State transfer has great significance due to its important applications in quantum information processing and quantum computing. The ability to transfer quantum states efficiently is critical for the development of quantum networks and various quantum algorithms. In this paper, we delve into the exploration of pretty good state transfer on Cayley graphs over <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="25_2025_2472_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="TEX">$U_{6n}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>U</mi> <mrow> <mn>6</mn> <mi>n</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> for <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="25_2025_2472_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="116" /> </InlineMediaObject> <EquationSource Format="TEX">$n = 2^r, n = 2^rp^t$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>=</mo> <msup> <mn>2</mn> <mi>r</mi> </msup> <mo>,</mo> <mi>n</mi> <mo>=</mo> <msup> <mn>2</mn> <mi>r</mi> </msup> <msup> <mi>p</mi> <mi>t</mi> </msup> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="25_2025_2472_Article_IEq5.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="59" /> </InlineMediaObject> <EquationSource Format="TEX">$n = mp$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>=</mo> <mi>m</mi> <mi>p</mi> </mrow> </math></EquationSource> </InlineEquation> (where m can be either odd or even and p is an odd prime number).

Pretty Good State Transfer on Cayley Graphs Associated with the $ U_{6n} $ Group

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发表日期：

2025年7月17日

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Majid Arezoomand,
Modjtaba Ghorbani,
Afsaneh Khalilipour

摘要

State transfer has great significance due to its important applications in quantum information processing and quantum computing. The ability to transfer quantum states efficiently is critical for the development of quantum networks and various quantum algorithms. In this paper, we delve into the exploration of pretty good state transfer on Cayley graphs over $U_{6n}$ $U_{6 n}$ for $n = 2^r, n = 2^rp^t$ $n = 2^{r}, n = 2^{r} p^{t}$ and $n = mp$ $n = m p$ (where m can be either odd or even and p is an odd prime number).

Pretty Good State Transfer on Cayley Graphs Associated with the \( U_{6n} \) Group

摘要