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1.
We study the separability of symmetric bipartite quantum states and show that a single correlation measurement is sufficient
to detect the entanglement of any bipartite symmetric state with a non-positive partial transpose. We also discuss entanglement
conditions and entanglement witnesses for states with a positive partial transpose. 相似文献
2.
Majorana's stellar representation provides an intuitive picture in which quantum states in high-dimensional Hilbert space can be observed using the trajectory of Majorana stars. We consider the Majorana's stellar representation of the quantum geometric tensor for a spin state up to spin-3/2. The real and imaginary parts of the quantum geometric tensor, corresponding to the quantum metric tensor and Berry curvature, are therefore obtained in terms of the Majorana stars. Moreover, we work out the expressions of quantum geometric tensor for arbitrary spin in some important cases. Our results will benefit the comprehension of the quantum geometric tensor and provide interesting relations between the quantum geometric tensor and Majorana's stars. 相似文献
3.
We complexify one of the Natanzon's exactly solvable potentials in
symmetric manner and discover that it supports the pairs of bound states with the same number of nodal zeros. This could indicate that the Sturm–Liouville oscillation theorem does not admit an immediate generalization. 相似文献
4.
We show that the maximal probability of equiprobable unambiguous discrimination of a set of pure quantum states is given by the minimal eigenvalue of the Gram matrix of this set. We illustrate this result with several examples important for the protocols of quantum key distribution realized with weak coherent states of light. 相似文献
5.
Masashi Ban Keiko Kurokawa Rei Momose Osamu Hirota 《International Journal of Theoretical Physics》1997,36(6):1269-1288
An optimum quantum measurement that minimizes the average probability of error is considered for symmetric quantum states.
The positive operator-valued measure (POM) which satisfies the necessary and sufficient condition for the minimization of
the average probability of error is derived by using the quantum Bayes strategy. It is also shown that the mutual information
obtained in the optimum quantum measurement becomes extremum. Furthermore, an optimum quantum measurement for parameter estimation
is found for symmetric quantum states by applying the maximum-likelihood estimation. The optimum POM for the parameter estimation
has the same structure as that for the quantum state discrimination. 相似文献
6.
Josip Šoln 《International Journal of Theoretical Physics》1981,20(10):723-738
It is shown that the flavor quantum numbers of the basic elementary particles, leptons and quarks, as well as hadrons (with quarks as constituents), can be described withSU(2)×U(1) type of algebras. To treat simultaneously leptons and quarks (hadrons), we introduce the grace quantum number,G, in place ofL (the total lepton quantum number) andB (the baryon quantum number). The formalism developed here requires the basic elementary particles to come in even numbers. For the case of four basic particles we have quantum numbers denoted asQ, X, andY and their duals denoted asQ, X, andY. For the four leptonsQ is the ordinary charge, while —Y andY areL
(the muon lepton number) andL
e (the electron lepton number), respectively. For the four quarksQ is the ordinary charge,Y the ordinary hypercharge, whileX, a new quantum number, is simply theX charge, which, however, can be related to charmC. 相似文献
7.
V. S. Bagaev L. K. Vodop’yanov V. S. Vinogradov V. V. Zaitsev S. P. Kozyrev N. N. Mel’nik E. E. Onishchenko G. Karczewski 《Physics of the Solid State》2004,46(1):173-175
Electronic and vibrational states in CdTe/ZnTe quantum dot superlattices are studied using optical spectroscopy techniques (photoluminescence in a wide temperature range, IR reflection, and Raman scattering). The effect of the ZnTe barrier layer thickness on the luminescence spectra of the structures is discussed. The luminescence from electronically coupled islands is assumed to be due to spatially indirect excitons because of the specific features of the CdTe/ZnTe heterostructure band structure. A combination of quantum-dot vibrational modes, which has not been observed earlier, is detected in the Raman spectra. Analysis of the lattice IR reflection spectra shows that, in the case of large barrier thicknesses between the quantum-dot planes, elastic stresses are concentrated in the Zn1?xCdxTe layers, whereas in structures with lower barrier thicknesses the elastic-strain distribution exhibits a more complicated pattern. 相似文献
8.
We show that for a fixed amount of entanglement, two-mode squeezed states are those that maximize Einstein-Podolsky-Rosen-like correlations. We use this fact to determine the entanglement of formation for all symmetric Gaussian states corresponding to two modes. This is the first instance in which this measure has been determined for genuine continuous variable systems. 相似文献
9.
The stabilizer group for an n-qubit state |Φ is the set of all invertible local operators(ILO) g = g1g2···gn,gi 2 GL(2,C) such that |Φ= g|Φ. Recently, Gour et al. [Gour G, Kraus B and Wallach N R 2017 J. Math. Phys. 58092204] presented that almost all n-qubit states jyi own a trivial stabilizer group when n≥5. In this article, we consider the case when the stabilizer group of an n-qubit symmetric pure state jyi is trivial. First we show that the stabilizer group for an n-qubit symmetric pure state |Φ is nontrivial when n≤4. Then we present a class of n-qubit symmetric states |Ψ with a trivial stabilizer group when n≥5. Finally, we propose a conjecture and prove that an n-qubit symmetric pure state owns a trivial stabilizer group when its diversity number is bigger than 5 under the conjecture we make, which confirms the main result of Gour et al. partly. 相似文献
10.
