相关论文: Moment maps and Galois orbits in quantum informati…
We consider the existence in arbitrary finite dimensions d of a POVM comprised of d^2 rank-one operators all of whose operator inner products are equal. Such a set is called a ``symmetric, informationally complete'' POVM (SIC-POVM) and is…
Symmetric informationally complete positive operator valued measures (SIC-POVMs) are studied within the framework of the probability representation of quantum mechanics. A SIC-POVM is shown to be a special case of the probability…
In this paper we examine a generalization of the symmetric informationally complete POVMs. SIC-POVMs are the optimal measurements for full quantum tomography, but if some parameters of the density matrix are known, then the optimal SIC POVM…
This is a survey of some very old knowledge about Mutually Unbiased Bases (MUB) and Symmetric Informationally Complete POVMs (SIC). In prime dimensions the former are closely tied to an elliptic normal curve symmetric under the Heisenberg…
The notion of Symmetric Informationally Complete Positive Operator-Valued Measures (SIC-POVMs) arose in physics as a kind of optimal measurement basis for quantum systems. However the question of their existence is equivalent to that of the…
An unavoidable task in quantum information processing is how to obtain data about the state of an individual system by suitable measurements. Informationally complete measurements are relevant in quantum state tomography, quantum…
Symmetric informationally complete positive operator-valued measurement (SIC-POVM) is one important class of quantum measurement which is crucial for various quantum information processing tasks. SIC-POVMs have the advantage of providing an…
Generalized quantum measurements (also known as POVMs) are of great importance in quantum information and quantum foundations, but often difficult to perform. We present an experimental approach which can in principle be used to perform…
The geometry of the Quantum State Space, described by Bloch vectors, is a very intricate one. A deeper understanding of this geometry could lead to the solution of some difficult problems in Quantum Foundations and Quantum Information such…
These notes treat a momentum map associated to the Heisenberg group. We classify the coadjoint orbits of the Heisenberg group and show that the cocycle associated to the momentum map becomes a value of the modulus of a coadjoint orbit. We…
We consider group-covariant positive operator valued measures (POVMs) on a finite dimensional quantum system. Following Neumark's theorem a POVM can be implemented by an orthogonal measurement on a larger system. Accordingly, our goal is to…
We show that in prime dimensions not equal to three, each group covariant symmetric informationally complete positive operator valued measure (SIC~POVM) is covariant with respect to a unique Heisenberg--Weyl (HW) group. Moreover, the…
Generalized quantum measurements play a crucial role in quantum mechanics, and symmetric informationally complete positive operator-valued measurements (SIC POVMs) provide a powerful and flexible framework for extracting information from…
A version of quantum orbit method is presented for real forms of equal rank of quantum complex simple groups. A quantum moment map is constructed, based on the canonical isomorphism between a quantum Heisenberg algebra and an algebra of…
It is crucial for various quantum information processing tasks that the state of a quantum system can be determined reliably and efficiently from general quantum measurements. One important class of measurements for this purpose is…
The Symmetric Informationally Complete Positive Operator-Valued Measures (SIC-POVMs) are known to exist in all dimensions $\leq 151$ and few higher dimensions as high as $1155$. All known solutions with the exception of the Hoggar solutions…
Symmetric Informationally Complete Positive Operator-Valued Measures (SIC-POVMs) have been constructed in many dimensions using the Weyl-Heisenberg group. In the quantum information community, it is commonly believed that SCI-POVMs exist in…
It is a well-known fact that the optimal POVM for quantum state tomography is the symmetric, informationally complete, positive operator valued measure (SIC-POVM). We investigate the same problem only in the case when there are some a…
In this work, we consider a probability representation of quantum dynamics for finite-dimensional quantum systems with the use of pseudostochastic maps acting on true probability distributions. These probability distributions are obtained…
There has been much interest in so-called SIC-POVMs: rank 1 symmetric informationally complete positive operator valued measures. In this paper we discuss the larger class of POVMs which are symmetric and informationally complete but not…