scholarly journals The mutually unbiased bases revisited

Author(s):  
Monique Combescure
2021 ◽  
Vol 7 (7) ◽  
pp. eabc3847
Author(s):  
Armin Tavakoli ◽  
Máté Farkas ◽  
Denis Rosset ◽  
Jean-Daniel Bancal ◽  
Jedrzej Kaniewski

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 of Bell inequalities that are maximally violated by d-dimensional MUBs and SICs, respectively, (ii) proving device-independent certification of natural operational notions of MUBs and SICs, and (iii) using MUBs and SICs to develop optimal-rate and nearly optimal-rate protocols for device-independent quantum key distribution and device-independent quantum random number generation, respectively. Moreover, we also present the first example of an extremal point of the quantum set of correlations that admits physically inequivalent quantum realizations. Our results elaborately demonstrate the foundational and practical relevance of the two most important discrete Hilbert space structures to the field of quantum nonlocality.


2016 ◽  
Vol 94 (1) ◽  
Author(s):  
E. C. Paul ◽  
D. S. Tasca ◽  
Łukasz Rudnicki ◽  
S. P. Walborn

2018 ◽  
Vol 94 (1) ◽  
pp. 014007 ◽  
Author(s):  
Gernot Alber ◽  
Christopher Charnes

2021 ◽  
Vol 20 (10) ◽  
Author(s):  
Xiaoyu Chen ◽  
Mengfan Liang ◽  
Mengyao Hu ◽  
Lin Chen

2009 ◽  
Vol 324 (1) ◽  
pp. 53-72 ◽  
Author(s):  
A.B. Klimov ◽  
J.L. Romero ◽  
G. Björk ◽  
L.L. Sánchez-Soto

2018 ◽  
Vol 18 (13&14) ◽  
pp. 1152-1164
Author(s):  
Xiaoya Cheng ◽  
Yun Shang

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 \cd by properties of Guss sums for arbitrary odd d. It improves the known lower bound p^a-1 for odd d. Certainly, it also generalizes the lower bound 2(p^a-1) for d being a single prime power. Furthermore, we construct MUMEBs in \ckd for general k\geq 2 and odd d. We get the similar lower bounds as k,b are both single prime powers. Particularly, when k is a square number, by using mutually orthogonal Latin squares, we can construct more MUMEBs in \ckd, and obtain greater lower bounds than reducing the problem into prime power dimension in some cases.


2007 ◽  
Vol 7 (3) ◽  
pp. 184-208
Author(s):  
W. Hall

The cluster state model for quantum computation [Phys. Rev. Lett. \textbf{86}, 5188] outlines a scheme that allows one to use measurement on a large set of entangled quantum systems in what is known as a cluster state to undertake quantum computations. The model itself and many works dedicated to it involve using entangled qubits. In this paper we consider the issue of using entangled qudits instead. We present a complete framework for cluster state quantum computation using qudits, which not only contains the features of the original qubit model but also contains the new idea of adaptive computation: via a change in the classical computation that helps to correct the errors that are inherent in the model, the implemented quantum computation can be changed. This feature arises through the extra degrees of freedom that appear when using qudits. Finally, for prime dimensions, we give a very explicit description of the model, making use of mutually unbiased bases.


2008 ◽  
Vol 8 (5) ◽  
pp. 386-398
Author(s):  
Y.-T. Chen ◽  
G. Bjork

We address the problem of generation and detection of the four mutually unbiased biphoton polarization-qutrit bases by linear optics. First, the generation of the bases is studied. Our numeric results show that the linear optics method can be used to generate the 4 mutually unbiased basis qutrit states probabilistically with high fidelity. Second, we investigate whether or not linear polarization-optics components are sufficient to realize the simultaneous detection of the qutrit states forming a complete basis. Analytical results show that every state in two of the bases, namely only half of the 4 mutually unbiased bases qutrit states can be identified.


Sign in / Sign up

Export Citation Format

Share Document