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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…

Quantum Physics · Physics 2011-09-02 Wim van Dam , Alexander Russell

Mutually unbiased bases (MUBs) provide a standard tool in the verification of quantum states, especially when harnessing a complete set for optimal quantum state tomography. In this work, we investigate the detection of entanglement via…

Quantum Physics · Physics 2021-09-14 B. C. Hiesmayr , D. McNulty , S. Baek , S. Singha Roy , J. Bae , D. Chruściński

Mutually unbiased bases (MUBs), which are such that the inner product between two vectors in different orthogonal bases is constant equal to the inverse $1/\sqrt{d}$, with $d$ the dimension of the finite Hilbert space, are becoming more and…

Quantum Physics · Physics 2009-11-11 Michel Planat , Haret Rosu

Mutually Unbiased Bases (MUBs) constitute a fundamental geometric structure in quantum theory, known for providing an optimal measurement scheme for quantum state tomography. In prime and prime-power dimensions, analytical constructions of…

Quantum Physics · Physics 2026-04-07 Buğra Gültekin , Solomon B. Samuel , Zafer Gedik

In quantum physics, multiparticle systems are described by quantum states acting on tensor products of Hilbert spaces. This product structure leads to the distinction between product states and entangled states; moreover, one can quantify…

Quantum Physics · Physics 2026-03-06 Lisa T. Weinbrenner , Albert Rico , Kenneth Goodenough , Xiao-Dong Yu , Otfried Gühne

In the present paper, a novel framework to detect genuine multipartite entanglement (GME) has been presented by computing correlations in mutually unbiased bases (MUBs). It has been shown that correlation obtained by measuring in MUBs of…

Quantum Physics · Physics 2025-09-30 Sumit Nandi

We introduce the notion of the unextendible maximally entangled basis (UMEB), a set of orthonormal maximally entangled states in d \times d consisting of fewer that d^2 vectors which have no additional maximally entangled vectors orthogonal…

Quantum Physics · Physics 2009-11-23 Sergei Bravyi , John A. Smolin

The aim of the paper is to propose geometric descriptions of multipartite entangled states using algebraic geometry. In the context of this paper, geometric means each stratum of the Hilbert space, corresponding to an entangled state, is an…

Mathematical Physics · Physics 2013-02-12 Frédéric Holweck , Jean-Gabriel Luque , Jean-Yves Thibon

In quantum mechanics, mutually unbiased bases (MUBs) represent orthonormal bases that are as "far apart" as possible, and their classification reveals rich underlying geometric structure. Given a complex inner product space, we construct…

Mathematical Physics · Physics 2025-08-22 Amit Te'eni , Eliahu Cohen

An unextendible product basis (UPB) for a multipartite quantum system is an incomplete orthogonal product basis whose complementary subspace contains no product state. We give examples of UPBs, and show that the uniform mixed state over the…

Quantum Physics · Physics 2009-10-31 C. H. Bennett , D. P. DiVincenzo , T. Mor , P. W. Shor , J. A. Smolin , B. M. Terhal

A collection of orthonormal bases for a complex dXd Hilbert space is called mutually unbiased (MUB) if for any two vectors v and w from different bases the square of the inner product equals 1/d: |<v,w>| ^{2}=1/d. The MUB problem is to…

Quantum Physics · Physics 2007-05-23 Arthur O. Pittenger , Morton H. Rubin

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…

Quantum Physics · Physics 2018-06-11 Xiaoya Cheng , Yun Shang

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…

Quantum Physics · Physics 2019-03-04 Thomas Durt , Berthold-Georg Englert , Ingemar Bengtsson , Karol Życzkowski

A complete set of mutually unbiased bases in a Hilbert space of dimension $d$ defines a set of $d+1$ orthogonal measurements. Relative to such a set, we define a "MUB-balanced state" to be a pure state for which the list of probabilities of…

Quantum Physics · Physics 2015-06-22 Ilya Amburg , Roshan Sharma , Daniel Sussman , William K. Wootters

An unextendible product basis (UPB) is a set of orthogonal product states which span a subspace of a given Hilbert space while the complementary subspace contains no product state. These product bases are useful to produce bound entangled…

Quantum Physics · Physics 2021-02-03 Pratapaditya Bej , Saronath Halder

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…

Information Theory · Computer Science 2020-01-01 Dengming Xu

We present a complete classification of the geometry of the mutually complementary sets of entangled and separable states in three-dimensional Hilbert subspaces of bipartite and multipartite quantum systems. Our analysis begins by finding…

Quantum Physics · Physics 2024-06-24 Rotem Liss , Tal Mor , Andreas Winter

Entanglement for pure bipartite states is most commonly quantified in a state-by-state manner to each pure state of a bipartite system a scalar quantity, such as the von Neumann entropy of a reduced density matrix. This provides a precise…

Quantum Physics · Physics 2025-11-27 Loris Di Cairano

Mutually unbiased bases (MUBs) are considered within the framework of a generic star-product scheme. We rederive that a full set of MUBs is adequate for a spin tomography, i.e. knowledge of all probabilities to find a system in each…

Quantum Physics · Physics 2011-03-01 S. N. Filippov , V. I. Man'ko

The basic methods of constructing the sets of mutually unbiased bases in the Hilbert space of an arbitrary finite dimension are discussed and an emerging link between them is outlined. It is shown that these methods employ a wide range of…

Quantum Physics · Physics 2009-11-10 Michel R. P. Planat , Haret Rosu , Serge Perrine , Metod Saniga