《Nuclear Physics A》1998,637(4):520-528
The inherent nodal structures of the wavefunctions of 4-nucleon systems have been investigated. The existence of two groups of low-lying states with specific quantum numbers dominated by total orbital angular momentum L = 0 and L = 1, respectively, has been deduced. The understanding of the inherent nodal structure is found to be crucial to a systematic understanding of the spectrum. 相似文献
11.
Richard L. Liboff 《Foundations of Physics》1975,5(2):271-293
Periodic systems are considered whose increments in quantum energy grow with quantum number. In the limit of large quantum number, systems are found to give correspondence in form between classical and quantum frequency-energy dependences. Solely passing to large quantum numbers, however, does not guarantee the classical spectrum. For the examples cited, successive quantum frequencies remain separated by the incrementhI ?1, whereI is independent of quantum number. Frequency correspondence follows in Planck's limit,h → 0. The first example is that of a particle in a cubical box with impenetrable walls. The quantum emission spectrum is found to be uniformly discrete over the whole frequency range. This quality holds in the limitn → ∞. The discrete spectrum due to transitions in the high-quantum-number bound states of a particle in a box with penetrable walls is shown to grow uniformly discrete in the limit that the well becomes infinitely deep. For the infinitely deep spherical well, on the other hand, correspondence is found to be obeyed both in emission and configuration. In all cases studied the classical ensemble gives a continuum of frequencies. 相似文献
12.
13.
We characterize equilibrium states of quantum systems by a condition of passivity suggested by the second principle of thermodynamics. Ground states and -KMS states for all inverse temperatures 0 are completely passive. We prove that these states are the only completely passive ones. For the special case of states describing pure phases, assuming the passivity we reproduce the results of Haag et al. 相似文献
14.
S. A. Bulgadaev 《Journal of Experimental and Theoretical Physics》1999,89(4):603-611
The paper shows how vector topological charges for topological excitations in nonlinear σ-models on compact one-dimensional spaces T
G
and G/T
G
can be defined (here G is a simple compact Lie group and T
G
is its maximal commutative subgroup). Explicit solutions, their energies and interactions between different topological charges
have been obtained. A possibility of topological interpretation of quantum numbers of groups and particles is discussed.
Zh. éksp. Teor. Fiz. 116, 1131–1147 (October 1999) 相似文献
15.
We investigate the entanglement properties of multimode Gaussian states, which have some symmetry with respect to the ordering of the modes. We show how the symmetry constrains the entanglement between two modes of the system. In particular, we determine the maximal entanglement of formation that can be achieved in symmetric graphs like chains, 2D and 3D lattices, mean field models and the platonic solids. The maximal entanglement is always attained for the ground state of a particular quadratic Hamiltonian. The latter thus yields the maximal entanglement among all quadratic Hamiltonians having the considered symmetry. 相似文献
16.
A. M. Perelomov 《Communications in Mathematical Physics》1975,44(2):197-210
Properties of system of the coherent states related to representations of the class I of principal series of the motion groups of symmetric spaces of rank 1 have been studied. It has been proved that such states are given by horospherical kernels and are the generalization of the plane waves for the case of symmetric spaces. 相似文献
17.
There is a natural connection and parallel transport on the Hilbert tensor product (or, equivalently, the space of Hilbert-Schmidt operators), the elements of which represent density matrices in up to unitary operators. We postulate a time evolution equation, which leads to this connection after extracting a proper dynamical unitary phase. As an example, we compute the holonomy of a loop of temperature states for the spin in a rotating magnetic field.Supported by Fonds zur Förderung der wissenschaftlichen Forschung in Österreich, Project No. P5588. 相似文献
18.
Coherent states are introduced and their properties are discussed for simple quantum compact groupsA
l, Bl, Cl andD
l. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates
on a general quantum dressing orbit. The coherent state is interpreted as a holomorphic function on this orbit with values
in the carrier Hilbert space of an irreducible representation of the corresponding quantized enveloping algebra. Using Gauss
decomposition, the commutation relations for the holomorphic coordinates on the dressing orbit are derived explicitly and
given in a compactR-matrix formulation (generalizing this way theq-deformed Grassmann and flag manifolds). The antiholomorphic realization of the irreducible representations of a compact quantum
group (the analogue of the Borel-Weil construction) is described using the concept of coherent state. The relation between
representation theory and non-commutative differential geometry is suggested.
Dedicated to Professor L.D. Faddeev on his 60th birthday 相似文献
19.
20.
The principle of ergodicity of the quantum theory has been used for elaboration of a new technique for numerical simulation
of the Wigner function of open dissipative quantum systems. With this purpose the density matrix of a quantum system is represented
via averaging over the ensemble of quantum states in time intervals instead of averaging over the ensemble of stochastic variables.
It is shown that this approach leads to new approximate expressions for quantum distributions in the phase space, in particular,
Wigner functions for systems localized in the region of classical phase trajectories. As an application, the Wigner functions
are calculated for the process of intracavity second harmonic generation in the region of Hopf bifurcations. 相似文献