English
Related papers

Related papers: Mutually unbiased bases with free parameters

200 papers

Quantum machine learning has shown promise for high-dimensional data analysis, yet many existing approaches rely on linear unitary operations and shared trainable parameters across outputs. These constraints limit expressivity and…

Quantum Physics · Physics 2026-02-17 Viktoria Patapovich , Maniraman Periyasamy , Mo Kordzanganeh , Alexey Melnikov

Mutually unbiased bases (MUBs) and symmetric informationally complete projectors (SICs) are crucial to many conceptual and practical aspects of quantum theory. Here, we develop their role in quantum nonlocality by: i) introducing families…

Quantum Physics · Physics 2021-02-12 Armin Tavakoli , Máté Farkas , Denis Rosset , Jean-Daniel Bancal , Jędrzej Kaniewski

We construct general schemes for multi-partite quantum secret sharing using multi-level systems, and find that the consistent conditions for valid measurements can be summarized in two simple algebraic conditions. The scheme using the very…

Quantum Physics · Physics 2015-07-22 I-Ching Yu , Feng-Li Lin , Ching-Yu Huang

In this paper we derive a new bound on the secret key-rate of the High Dimensional BB84 protocol operating with multiple mutually unbiased bases (MUBs). To our knowledge, our proof is the first for this protocol that is both general (in…

Quantum Physics · Physics 2025-04-16 Trevor N. Thomas , Walter O. Krawec

Mutually unbiased measurements are a generalization of mutually unbiased bases in which the measurement operators need not to be rank one projectors. In a $d$-dimension space, the purity of measurement elements ranges from $1/d$ for the…

Quantum Physics · Physics 2021-11-30 Mahdi Salehi , Seyed Javad Akhtarshenas , Mohsen Sarbishaei , Hakimeh Jaghouri

The complete classification of all 6x6 complex Hadamard matrices is an open problem. The 3-parameter Karlsson family encapsulates all Hadamards that have been parametrised explicitly. We prove that such matrices satisfy a non-trivial…

Quantum Physics · Physics 2014-10-30 Andrew Maxwell , Stephen Brierley

We present an experimental study of higher-dimensional quantum key distribution protocols based on mutually unbiased bases, implemented by means of photons carrying orbital angular momentum. We perform (d+1) mutually unbiased measurements…

In this contribution we group the operator basis for d^2 dimensional Hilbert space in a way that enables us to relate bases of entangled states with single particle mutually unbiased state bases (MUB), each in dimensionality d. We utilize…

Quantum Physics · Physics 2015-05-13 A. Kalev , F. C. Khanna , M. Revzen

We describe a particular class of pairs of quantum observables which are extremal in the convex set of all pairs of compatible quantum observables. The pairs in this class are constructed as uniformly noisy versions of two mutually unbiased…

Quantum Physics · Physics 2019-07-24 Claudio Carmeli , Gianni Cassinelli , Alessandro Toigo

Mutually unbiased bases (MUBs) constitute the canonical example of incompatible quantum measurements. One standard application of MUBs is the task known as quantum random access code (QRAC), in which classical information is encoded in a…

Quantum Physics · Physics 2020-04-02 Máté Farkas , Jędrzej Kaniewski

Quantum uncertainty relations impose fundamental limits on the joint knowledge that can be acquired from complementary observables: perfect knowledge of a quantum state in one basis implies maximal indetermination in all other mutually…

In this study, we first use a three-qubit system as an example to demonstrate the construction of quantum circuits for the eight maximally entangled basis vectors, subsequently extending the approach to N-qubit systems. We employ a…

Quantum Physics · Physics 2025-10-29 Chi-Chuan Hwang

We introduce orthogonal quantum Latin squares, which restrict to traditional orthogonal Latin squares, and investigate their application in quantum information science. We use quantum Latin squares to build maximally entangled bases, and…

Quantum Physics · Physics 2017-01-04 Benjamin Musto

The characterization of quantum processes is a key tool in quantum information processing tasks for several reasons: on one hand, it allows to acknowledge errors in the implementations of quantum algorithms; on the other, it allows to…

Quantum Physics · Physics 2018-12-12 Ignacio Perito , Augusto Roncaglia , Ariel Bendersky

The notation of mutually unbiased bases(MUB) was first introduced by Ivanovic to reconstruct density matrixes\cite{Ivanovic}. The subject about how to use MUB to analyze, process, and utilize the information of the second moments between…

Information Theory · Computer Science 2007-12-19 Hongyi Yao

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…

Quantum Physics · Physics 2015-06-26 Metod Saniga , Michel Planat

We prove the following two results relating real mutually unbiased bases and representations of finite groups of odd order. Let $q$ be a power of 2 and $r$ a positive integer. Then we can find a $q^{2r}\times q^{2r}$ real orthogonal matrix…

Group Theory · Mathematics 2017-11-30 Rod Gow

In our previous paper \cite{co1} we have shown that the theory of circulant matrices allows to recover the result that there exists $p+1$ Mutually Unbiased Bases in dimension $p$, $p$ being an arbitrary prime number. Two orthonormal bases…

Mathematical Physics · Physics 2009-04-24 M. Combescure

We prove tight entropic uncertainty relations for a large number of mutually unbiased measurements. In particular, we show that a bound derived from the result by Maassen and Uffink for 2 such measurements can in fact be tight for up to…

Quantum Physics · Physics 2007-05-23 Manuel A. Ballester , Stephanie Wehner

We employ a straightforward relation between mutually unbiased and Bell bases to extend the latter in terms of a direct construction for the former. We analyze in detail the properties of these new generalized Bell states, showing that they…

Quantum Physics · Physics 2009-10-23 A. B. Klimov , D. Sych , L. L. Sanchez-Soto , G. Leuchs