Quantum Frequency Arrangements, Quantum Mixed Orthogonal Arrays and Entangled States

Pang, Shanqi; Zhang, Ruining; Xiao, Zhili

doi:10.1587/transfun.2020eal2007

Cited by 6 publications

(4 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Now we give a definition of mutually orthogonal quantum Latin cubes, which differs from the one given in [18] by adding a condition similar to property (B), and is analogous to Definition 11 of m triplewise orthogonal quantum frequency cubes in Ref. [37]. This will establish a direct link of this notion with that of a quantum orthogonal array in Definition 4.1.…”

Section: Quantum Latin Cubesmentioning

confidence: 99%

Quantum combinatorial designs and $k$-uniform states

Zang,

Facchi,

Tian

2021

Preprint

View full text Add to dashboard Cite

Goyeneche et al. [Phys. Rev. A 97, 062326 (2018)] introduced several classes of quantum combinatorial designs, namely quantum Latin squares, quantum Latin cubes, and the notion of orthogonality on them. They also showed that mutually orthogonal quantum Latin arrangements can be entangled in the same way in which quantum states are entangled. Moreover, they established a relationship between quantum combinatorial designs and a remarkable class of entangled states called k-uniform states, i.e., multipartite pure states such that every reduction to k parties is maximally mixed. In this article, we put forward the notions of incomplete quantum Latin squares and orthogonality on them and present construction methods for mutually orthogonal quantum Latin squares and mutually orthogonal quantum Latin cubes. Furthermore, we introduce the notions of generalized mutually orthogonal quantum Latin squares and generalized mutually orthogonal quantum Latin cubes, which are equivalent to quantum orthogonal arrays of size d 2 and d 3 , respectively, and thus naturally provide 2-and 3-uniform states.2000 Mathematics Subject Classification.

show abstract

Section: Quantum Latin Cubesmentioning

confidence: 99%

Quantum combinatorial designs and $k$-uniform states

Zang,

Facchi,

Tian

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Now we give a definition of mutually orthogonal quantum Latin cubes, which differs from the one given in [17] by adding a condition similar to property (B), and is analogous to definition 11 of m triplewise orthogonal quantum frequency cubes in reference [36]. This will establish a direct link of this notion with that of a quantum orthogonal array in definition 4.1.…”

Section: Lemma 35 If φ Is a Classical Quantum Latin Cube Of Dimension...mentioning

confidence: 99%

Quantum combinatorial designs and k-uniform states

Zang¹,

Facchi²,

Tian³

2021

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

Goyeneche et al.\ [Phys.\ Rev.\ A \textbf{97}, 062326 (2018)] introduced several classes of quantum combinatorial designs, namely quantum Latin squares, quantum Latin cubes, and the notion of orthogonality on them. They also showed that mutually orthogonal quantum Latin arrangements can be entangled in the same way in which quantum states are entangled. Moreover, they established a relationship between quantum combinatorial designs and a remarkable class of entangled states called $k$-uniform states, i.e., multipartite pure states such that every reduction to $k$ parties is maximally mixed. In this article, we put forward the notions of incomplete quantum Latin squares and orthogonality on them and present construction methods for mutually orthogonal quantum Latin squares and mutually orthogonal quantum Latin cubes. Furthermore, we introduce the notions of generalized mutually orthogonal quantum Latin squares and generalized mutually orthogonal quantum Latin cubes, which are equivalent to quantum orthogonal arrays of size $d^2$ and $d^3$, respectively, and thus naturally provide $2$- and $3$-uniform states.

show abstract

“…Orthogonal arrays (OAs) play a more and more important role in quantum information theory [ 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 ]. An

array A with entries from a set

is said to be an orthogonal array with s levels, strength t (for some t in the range

if every

subarray of A contains each t -tuple based on S as a row with the same frequency.…”

Section: Introductionmentioning

confidence: 99%

“…Orthogonal arrays (OAs) play a more and more important role in quantum information theory [15][16][17][18][19][20][21][22]. An r × N array A with entries from a set S = {0, 1, .…”

Section: Introductionmentioning

confidence: 99%

Construction of Binary Quantum Error-Correcting Codes from Orthogonal Array

Pang

Xu²,

Chen³

2022

Entropy

Self Cite

View full text Add to dashboard Cite

By using difference schemes, orthogonal partitions and a replacement method, some new methods to construct pure quantum error-correcting codes are provided from orthogonal arrays. As an application of these methods, we construct several infinite series of quantum error-correcting codes including some optimal ones. Compared with the existing binary quantum codes, more new codes can be constructed, which have a lower number of terms (i.e., the number of computational basis states) for each of their basis states.

show abstract

Quantum Frequency Arrangements, Quantum Mixed Orthogonal Arrays and Entangled States

Cited by 6 publications

References 20 publications

Quantum combinatorial designs and $k$-uniform states

Quantum combinatorial designs and $k$-uniform states

Quantum combinatorial designs and k-uniform states

Construction of Binary Quantum Error-Correcting Codes from Orthogonal Array

Contact Info

Product

Resources

About