Jump to navigation Jump to search

General

Display information for equation id:math.238502.9 on revision:238502

* Page found: No-communication theorem (eq math.238502.9)

(force rerendering)

Cannot find the equation data in the database. Fetching from revision text.

Occurrences on the following pages:

Hash: f11ec3494e6006ffe40c5b113d476613

TeX (original user input):

 = \operatorname{tr}_{H_A} \left(\sum_k \sum_i V_k^* T_i V_k \otimes S_i \right)

TeX (checked):

=\operatorname {tr} _{H_{A}}\left(\sum _{k}\sum _{i}V_{k}^{*}T_{i}V_{k}\otimes S_{i}\right)

LaTeXML (experimental; uses MathML) rendering

MathML (7.817 KB / 1.2 KB) :

= tr H A ( k i V k * T i V k S i ) absent subscript tr subscript H A subscript k subscript i tensor-product superscript subscript V k subscript T i subscript V k subscript S i {\displaystyle=\operatorname{tr}_{{H_{A}}}\left(\sum_{k}\sum_{i}V_{k}^{*}T_{i}% V_{k}\otimes S_{i}\right)}
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle=\operatorname{tr}_{{H_{A}}}\left(\sum_{k}\sum_{i}V_{k}^{*}T_{i}%&#10;V_{k}\otimes S_{i}\right)}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.21" xref="p1.1.m1.1.21.cmml">
      <mi id="p1.1.m1.1.21.1" xref="p1.1.m1.1.21.1.cmml"/>
      <mo id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">=</mo>
      <mrow id="p1.1.m1.1.21.2.2" xref="p1.1.m1.1.21.2.1.cmml">
        <msub id="p1.1.m1.1.21.2.2.1" xref="p1.1.m1.1.21.2.1.cmml">
          <mo id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">tr</mo>
          <msub id="p1.1.m1.1.4.1" xref="p1.1.m1.1.21.2.1.cmml">
            <mi id="p1.1.m1.1.4.1.1" xref="p1.1.m1.1.4.1.1.cmml">H</mi>
            <mi id="p1.1.m1.1.4.1.2.1" xref="p1.1.m1.1.4.1.2.1.cmml">A</mi>
          </msub>
        </msub>
        <mo id="p1.1.m1.1.21.2.2a" xref="p1.1.m1.1.21.2.1.cmml"></mo>
        <mrow id="p1.1.m1.1.21.2" xref="p1.1.m1.1.21.2.1.cmml">
          <mo id="p1.1.m1.1.5" xref="p1.1.m1.1.21.2.1.cmml">(</mo>
          <mrow id="p1.1.m1.1.21.2.2.2" xref="p1.1.m1.1.21.2.1.cmml">
            <mstyle displaystyle="true" id="p1.1.m1.1.21.2.2.2.1" xref="p1.1.m1.1.21.2.1.cmml">
              <munder id="p1.1.m1.1.21.2.2.2.1a" xref="p1.1.m1.1.21.2.1.cmml">
                <mo largeop="true" movablelimits="false" symmetric="true" id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml"></mo>
                <mi id="p1.1.m1.1.7.1" xref="p1.1.m1.1.7.1.cmml">k</mi>
              </munder>
            </mstyle>
            <mrow id="p1.1.m1.1.21.2.2.2.2" xref="p1.1.m1.1.21.2.1.cmml">
              <mstyle displaystyle="true" id="p1.1.m1.1.21.2.2.2.2.1" xref="p1.1.m1.1.21.2.1.cmml">
                <munder id="p1.1.m1.1.21.2.2.2.2.1a" xref="p1.1.m1.1.21.2.1.cmml">
                  <mo largeop="true" movablelimits="false" symmetric="true" id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml"></mo>
                  <mi id="p1.1.m1.1.9.1" xref="p1.1.m1.1.9.1.cmml">i</mi>
                </munder>
              </mstyle>
              <mrow id="p1.1.m1.1.21.2.2.2.2.2" xref="p1.1.m1.1.21.2.1.cmml">
                <mrow id="p1.1.m1.1.21.2.2.2.2.2.1" xref="p1.1.m1.1.21.2.1.cmml">
                  <msubsup id="p1.1.m1.1.21.2.2.2.2.2.1.2" xref="p1.1.m1.1.21.2.1.cmml">
                    <mi id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">V</mi>
