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BellInequalityMaxQubits - Revision history
2026-09-15T16:09:06Z
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Rmmateri at 16:38, 13 June 2018
2018-06-13T16:38:29Z
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<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>|req=[http://cvxr.com/cvx/ <del style="font-weight: bold; text-decoration: none;">cvx</del>]</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>|req=[http://cvxr.com/cvx/ <ins style="font-weight: bold; text-decoration: none;">CVX</ins>]</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|cat=[[List of functions#Nonlocality_and_Bell_inequalities|Nonlocality and Bell inequalities]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|cat=[[List of functions#Nonlocality_and_Bell_inequalities|Nonlocality and Bell inequalities]]</div></td></tr>
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Rmmateri
https://qetlab.com/wiki/index.php?title=BellInequalityMaxQubits&diff=794&oldid=prev
Nathaniel: /* Examples */
2015-04-13T19:13:41Z
<p><span class="autocomment">Examples</span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 19:13, 13 April 2015</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>It is worth taking a look <del style="font-weight: bold; text-decoration: none;">at the examples </del>at the $I_{3322}$ example at the <tt>[[BellInequalityMax]]</tt> page to compare the computations provided there.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>It is worth taking a look at the $I_{3322}$ example at the <tt>[[BellInequalityMax]]</tt> page to compare the computations provided there.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{SourceCode|name=BellInequalityMaxQubits}}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{SourceCode|name=BellInequalityMaxQubits}}</div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==References==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==References==</div></td></tr>
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Nathaniel
https://qetlab.com/wiki/index.php?title=BellInequalityMaxQubits&diff=793&oldid=prev
Nathaniel: Created page with "{{Function |name=BellInequalityMaxQubits |desc=Approximates the optimal value of a Bell inequality in qubit (i.e., 2-dimensional quantum) settings |rel=BellInequalityMax<b..."
2015-04-13T19:13:06Z
<p>Created page with "{{Function |name=BellInequalityMaxQubits |desc=Approximates the optimal value of a Bell inequality in qubit (i.e., 2-dimensional quantum) settings |rel=<a href="/BellInequalityMax" title="BellInequalityMax">BellInequalityMax</a><b..."</p>
<p><b>New page</b></p><div>{{Function<br />
|name=BellInequalityMaxQubits<br />
|desc=Approximates the optimal value of a Bell inequality in qubit (i.e., 2-dimensional quantum) settings<br />
|rel=[[BellInequalityMax]]<br />[[NonlocalGameValue]]<br />[[XORGameValue]]<br />
|req=[http://cvxr.com/cvx/ cvx]<br />
|cat=[[List of functions#Nonlocality_and_Bell_inequalities|Nonlocality and Bell inequalities]]<br />
|cvx=no}}<br />
<tt>'''BellInequalityMaxQubits'''</tt> is a [[List of functions|function]] that computes an upper bound for the maximum possible value of a given [http://en.wikipedia.org/wiki/Bell%27s_theorem Bell inequality] in a quantum mechanical setting where the two parties each have access to qubits (i.e., 2-dimensional quantum systems). This bound is computed using the method presented in <ref name="NTV14">M. Navascués, G. de la Torre, and T. Vértesi. Characterization of quantum correlations with local dimension constraints and its device-independent applications. <em>Phys. Rev. X</em>, 4:011011, 2014. E-print: [http://arxiv.org/abs/1308.3410 arXiv:1308.3410] [quant-ph]</ref>.<br />
<br />
==Syntax==<br />
* <tt>BMAX = BellInequalityMaxQubits(JOINT_COE,A_COE,B_COE,A_VAL,B_VAL)</tt><br />
* <tt>[BMAX,RHO] = BellInequalityMaxQubits(JOINT_COE,A_COE,B_COE,A_VAL,B_VAL)</tt><br />
<br />
==Argument descriptions==<br />
===Input arguments===<br />
* <tt>JOINT_COE</tt>: A matrix whose $(i,j)$-entry gives the coefficient of $\langle A_i B_j \rangle$ in the Bell inequality.<br />
* <tt>A_COE</tt>: A vector whose $i$-th entry gives the coefficient of $\langle A_i \rangle$ in the Bell inequality.<br />
* <tt>B_COE</tt>: A vector whose $i$-th entry gives the coefficient of $\langle B_i \rangle$ in the Bell inequality.<br />
* <tt>A_VAL</tt>: A vector whose $i$-th entry gives the value of the $i$-th measurement result on Alice's side.<br />
* <tt>B_VAL</tt>: A vector whose $i$-th entry gives the value of the $i$-th measurement result on Bob's side.<br />
<br />
===Output arguments===<br />
* <tt>BMAX</tt>: An upper bound on the qubit value of the Bell inequality.<br />
* <tt>RHO</tt>: A many-qubit quantum state that acts as a witness that verifies the bound provided by <tt>BMAX</tt>. This is the positive-partial-transpose (PPT) state described by <ref name="NTV14"></ref>.<br />
<br />
==Examples==<br />
===The I<sub>3322</sub> inequality===<br />
The I<sub>3322</sub> inequality<ref>M. Froissart. Constructive generalization of Bell's inequalities. <em>Nuov. Cim. B</em>, 64:241, 1981</ref><ref>D. Collins and N. Gisin. A relevant two qubit Bell inequality inequivalent to the CHSH inequality. J. Phys. A: Math. Gen., 37(5):1175, 2004. E-print: [http://arxiv.org/abs/quant-ph/0306129 arXiv:quant-ph/0306129]</ref> is a Bell inequality that says that if $\{A_1,A_2,A_3\}$ and $\{B_1,B_2,B_3\}$ are $\{0,1\}$-valued measurement settings, then in classical physics the following inequality holds:<br />
: <math>\langle A_1 B_1 \rangle + \langle A_1 B_2 \rangle - \langle A_1 B_3 \rangle + \langle A_2 B_1 \rangle + \langle A_2 B_2 \rangle + \langle A_2 B_3 \rangle - \langle A_3 B_1 \rangle + \langle A_3 B_2 \rangle - \langle A_2 \rangle - \langle B_1 \rangle - 2\langle B_2 \rangle \leq 0.</math><br />
It is straightforward to check that a 2-qubit maximally-entangled Bell state allows for a value of $1/4$ in this Bell inequality. The following code verifies that it is not possible to get a value of larger than $1/4$ using $2$-dimensional systems:<br />
<syntaxhighlight><br />
>> BellInequalityMaxQubits([1 1 -1;1 1 1;-1 1 0], [0 -1 0], [-1 -2 0], [0 1], [0 1])<br />
<br />
ans =<br />
<br />
0.2500<br />
</syntaxhighlight><br />
<br />
It is worth taking a look at the examples at the $I_{3322}$ example at the <tt>[[BellInequalityMax]]</tt> page to compare the computations provided there.<br />
{{SourceCode|name=BellInequalityMaxQubits}}<br />
<br />
==References==<br />
<references /></div>
Nathaniel