Related papers: Orbits of mutually unbiased bases
We systematically study the construction of mutually unbiased bases in $\mathbb{C}^{2}\bigotimes\mathbb{C}^{3}$, such that all the bases are unextendible maximally entangled ones. Necessary conditions of constructing a pair of mutually…
The connection between maximal sets of mutually unbiased bases (MUBs) in a prime-power dimensional Hilbert space and finite phase-space geometries is well known. In this article we classify MUBs according to their degree of covariance with…
Based on maximally entangled states, we explore the constructions of mutually unbiased bases in bipartite quantum systems. We present a new way to construct mutually unbiased bases by difference matrices in the theory of combinatorial…
Analogous to the notion of mutually unbiased bases for Hilbert spaces, we consider mutually unbiased unitary bases (MUUB) for the space of operators, $M(d, \mathbb{C})$, acting on such Hilbert spaces. The notion of MUUB reflects the…
We present a systematic method to introduce free parameters in sets of mutually unbiased bases. In particular, we demonstrate that any set of m real mutually unbiased bases in dimension N>2 admits the introduction of (m-1)N/2 free…
For certain nilpotent real Lie groups constructed as semidirect products, algebras of invariant differential operators on some coadjoint orbits are used in the study of boundedness properties of the Weyl-Pedersen calculus of their…
We show that k=w+2 mutually unbiased bases can be constructed in any square dimension d=s^2 provided that there are w mutually orthogonal Latin squares of order s. The construction combines the design-theoretic objects (k,s)-nets (which can…
We consider the average distance between four bases in dimension six. The distance between two orthonormal bases vanishes when the bases are the same, and the distance reaches its maximal value of unity when the bases are unbiased. We…
Mutually unbiased bases plays a central role in quantum mechanics and quantum information processing. As an important class of mutually unbiased bases, mutually unbiased maximally entangled bases (MUMEBs) in bipartite systems have attracted…
Finding all the mutually unbiased bases in various dimensions is a problem of fundamental interest in quantum information theory and pure mathematics. The general problem formulated in finite-dimensional Hilbert spaces is open. In the…
Mutually unbiased bases which is also maximally entangled bases is called mutually unbiased maximally entangled bases (MUMEBs). We study the construction of MUMEBs in bipartite system. In detail, we construct 2(p^a-1) MUMEBs in C^d\otimes…
It is conjectured that the question of the existence of projective planes whose order is not a power of prime is intimately linked with the problem whether there exists a set of d+1 mutually unbiased bases in a d-dimensional Hilbert space…
Mutually unbiased bases for quantum degrees of freedom are central to all theoretical investigations and practical exploitations of complementary properties. Much is known about mutually unbiased bases, but there are also a fair number of…
The classification of the unitary irreducible representations of symmetry groups is a cornerstone of modern quantum physics, as it provides the fundamental building blocks for constructing the Hilbert spaces of theories admitting these…
A non-degenerate associative bilinear form and a positive definite symmetric bilinear form on Weyl algebra are constructed.
In this work, the concept of mutually unbiased frames is introduced as the most general notion of unbiasedness for sets composed by linearly independent and normalized vectors. It encompasses the already existing notions of unbiasedness for…
A complete set of N+1 mutually unbiased bases (MUBs) exists in Hilbert spaces of dimension N = p^k, where p is a prime number. They mesh naturally with finite affine planes of order N, that exist when N = p^k. The existence of MUBs for…
We report on a search for mutually unbiased bases (MUBs) in 6 dimensions. We find only triplets of MUBs, and thus do not come close to the theoretical upper bound 7. However, we point out that the natural habitat for sets of MUBs is the set…
In the first part we present the Weyl algebra and our results concerning its finite-dimensional Lie subalgebras. The second part is devoted to a more exotic algebraic structure, the Lie algebra of order 3. We set the basis of a theory of…
A set of mutually unbiased bases (MUBs) is said to be unextendible if there does not exist another basis that is unbiased with respect to the given set. Here, we prove the existence of smaller sets of MUBs in prime-squared dimensions…