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<p>Consider a one-dimensional spin chain, from spin 1 to spin <i>N</i>, such that each spin interacts with its nearest neighbors. Performing a local operation (measurement) on spin <i>N</i>, we expect from the Lieb–Robinson velocity that, in general, the effect of this measurement achieves spin 1 after some while. But, in this paper, we show that if (a) the measurement on spin <i>N</i> is performed instantaneously and (b) the initial state of the spin chain is chosen appropriately, then the effect of the measurement on spin <i>N</i> never achieves spin 1. In other words, performing or not performing an instantaneous measurement on spin <i>N</i> at <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4708_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="38" /> </InlineMediaObject> <EquationSource Format="TEX">\(t=0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>t</mi> <mo>=</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation> does not alter the reduced dynamics of spin 1 for all the times <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4708_Article_IEq2.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="39" /> </InlineMediaObject> <EquationSource Format="TEX">\(t\ge 0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>t</mi> <mo>≥</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>. We can interpret this as the following: The information of performing an instantaneous measurement on spin <i>N</i> is isolated such that it cannot achieve spin 1.</p>

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Instantaneous measurement can isolate the information

  • 期刊论文

  • 发表日期：

    2025年3月19日

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  • Iman Sargolzahi

摘要

Consider a one-dimensional spin chain, from spin 1 to spin N, such that each spin interacts with its nearest neighbors. Performing a local operation (measurement) on spin N, we expect from the Lieb–Robinson velocity that, in general, the effect of this measurement achieves spin 1 after some while. But, in this paper, we show that if (a) the measurement on spin N is performed instantaneously and (b) the initial state of the spin chain is chosen appropriately, then the effect of the measurement on spin N never achieves spin 1. In other words, performing or not performing an instantaneous measurement on spin N at \(t=0\) t = 0 does not alter the reduced dynamics of spin 1 for all the times \(t\ge 0\) t ≥ 0 . We can interpret this as the following: The information of performing an instantaneous measurement on spin N is isolated such that it cannot achieve spin 1.