<p>We propose the scheme realizing the two-level control over the unitary operators <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4677_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(U_k\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>U</mi> <mi>k</mi> </msub> </math></EquationSource> </InlineEquation> creating the required quantum state of the system <i>S</i>. These operators are controlled by the superposition state of the auxiliary subsystem <i>R</i> which is governed by two control centers. The first-level control center (main control) creates the equal-probability pure state of <i>R</i> with certain distribution of phase factors that, in turn, govern the power of the second-level control center <i>C</i> that applies the special <i>V</i>-operators to the same subsystem <i>R</i> changing its state and thus controlling the applicability of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4677_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(U_k\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>U</mi> <mi>k</mi> </msub> </math></EquationSource> </InlineEquation>. In addition, the above phases are responsible for the entanglement in the subsystem <i>R</i>. We find the direct relation between this entanglement and the number of operators <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4677_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(U_k\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>U</mi> <mi>k</mi> </msub> </math></EquationSource> </InlineEquation> that can be controlled by <i>C</i>. The simple example of a two-level control system governing the creation of entangled state of the two-qubit system <i>S</i> is presented.</p>

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Two-level control over quantum state creation via entangled equal-probability state

  • S. I. Doronin,
  • E. B. Fel’dman,
  • A. I. Zenchuk

摘要

We propose the scheme realizing the two-level control over the unitary operators \(U_k\) U k creating the required quantum state of the system S. These operators are controlled by the superposition state of the auxiliary subsystem R which is governed by two control centers. The first-level control center (main control) creates the equal-probability pure state of R with certain distribution of phase factors that, in turn, govern the power of the second-level control center C that applies the special V-operators to the same subsystem R changing its state and thus controlling the applicability of \(U_k\) U k . In addition, the above phases are responsible for the entanglement in the subsystem R. We find the direct relation between this entanglement and the number of operators \(U_k\) U k that can be controlled by C. The simple example of a two-level control system governing the creation of entangled state of the two-qubit system S is presented.