduced as particles with creation and annihilation operators obeying the simple nonlinear anticommutation relation $AA^dagger + {A^dagger}^n A^n = 1$. The ($n+1$)-order nilpotency of these opera
tors follows from the existence of unique $A$-vacuum. Supposing appropreate ($n+1$)-order nilpotent para-Grassmann variables and integration rules the sets of $n$-fermion number states, right and left ladder operator coherent states (CS) and displacement-operator-like CS are constructed. The $(n+1)times(n+1)$ matrix realization of the related para-Grassmann algebra is provided. General $(n+1)$-order nilpotent ladder operators of finite dimensional systems are expressed as polynomials in terms of $n$-fermion operators. Overcomplete sets of (normalized) right and left eigenstates of such general ladder operators are constructed and their properties briefly discussed.
I generalize the concept of balancedness to qudits with arbitrary dimension $d$. It is an extension of the concept of balancedness in New J. Phys. {bf 12}, 075025 (2010) [1]. At first, I define maximally entangled states as being the stochastic state
s (with local reduced density matrices $id/d$ for a $d$-dimensional local Hilbert space) that are not product states and show that every so-defined maximal genuinely multi-qudit entangled state is balanced. Furthermore, all irreducibly balanced states are genuinely multi-qudit entangled and are locally equivalent with respect to $SL(d)$ transformations (i.e. the local filtering transformations (LFO)) to a maximally entangled state. In particular the concept given here gives the maximal genuinely multi-qudit entangled states for general local Hilbert space dimension $d$. All genuinely multi-qudit entangled states are an element of the partly balanced $SU(d)$-orbits.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
