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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] A general scenario for an N-sequential conclusive state discrimination introduced recently in Loubenets and Namkung [arXiv:2102.04747] can provide a multipartite quantum communication realizable in the presence of a noise. In the present article, we propose a new experimental scheme for the implementation of a sequential conclusive discrimination between binary coherent states via indirect measurements within the Jaynes–Cummings interaction model. We find that if the mean photon number is less than 1.6, then, for our two-sequential state discrimination scheme, the optimal success probability is larger than the one presented in Fields, Bergou, and Varga (2020, IEEE Int. Conf. Quant. Comp. Eng.). We also show that, if the mean photon number is almost equal to 1.2, then the optimal success probability nearly approaches the Helstrom bound. (paper)
[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] 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] New bounded coherent state construction, based in a Keldysh conjecture, is presented. The particular group structure arising from the model leads a new symmetry transformations for the coherent state system. The emergent new symmetry transformations are reminiscent of the Bogoliubov ones. This construction is applied to describe an excitonic system. We discuss how the symmetry of these transformations is intrinsically related with the stability and the behavior of the physical systems as in the excitonic case.