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[en] The long-standing problem of finding coherent states for the (bound state portion of the) hydrogen atom is positively resolved. The states in question (i) are normalized and parametrized continuously, (ii) admit a resolution of unity with a positive measure, and (iii) enjoy the property that the temporal evolution of any coherent state by the hydrogen atom Hamiltonian remains a coherent state for all time. (author). Letter-to-the-editor
[en] We define the stringent coherence witness as an observable whose mean value vanishes for all incoherent states but nonzero for some coherent states. Such witnesses are proved to exist for any finite-dimension states. Not only is the witness efficient in testing whether a state is coherent, but also its mean value can quantitatively reveal the amount of coherence. For an unknown state, the modulus of the mean value of a normalized witness provides a tight lower bound to the -norm of coherence. When we have some previous knowledge of a state, the optimal witness which has the maximal mean value is derived. It is proved that for any finite dimension state, the mean value of the optimal witness, which we call the witnessed coherence, equals the -norm of coherence. In the case that the witness is fixed and the incoherent operations are allowed, the maximal mean value can reach the witnessed coherence if and only if certain relations between the fixed witness and the initial state are satisfied. Our results provide a way to directly measure the coherence in arbitrary finite dimension states and an operational interpretation of the -norm of coherence.
[en] Generalized permutation relation determined by a set of coefficients μ=(μ1,...,μsub(k)) are under consideration for a pair of operators a and a+ conjugated to each other. The totality of operator functions of a and a+ (the μ-algebra) is investigated. It is shown that a and a+ can be interpreted as the annihilation and creation operators of some 'particles'. Unlike the well known types of the quantization of Bose-Einstein and Fermi-Dirac the μ-quantization generally violates the proportionality between the energy of a state and its number of 'particles', a fact which is treated as a certain interaction between the 'particles'. All the particular cases of μ-quantization free from interaction are determined
[fr]On considere les relations de permutation generalisees determinees par un ensemble de coefficients μ=(μ1,...,μsub(k)), pour un couple d'operateurs a et a+ adjoints l'un de l'autre. On etudie les familles des operateurs (μ-algebres) fonctions de a et a+. Il est montre que a et a+ peuvent etre interpretes comme operateurs d'annihilation et de creation de certaines 'particules'. Contrairement aux types de quantification de Bose-Einstein et de Fermi-Dirac bien connus, la μ-quantification viole, en general, la proportionnalite entre l'energie d'un etat et son nombre de 'particules' ce qu'on peut interpreter comme une certaine interaction des 'particules'. Tous les cas particuliers de la μ-quantification, ou l'interaction n'a pas lieu, sont determines
[en] We find that the mapping from classical optical transformations to the optical operator method can be realized by using the coherent state representation and the technique of integration within an ordered product of operators. The optical Fresnel operator derived in (Commun. Theor. Phys. (Beijing, China) 38 (2002) 147) can unify those frequently used optical operators. Various decompositions of Fresnel operator into the exponential canonical operators are obtained
[en] In this paper, we discuss a general strategy to construct vector coherent states of the Gazeau-Klauder type and we use them to build up examples of isospectral Hamiltonians. For that we use a general strategy recently proposed by the author, which extends well-known facts on intertwining operators. We also discuss the possibility of constructing non-isospectral Hamiltonians with related eigenstates
[en] This paper was published online on 9 August 2011 with a duplication of Fig. 4 in place of Fig. 1. Figure 1 has been correctly replaced as of 22 August 2011. Figure 1 is correct in the printed version of the journal.
[en] Monogamy is a fundamental property of multi-partite entangled states. Recently, Kim J S [Phys. Rev. A 93 032331] showed that a partially coherent superposition (PCS) of a generalized W-class state and the vacuum saturates the strong monogamy inequality proposed by Regula B et al. [Phys. Rev. Lett. 113 110501] in terms of squared convex roof extended negativity; and this fact may present that this class of states are good candidates for studying the monogamy of entanglement. Hence in this paper, we will investigate the monogamy relations for the PCS states. We first present some properties of the PCS states that are useful for providing our main theorems. Then we present several monogamy inequalities for the PCS states in terms of some entanglement measures. (paper)
[en] We consider the problem of discriminating between two quantum coherent states by interpreting a single state as being a collection of several successive copies of weaker coherent states. By means of recent results on multiple-copy state discrimination, it is possible to give a reinterpretation of the Dolinar receiver and carry out a quite-straightforward analysis of its behavior. We also propose and investigate a suboptimal detection scheme derived from the Dolinar's architecture, which is shown to slightly outperform some other near-optimal schemes available in the literature.
[en] Quantum dots provide a natural system in which to study both quantum and classical features of transport. As a closed testbed, they provide a natural system with a very rich set of eigenstates. When coupled to the environment through a pair of quantum point contacts, each of which passes several modes, the original quantum environment evolves into a set of decoherent and coherent states, which classically would compose a mixed phase space. The manner of this breakup is governed strongly by Zurek's decoherence theory, and the remaining coherent states possess all the properties of his pointer states. These states are naturally studied via traditional magnetotransport at low temperatures. More recently, we have used scanning gate (conductance) microscopy to probe the nature of the coherent states, and have shown that families of states exist through the spectrum in a manner consistent with quantum Darwinism. In this review, we discuss the nature of the various states, how they are formed, and the signatures that appear in magnetotransport and general conductance studies. (topical review)