相关论文: Restrictions of holomorphic sections to products
Let $M$ be a connected compact quantizable K\"ahler manifold equipped with a Hamiltonian action of a connected compact Lie group $G$. Let $M//G=\phi^{-1}(0)/G=M_0$ be the symplectic quotient at value 0 of the moment map $\phi$. The space…
The existing relation between the tomographic description of quantum states and the convolution algebra of certain discrete groupoids represented on Hilbert spaces will be discussed. The realizations of groupoid algebras based on qudit,…
To every binary linear [n,k]-code C we associate a quantum state ("codeket") belonging to the n-th tensor power of the 2-dimensional complex Hilbert space associated to the spin 1/2 particle. We completely characterize the expectation…
The manifold of pure quantum states is a complex projective space endowed with the unitary-invariant geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given…
We define bulk/boundary maps corresponding to quantum gravity states in the tensorial group field theory formalism, for quantum geometric models sharing the same type of quantum states of loop quantum gravity. The maps are defined in terms…
We examine relationships between various quantization schemes for an electrically charged particle in the field of a magnetic monopole. Quantization maps are defined in invariant geometrical terms, appropriate to the case of nontrivial…
This PHD thesis is concerned with uncertainty relations in quantum probability theory, state estimation in quantum stochastics, and natural bundles in differential geometry. After some comments on the nature and necessity of decoherence in…
Geometric properties of the set of quantum entangled states are investigated. We propose an explicit method to compute the dimension of local orbits for any mixed state of the general K x M problem and characterize the set of effectively…
We consider a nonrelativistic quantum particle constrained to a curved layer of constant width built over a non-compact surface embedded in $R^3$. We suppose that the latter is endowed with the geodesic polar coordinates and that the layer…
Subsystems of composite quantum systems are described by reduced density matrices, or quantum marginals. Important physical properties often do not depend on the whole wave function but rather only on the marginals. Not every collection of…
The classification of topological phases of matter is fundamental to understand and characterize the properties of quantum materials. In this paper we study phases of matter in one-dimensional open quantum systems. We define two mixed…
We present a general method to characterize the quantum correlations obtained after local measurements on multipartite systems. Sufficient conditions for a quantum system to be fully-nonlocal according to a given partition, as well as being…
We demonstrate that the task of determining an unknown quantum state can be accomplished efficiently by making a sequential measurement of two observables $\hat{A}$ and $\hat{B}$, provided that the two observables are chosen in such a way…
A quantization scheme based on the extension of phase space with application of constrained quantization technic is considered. The obtained method is similar to the geometric quantization. For constrained systems the problem of scalar…
A quantum theory is constructed for the system of a relativistic particle with mass m moving freely on the SL(2,R) group manifold. Applied to the cotangent bundle of SL(2,R), the method of Hamiltonian reduction allows us to split the…
The pure states that can be uniquely determined among all (UDA) states by their marginals are essential to efficient quantum state tomography. We generalize the UDA states from the context of pure states to that of arbitrary (no matter pure…
Provided a complete set of putative $k$-body reductions of a multipartite quantum state, can one determine if a joint state exists? We derive necessary conditions for this to be true. In contrast to what is known as the quantum marginal…
This work studies how a suitably-designed classical system generates with a quantum-like (QL) state space mediated by a graph. The graph plays a special dual role by directing the topology of the classical network and defining a state space…
With any state of a multipartite quantum system its separability polytope is associated. This is an algebro-topological object (non-trivial only for mixed states) which captures the localisation of entanglement of the state. Particular…
Quantum entanglement, as the strictly non-classical phenomena, is the kernel of quantum computing and quantum simulation, and has been widely applied ranging from fundamental tests of quantum physics to quantum information processing. The…