Related papers: A transform of complementary aspects with applicat…
The current study aims to examine uncertainty relations for measurements from generalized equiangular tight frames. Informationally overcomplete measurements are a valuable tool in quantum information processing, including tomography and…
Finite tight frames are interesting in various topics including questions of quantum information. Each complex tight frame leads to a resolution of the identity in the Hilbert space. Symmetric informationally complete measurements are a…
Entropic uncertainty relations, based on sums of entropies of probability distributions arising from different measurements on a given pure state, can be seen as a generalization of the Heisenberg uncertainty relation that is in many cases…
Entropic uncertainty relations play a fundamental role in quantum information theory. However, determining optimal (tight) entropic uncertainty relations for general observables remains a formidable challenge and has so far been achieved…
The uncertainty principle sets limit on our ability to predict the values of two incompatible observables measured on a quantum particle simultaneously. This principle can be stated in various forms. In quantum information theory, it is…
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 $|\braket{v_1|v_2}| = \frac{1}{\sqrt{d}}$.…
Constructing four six-dimensional mutually unbiased bases (MUBs) is an open problem in quantum physics and measurement. We investigate the existence of four MUBs including the identity, and a complex Hadamard matrix (CHM) of Schmidt rank…
In quantum information theory, it is a fundamental problem to construct multipartite unextendible product bases (UPBs). We show that there exist two families UPBs in Hilbert space…
Entropic uncertainty relations demonstrate the intrinsic uncertainty of nature from an information-theory perspective. Recently, a quantum-memory-assisted entropic uncertainty relation for multiple measurements was proposed by Wu $et\ al.$…
We describe sets of mutually unbiased bases (MUBs) for quantum states defined over the p-adic numbers Q_p, i.e. the states that can be described as elements of the (rigged) Hilbert space L2(Q_p). We find that for every prime p>2 there are…
We develop a strong connection between maximally commuting bases of orthogonal unitary matrices and mutually unbiased bases. A necessary condition of the existence of mutually unbiased bases for any finite dimension is obtained. Then a…
Mutually unbiased bases (MUBs) play a crucial role in numerous applications within quantum information science, such as quantum state tomography, error correction, entanglement detection, and quantum cryptography. Utilizing \(2^n + 1\) MUB…
The well-known Heisenberg--Robertson uncertainty relation for a pair of noncommuting observables, is expressed in terms of the product of variances and the commutator among the operators, computed for the quantum state of a system.…
We study fine-grained uncertainty relations for several quantum measurements in a finite-dimensional Hilbert space. The proposed approach is based on exact calculation or estimation of the spectral norms of corresponding positive matrices.…
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 study entropic uncertainty relations by using stepwise linear functions and quadratic functions. Two kinds of improved uncertainty lower bounds are constructed: the state-independent one based on the lower bound of Shannon entropy and…
Majorization uncertainty relations are derived for arbitrary quantum operations acting on a finite-dimensional space. The basic idea is to consider submatrices of block matrices comprised of the corresponding Kraus operators. This is an…
We study the robustness of various protocols for quantum key distribution. We first consider the case of qutrits and study quantum protocols that employ two and three mutually unbiased bases. We then derive the optimal eavesdropping…
We review the plethora of uncertainty relations that appear in quantum mechanics and their nuances. We present both foundational applications, e.g. in understanding and defining complementarity, and practical applications, e.g. in quantum…
Quantum control in large dimensional Hilbert spaces is essential for realizing the power of quantum information processing. For closed quantum systems the relevant input/output maps are unitary transformations, and the fundamental challenge…