                    <mi id="p1.1.m1.1.11.1" xref="p1.1.m1.1.11.1.cmml">k</mi>
                    <mo id="p1.1.m1.1.12.1" xref="p1.1.m1.1.12.1.cmml">*</mo>
                  </msubsup>
                  <mo id="p1.1.m1.1.21.2.2.2.2.2.1.1" xref="p1.1.m1.1.21.2.2.2.2.2.1.1.cmml"></mo>
                  <msub id="p1.1.m1.1.21.2.2.2.2.2.1.3" xref="p1.1.m1.1.21.2.1.cmml">
                    <mi id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">T</mi>
                    <mi id="p1.1.m1.1.14.1" xref="p1.1.m1.1.14.1.cmml">i</mi>
                  </msub>
                  <mo id="p1.1.m1.1.21.2.2.2.2.2.1.1a" xref="p1.1.m1.1.21.2.2.2.2.2.1.1.cmml"></mo>
                  <msub id="p1.1.m1.1.21.2.2.2.2.2.1.4" xref="p1.1.m1.1.21.2.1.cmml">
                    <mi id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">V</mi>
                    <mi id="p1.1.m1.1.16.1" xref="p1.1.m1.1.16.1.cmml">k</mi>
                  </msub>
                </mrow>
                <mo id="p1.1.m1.1.17" xref="p1.1.m1.1.17.cmml"></mo>
                <msub id="p1.1.m1.1.21.2.2.2.2.2.2" xref="p1.1.m1.1.21.2.1.cmml">
                  <mi id="p1.1.m1.1.18" xref="p1.1.m1.1.18.cmml">S</mi>
                  <mi id="p1.1.m1.1.19.1" xref="p1.1.m1.1.19.1.cmml">i</mi>
                </msub>
              </mrow>
            </mrow>
          </mrow>
          <mo id="p1.1.m1.1.20" xref="p1.1.m1.1.21.2.1.cmml">)</mo>
        </mrow>
      </mrow>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.21.cmml" xref="p1.1.m1.1.21">
        <eq id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1"/>
        <csymbol cd="latexml" id="p1.1.m1.1.21.1.cmml" xref="p1.1.m1.1.21.1">absent</csymbol>
        <apply id="p1.1.m1.1.21.2.1.cmml" xref="p1.1.m1.1.21.2.2">
          <apply id="p1.1.m1.1.21.2.2.1.cmml" xref="p1.1.m1.1.21.2.2">
            <csymbol cd="ambiguous" id="p1.1.m1.1.21.2.2.1.1.cmml">subscript</csymbol>
            <ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">tr</ci>
            <apply id="p1.1.m1.1.4.1.cmml" xref="p1.1.m1.1.21.2.2">
              <csymbol cd="ambiguous" id="p1.1.m1.1.4.1.3.cmml">subscript</csymbol>
              <ci id="p1.1.m1.1.4.1.1.cmml" xref="p1.1.m1.1.4.1.1">H</ci>
              <ci id="p1.1.m1.1.4.1.2.1.cmml" xref="p1.1.m1.1.4.1.2.1">A</ci>
            </apply>
          </apply>
          <apply id="p1.1.m1.1.21.2.2.2.cmml" xref="p1.1.m1.1.21.2.2">
            <apply id="p1.1.m1.1.21.2.2.2.1.cmml" xref="p1.1.m1.1.21.2.2">
              <csymbol cd="ambiguous" id="p1.1.m1.1.21.2.2.2.1.1.cmml">subscript</csymbol>
              <sum id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6"/>
              <ci id="p1.1.m1.1.7.1.cmml" xref="p1.1.m1.1.7.1">k</ci>
            </apply>
            <apply id="p1.1.m1.1.21.2.2.2.2.cmml" xref="p1.1.m1.1.21.2.2">
              <apply id="p1.1.m1.1.21.2.2.2.2.1.cmml" xref="p1.1.m1.1.21.2.2">
                <csymbol cd="ambiguous" id="p1.1.m1.1.21.2.2.2.2.1.1.cmml">subscript</csymbol>
                <sum id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8"/>
                <ci id="p1.1.m1.1.9.1.cmml" xref="p1.1.m1.1.9.1">i</ci>
              </apply>
              <apply id="p1.1.m1.1.21.2.2.2.2.2.cmml" xref="p1.1.m1.1.21.2.2">
