Related papers: Mutually unbiased bases as submodules and subspace…
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…
We consider the problem of mutually unbiased bases as a polynomial optimization problem over the reals. We heavily reduce it using known symmetries before exploring it using two methods, combining a number of optimization techniques. The…
This note is a short elaboration of the conjecture of Saniga et al (J. Opt. B: Quantum Semiclass. 6 (2004) L19-L20) by regarding a set of mutually unbiased bases (MUBs) in a d-dimensional Hilbert space, d being a power of a prime, as an…
Mutually unbiased bases (MUBs) are a crucial ingredient for many protocols in quantum information processing. Measurements performed in these bases are unbiased to the maximally possible extent, which is used to prove randomness or secrecy…
The study of Mutually Unbiased Bases continues to be developed vigorously, and presents several challenges in the Quantum Information Theory. Two orthonormal bases in $\mathbb C^d, B {and} B'$ are said mutually unbiased if $\forall b\in B,…
We construct an informationally complete set of mutually unbiased - like bases for N ququarts. These bases are used in an explicit tomographic protocol which performance is analyzed by estimating quadratic errors and compared to other…
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…
We present a detailed computational and algebraic study of Mutually Unbiased Bases (MUBs) in finite-dimensional Hilbert spaces, with a particular focus on dimensions 2, 3, 4, and the challenging case of 6. Starting from the Hadamard-phase…
The concept of mutually unbiased bases is studied for N pairs of continuous variables. To find mutually unbiased bases reduces, for specific states related to the Heisenberg-Weyl group, to a problem of symplectic geometry. Given a single…
A complex Hilbert space of dimension six supports at least three but not more than seven mutually unbiased bases. Two computer-aided analytical methods to tighten these bounds are reviewed, based on a discretization of parameter space and…
We study mutually unbiased bases (MUBs) in which all the bases are unextendible maximally entangled ones. We first present a necessary and sufficient condition of constructing a pair of MUBs in $C^2 \otimes C^4$. Based on this condition, an…
A pair of orthonormal bases is called mutually unbiased if all mutual overlaps between any element of one basis with an arbitrary element of the other basis coincide. In case the dimension, $d$, of the considered Hilbert space is a power of…
In quantum information, complementarity of quantum mechanical observables plays a key role. If a system resides in an eigenstate of an observable, the probability distribution for the values of a complementary observable is flat. The…
We show that in a complex d-dimensional vector space, one can find O(d) bases whose elements form a 2-design. Such vector sets generalize the notion of a maximal collection of mutually unbiased bases (MUBs). MUBs have manifold applications…
In dimension $d$, Mutually Unbiased Bases (MUBs) are a collection of orthonormal bases over $\mathbb{C}^d$ such that for any two vectors $v_1, v_2$ belonging to different bases, the scalar product $|\braket{v_1|v_2}| = \frac{1}{\sqrt{d}}$.…
We give a synthetic construction of a complete system of mutually unbiased bases in $\mathbb{C}^3$.
Finite geometry is employed to underpin operators in finite, d, dimensional Hilbert space. The central role of mutual unbiased bases (MUB) states projectors is exhibited. Interrelation among operators in Hilbert space, revealed through…
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…
The thesis is mainly about the construction and implementation of cyclic mutually unbiased bases, dealing with different entanglement structures by discussing the related group structures. A recursive construction for Fermat number…
In this paper, we explore the concept of Mutually Unbiased Bases (MUBs) in discrete quantum systems. It is known that for dimensions $d$ that are powers of prime numbers, there exists a set of up to $d+1$ bases that form an MUB set.…