Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Modern Physics Letters B

Mutually unbiased unextendible maximally entangled bases in Cd ⊗ Cq(d+1)

Liang Bao Tang, Yi Xiang, Zhiwen Mo, Ming-Qiang Bai

Published Oct 20, 2020• 3 citations
Publisher

Abstract

Quantum measurements based on mutually unbiased base (MUB) are commonly used in quantum information processing. Firstly, we construct two completed unextendible maximally entangled bases (UMEBs) in bipartite systems [Formula: see text]. Then, the sufficient and necessary conditions of these two UMEBs develop into MUB can be obtained. Finally, we present some UMEBs that are mutually unbiased in concrete bipartite systems. These results provide a method to construct the best measurement bases.

DOI
10.1142/s0217984921500196

Related papers

Construction of a Family of Maximally Entangled Bases in ℂd ⊗ ℂd′

Chenghong Wang, Kun Wang, Zhu‐Jun Zheng

In this paper, we present a new method for the construction of maximally entangled states in Cd⊗Cd′ when d′≥2d. A systematic way of constructing a set of maximally entangled bases (MEBs) in Cd⊗Cd′ was established. Both cases when d′ is divisible by d and not divisible by d are discussed. We give two examples of maximally entangled bases in C2⊗C4, which are mutually unbiased bases. Finally, we found a new example of an unextendible maximally entangled basis (UMEB) in C2⊗C5.

Entropy•Mar 6, 2022•1 citation

A note on the construction of unextendible maximally entangled bases in ℂd ⊗ ℂd′

Chenghong Wang, Kun Wang

We study the construction of unextendible maximally entangled bases in bipartite systems [Formula: see text] ([Formula: see text], [Formula: see text], [Formula: see text]). We provide a class of maximally entangled states in [Formula: see text] by constructing some unitary matrices in [Formula: see text]. In particular, we present two complete unextendible maximally entangled bases in [Formula: see text] which are mutually unbiased.

International Journal of Modern Physics B•Oct 14, 2022•0 citations

New bounds of mutually unbiased maximally entangled bases in ℂd ⊗ ℂkd

ChengXiaoya, ShangYun

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, w...

Quantum Information and Computation•Nov 1, 2018•0 citations

Mutually Unbiasedness between Maximally Entangled Bases and Unextendible Maximally Entangled Systems in ℂ 2 ⊗ ℂ 2 k $\mathbb {C}^{2}\otimes \mathbb {C}^{2^{k}}$

Jun Zhang, Hua Nan, Yuan-Hong Tao +1 more

The mutually unbiasedness between a maximally entangled basis (MEB) and an unextendible maximally entangled system (UMES) in the bipartite system $\mathbb {C}^{2}\otimes \mathbb {C}^{2^{k}} (k>1)$ are introduced and discussed first in this paper. Then two mutually unbiased pairs of a maximally entangled basis and an unextendible maximally entangled system are constructed; lastly, explicit constructions are obtained for mutually unbiased MEB and UMES in $\mathbb {C}^{2}\otimes \mathbb {C}^{4}$ and $\mathbb {C}^{2}\otimes \mathbb {C}^{8}$ , respectively.

International Journal of Theoretical Physics•Jul 7, 2015•6 citations

Mutually unbiased maximally entangled bases from difference matrices

Yajuan Zang, Zihong Tian, Hui-Juan Zuo +1 more

Abstract 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 designs. In particular, we establish q mutually unbiased bases with q − 1 maximally entangled bases and one product basis in C q ⊗ C q for arbitrary prime power q . In addition, we construct maximally entangled bases for dimension of composite numbers of non-prime power, such as five maximally entangled bases in C 12 ⊗ C 12 and C 21 ⊗ C 21 , which improve the known lower bounds for d = 3 m , with (3, m ) = 1 in C d ⊗ C d . Furthermore, we construct p + 1 mutually unbiased bases with p maximally entangled bases and one product basis in C p ⊗ C p 2 for arbitrary prime number p .

arXiv:2210.01517•Journal of Physics A Mathematical and Theoretical•Sep 14, 2022•5 citations

Detecting entanglement can be more effective with inequivalent mutually unbiased bases

Beatrix C. Hiesmayr, D McNulty, S Baek +3 more

Abstract 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 inequivalent sets of MUBs, with a particular focus on unextendible MUBs. These are bases for which an additional unbiased basis cannot be constructed and, consequently, are unsuitable for quantum state verification. Here, we show that unextendible MUBs, as well as other inequivalent sets in higher dimensions, can be more effective in the verification of entanglement. Furthermore, we provide an efficient and systematic method to search for inequivalent MUBs and show that such sets occur regularly within the Heisenberg–Weyl MUBs, as the dimension increases. Our findings are particularly useful for experimentalists since they demonstrate that a clever selection of MUBs allows for entanglement detection with fewer measurements.

arXiv:2011.15078•New Journal of Physics•Aug 25, 2021•22 citations
Quantum measurements based on mutually unbiased base (MUB) are commonly used in quantum information processing. Firstly, we construct two completed unextendible maximally entangled bases (UMEBs) in bipartite systems [Formula: see text]. Then, the sufficient and necessary conditions of these two UMEBs develop into MUB can be obtained. Finally, we present some UMEBs that are mutually unbiased in concrete bipartite systems. These results provide a method to construct the best measurement bases.
Mutually Unbiasedness between Maximally Entangled Bases and Unextendible Maximally Entangled Systems in ℂ 2 ⊗ ℂ 2 k C2⊗C2k\mathbb {C}^{2}\otimes \mathbb {C}^{2^{k}}C2⊗C2k
The mutually unbiasedness between a maximally entangled basis (MEB) and an unextendible maximally entangled system (UMES) in the bipartite system C2⊗C2k(k>1)\mathbb {C}^{2}\otimes \mathbb {C}^{2^{k}} (k>1)C2⊗C2k(k>1) are introduced and discussed first in this paper. Then two mutually unbiased pairs of a maximally entangled basis and an unextendible maximally entangled system are constructed; lastly, explicit constructions are obtained for mutually unbiased MEB and UMES in C2⊗C4\mathbb {C}^{2}\otimes \mathbb {C}^{4}C2⊗C4 and C2⊗C8\mathbb {C}^{2}\otimes \mathbb {C}^{8}C2⊗C8 , respectively.
Abstract 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 designs. In particular, we establish q mutually unbiased bases with q − 1 maximally entangled bases and one product basis in C q ⊗ C q for arbitrary prime power q . In addition, we construct maximally entangled bases for dimension of composite numbers of non-prime power, such as five maximally entangled bases in C 12 ⊗ C 12 and C 21 ⊗ C 21 , which improve the known lower bounds for d = 3 m , with (3, m ) = 1 in C d ⊗ C d . Furthermore, we construct p + 1 mutually unbiased bases with p maximally entangled bases and one product basis in C p ⊗ C p 2 for arbitrary prime number p .
Abstract 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 inequivalent sets of MUBs, with a particular focus on unextendible MUBs. These are bases for which an additional unbiased basis cannot be constructed and, consequently, are unsuitable for quantum state verification. Here, we show that unextendible MUBs, as well as other inequivalent sets in higher dimensions, can be more effective in the verification of entanglement. Furthermore, we provide an efficient and systematic method to search for inequivalent MUBs and show that such sets occur regularly within the Heisenberg–Weyl MUBs, as the dimension increases. Our findings are particularly useful for experimentalists since they demonstrate that a clever selection of MUBs allows for entanglement detection with fewer measurements.