                <csymbol cd="latexml" id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17">tensor-product</csymbol>
                <apply id="p1.1.m1.1.21.2.2.2.2.2.1.cmml" xref="p1.1.m1.1.21.2.2">
                  <times id="p1.1.m1.1.21.2.2.2.2.2.1.1.cmml" xref="p1.1.m1.1.21.2.2.2.2.2.1.1"/>
                  <apply id="p1.1.m1.1.21.2.2.2.2.2.1.2.cmml" xref="p1.1.m1.1.21.2.2">
                    <csymbol cd="ambiguous" id="p1.1.m1.1.21.2.2.2.2.2.1.2.1.cmml">superscript</csymbol>
                    <apply id="p1.1.m1.1.21.2.2.2.2.2.1.2.2.cmml" xref="p1.1.m1.1.21.2.2">
                      <csymbol cd="ambiguous" id="p1.1.m1.1.21.2.2.2.2.2.1.2.2.1.cmml">subscript</csymbol>
                      <ci id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">V</ci>
                      <ci id="p1.1.m1.1.11.1.cmml" xref="p1.1.m1.1.11.1">k</ci>
                    </apply>
                    <times id="p1.1.m1.1.12.1.cmml" xref="p1.1.m1.1.12.1"/>
                  </apply>
                  <apply id="p1.1.m1.1.21.2.2.2.2.2.1.3.cmml" xref="p1.1.m1.1.21.2.2">
                    <csymbol cd="ambiguous" id="p1.1.m1.1.21.2.2.2.2.2.1.3.1.cmml">subscript</csymbol>
                    <ci id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">T</ci>
                    <ci id="p1.1.m1.1.14.1.cmml" xref="p1.1.m1.1.14.1">i</ci>
                  </apply>
                  <apply id="p1.1.m1.1.21.2.2.2.2.2.1.4.cmml" xref="p1.1.m1.1.21.2.2">
                    <csymbol cd="ambiguous" id="p1.1.m1.1.21.2.2.2.2.2.1.4.1.cmml">subscript</csymbol>
                    <ci id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15">V</ci>
                    <ci id="p1.1.m1.1.16.1.cmml" xref="p1.1.m1.1.16.1">k</ci>
                  </apply>
                </apply>
                <apply id="p1.1.m1.1.21.2.2.2.2.2.2.cmml" xref="p1.1.m1.1.21.2.2">
                  <csymbol cd="ambiguous" id="p1.1.m1.1.21.2.2.2.2.2.2.1.cmml">subscript</csymbol>
                  <ci id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18">S</ci>
                  <ci id="p1.1.m1.1.19.1.cmml" xref="p1.1.m1.1.19.1">i</ci>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle=\operatorname{tr}_{{H_{A}}}\left(\sum_{k}\sum_{i}V_{k}^{*}T_{i}%
V_{k}\otimes S_{i}\right)}</annotation>
  </semantics>
</math>

SVG image empty. Force Re-Rendering

SVG (13.813 KB / 5.196 KB) :

equals trace Subscript upper H Sub Subscript upper A Baseline left-parenthesis sigma-summation Underscript k Endscripts sigma-summation Underscript i Endscripts upper V Subscript k Superscript asterisk Baseline times upper T Subscript i Baseline times upper V Subscript k Baseline circled-times upper S Subscript i Baseline right-parenthesis

MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools) rendering

MathML (0 B / 8 B) :

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :


PNG (0 B / 8 B) :


Translations to Computer Algebra Systems

Translation to Maple

In Maple:

[ERROR] java.lang.IllegalArgumentException: java.lang.ClassCastException@5246835d

Translation to Mathematica

In Mathematica:

[ERROR] java.lang.IllegalArgumentException: java.lang.ClassCastException@5246835d

Similar pages

Calculated based on the variables occurring on the entire No-communication theorem page

Identifiers

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results