https://en.formulasearchengine.com/index.php?action=history&feed=atom&title=Spatial_multiplexing 2026-05-13T11:01:58Z Revision history for this page on the wiki MediaWiki 1.43.0-wmf.28 https://en.formulasearchengine.com/index.php?title=Spatial_multiplexing&diff=15546&oldid=prev 2013-09-25T16:00:36Z

<p>dl</p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 18:00, 25 September 2013</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</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><del style="font-weight: bold; text-decoration: none;">Greetings</del>. <del style="font-weight: bold; text-decoration: none;">Allow me start by telling you </del>the <del style="font-weight: bold; text-decoration: none;">writer's name </del>- <del style="font-weight: bold; text-decoration: none;">Phebe. Hiring has been my profession for </del>some <del style="font-weight: bold; text-decoration: none;">time but I've already applied for an additional 1. My family lives in Minnesota </del>and <del style="font-weight: bold; text-decoration: none;">my family members enjoys it</del>. <del style="font-weight: bold; text-decoration: none;">Doing ceramics </del>is <del style="font-weight: bold; text-decoration: none;">what her family </del>and <del style="font-weight: bold; text-decoration: none;">her appreciate.</del>&lt;<del style="font-weight: bold; text-decoration: none;">br</del>&gt;&lt;<del style="font-weight: bold; text-decoration: none;">br</del>&gt;<del style="font-weight: bold; text-decoration: none;">Also visit my web site - </del>[<del style="font-weight: bold; text-decoration: none;">http</del>://<del style="font-weight: bold; text-decoration: none;">Lankaclipstv</del>.<del style="font-weight: bold; text-decoration: none;">com</del>/<del style="font-weight: bold; text-decoration: none;">blog</del>/<del style="font-weight: bold; text-decoration: none;">165665 Lankaclipstv</del>.<del style="font-weight: bold; text-decoration: none;">com</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><ins style="font-weight: bold; text-decoration: none;">{{multiple issues|</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">{{Unreferenced|date=July 2009}}</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">{{Notability|date=August 2009}}</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">}}</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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> </div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">In [[mathematics]], the '''quantum Markov chain''' is a reformulation of the ideas of a classical [[Markov chain]], replacing the classical definitions of probability with [[quantum probability]]</ins>. <ins style="font-weight: bold; text-decoration: none;">Very roughly, </ins>the <ins style="font-weight: bold; text-decoration: none;">theory of a quantum Markov chain resembles that of a [[Quantum_finite_automaton#Measure-many_automata|measure</ins>-<ins style="font-weight: bold; text-decoration: none;">many automata]], with </ins>some <ins style="font-weight: bold; text-decoration: none;">important substitutions: the initial state is to be replaced by a [[density matrix]], </ins>and <ins style="font-weight: bold; text-decoration: none;">the projection operators are to be replaced by [[POVM|positive operator valued measures]]</ins>.</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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> </div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">More precisely, a quantum Markov chain </ins>is <ins style="font-weight: bold; text-decoration: none;">a pair &lt;math&gt;(E,\rho)&lt;/math&gt; with &lt;math&gt;\rho&lt;/math&gt; a [[density matrix]] </ins>and &lt;<ins style="font-weight: bold; text-decoration: none;">math</ins>&gt;<ins style="font-weight: bold; text-decoration: none;">E</ins>&lt;<ins style="font-weight: bold; text-decoration: none;">/math</ins>&gt; <ins style="font-weight: bold; text-decoration: none;">a [</ins>[<ins style="font-weight: bold; text-decoration: none;">quantum channel]] such that</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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> </div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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>:<ins style="font-weight: bold; text-decoration: none;">&lt;math&gt;E:\mathcal{B}\otimes\mathcal{B}\to\mathcal{B}&lt;</ins>/<ins style="font-weight: bold; text-decoration: none;">math&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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> </div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">is a [[completely positive trace-preserving]] map, and &lt;math&gt;\mathcal{B}&lt;/math&gt; a [[C-star algebra|C&lt;sup&gt;*&lt;</ins>/<ins style="font-weight: bold; text-decoration: none;">sup&gt;-algebra]] of bounded operators</ins>. <ins style="font-weight: bold; text-decoration: none;">The pair must obey the quantum Markov condition, that</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;"> </ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">:&lt;math&gt;\operatorname{Tr} \rho (b_1\otimes b_2) = \operatorname{Tr} \rho E(b_1, b_2)&lt;</ins>/<ins style="font-weight: bold; text-decoration: none;">math&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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> </div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">for all &lt;math&gt;b_1,b_2\in \mathcal{B}&lt;</ins>/<ins style="font-weight: bold; text-decoration: none;">math&gt;</ins>.</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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> </div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">{{DEFAULTSORT:Quantum Markov Chain}}</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">[[Category:Exotic probabilities]]</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">[[Category:Quantum information science]]</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">[[Category:Markov models]</ins>]</div></td></tr> </table>

en>Nikkimaria https://en.formulasearchengine.com/index.php?title=Spatial_multiplexing&diff=251537&oldid=prev 2012-07-22T01:58:50Z

<p><span class="autocomment">History</span></p> <p><b>New page</b></p><div>Greetings. Allow me start by telling you the writer&#039;s name - Phebe. Hiring has been my profession for some time but I&#039;ve already applied for an additional 1. My family lives in Minnesota and my family members enjoys it. Doing ceramics is what her family and her appreciate.&lt;br&gt;&lt;br&gt;Also visit my web site - [http://Lankaclipstv.com/blog/165665 Lankaclipstv.com]</div>

en>Jamessungjin.kim