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<div class="closed-captions"></div>
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var rb = String.fromCharCode(62);
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html += "contribute transcript fix" + mke("/a") + mke("/span");
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vblock.after(html)
}
$('#' + ftid).click(function(){
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var cindex = Number(cst.data('index'));
var gurl;
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gurl += mfnpre + ".txt#L" + String(cindex + 10 + 1);
console.log("going to ", gurl);
window.open(gurl, "MITx 8.370x subtitle source");
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try{
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<div class="video-player-pre"></div>
<div class="video-player">
<div id="M1L2e"></div>
<h4 class="hd hd-4 video-error is-hidden">No playable video sources found.</h4>
<h4 class="hd hd-4 video-hls-error is-hidden">
Your browser does not support this video format. Try using a different browser.
</h4>
</div>
<div class="video-player-post"></div>
<div class="closed-captions"></div>
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<h2 class="hd hd-2 unit-title">CQ: Isometries and quantum operations</h2>
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Isometries and quantum operations
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<p>
This is a concept question, provided to check your understanding of the previous video clip. </p>
<p>
Based on the lecture by Prof. Harrow, and what you know about quantum mechanics, which of the following equations could possibly be true for <em>some</em> choice of isometry [mathjaxinline]V[/mathjaxinline] and <em>all</em> possible quantum states [mathjaxinline]|\psi \rangle[/mathjaxinline] or [mathjaxinline]\rho[/mathjaxinline]? </p>
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<text>[mathjaxinline]V|\psi \rangle = |\psi \rangle \otimes |0\rangle[/mathjaxinline]</text>
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<text>[mathjaxinline]V|\psi \rangle = |\psi \rangle \otimes |\psi \rangle[/mathjaxinline]</text>
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<text>[mathjaxinline]V|\psi \rangle = |0 \rangle[/mathjaxinline]</text>
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<text>[mathjaxinline]V\rho V^\dagger = -\rho[/mathjaxinline]</text>
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<text>[mathjaxinline]V\rho V^\dagger = I[/mathjaxinline]</text>
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<text>[mathjaxinline]V\rho V^\dagger = \rho \otimes |0\rangle \langle 0|[/mathjaxinline]</text>
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<h2 class="hd hd-2 unit-title">Composition of quantum operations</h2>
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<h2 class="hd hd-2 unit-title">CQ: Kraus operator form of quantum operations</h2>
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Kraus operator form of quantum operations
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<p>
This is a concept question, provided to check your understanding of the previous video clip. </p>
<p>
Suppose [mathjaxinline]\{ E_1,\ldots ,E_ n \}[/mathjaxinline] is a complete set of [mathjaxinline]n[/mathjaxinline] Kraus operators (also known as <em>operation elements</em>) which define a <a href="https://en.wikipedia.org/wiki/Quantum_operation" target="_blank">quantum operation</a> [mathjaxinline]{\cal E}[/mathjaxinline]. Which of the following statements about these operators must be true? </p>
<p>
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<text>[mathjaxinline]\sum _ k E_ k \rho E_ k^\dagger[/mathjaxinline] is a valid density matrix, for all valid density matrices [mathjaxinline]\rho[/mathjaxinline].</text>
</label>
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<text>[mathjaxinline]\sum _ k E^\dagger _ k E_ k^\dagger = 0[/mathjaxinline]</text>
</label>
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<text>[mathjaxinline]\sum _ k E_ k^\dagger E_ k = I[/mathjaxinline]</text>
</label>
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<text>There exists a set of unitary operators [mathjaxinline]\{ U_ k\}[/mathjaxinline] and a probability distribution [mathjaxinline]\{ p_ k\}[/mathjaxinline] such that [mathjaxinline]E_ k = \sqrt{p_ k} U_ k[/mathjaxinline].</text>
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<h4 class="hd hd-4 video-hls-error is-hidden">
Your browser does not support this video format. Try using a different browser.
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</div>
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<div class="closed-captions"></div>
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var rb = String.fromCharCode(62);
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if (!$('#' + ftid).length){
var html = lb + "span id='" + ftid + "' style='float:right'" + rb + lb + "a href='#'" + rb;
html += "contribute transcript fix" + mke("/a") + mke("/span");
console.log("html = ", html);
vblock.after(html)
}
$('#' + ftid).click(function(){
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var cindex = Number(cst.data('index'));
var gurl;
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gurl += mfnpre + ".txt#L" + String(cindex + 10 + 1);
console.log("going to ", gurl);
window.open(gurl, "MITx 8.370x subtitle source");
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try{
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setTimeout(function(){ $('.math' + rb + 'span').css("border-left-color","transparent"); }, 8000);
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<div class="video-player">
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<h4 class="hd hd-4 video-hls-error is-hidden">
Your browser does not support this video format. Try using a different browser.
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</div>
<div class="video-player-post"></div>
<div class="closed-captions"></div>
<div class="video-controls is-hidden">
<div>
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<h2 class="hd hd-2 unit-title">CQ: Measurements and quantum operations</h2>
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Measurements and quantum operations
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<p>
This is a concept question, provided to check your understanding of the previous video clip. </p>
<p>
Which of the following statements are true, regarding quantum operations, and quantum measurements (specifically, complete <a href="https://en.wikipedia.org/wiki/POVM" target="_blank">positive operator-valued measures</a>, otherwise known as POVMs)? </p>
<p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_M1L2-cq-qop-meas_2_1">
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<text>If [mathjaxinline]\{ E_ k\}[/mathjaxinline] are the Kraus operators for a quantum operation, then [mathjaxinline]M_ k = E_ k^\dagger E_ k[/mathjaxinline] are well-defined corresponding POVM operators.</text>
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<text>If [mathjaxinline]\{ E_ k\}[/mathjaxinline] are the Kraus operators for a quantum operation, then [mathjaxinline]M_ k = E_ k[/mathjaxinline] are well-defined corresponding POVM operators.</text>
</label>
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<text>If [mathjaxinline]\{ M_ k\}[/mathjaxinline] are well-defined POVM operators, then [mathjaxinline]\sum _ k M_ k^\dagger M_ k = I[/mathjaxinline].</text>
</label>
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<text>If [mathjaxinline]\{ M_ k\}[/mathjaxinline] are well-defined POVM operators, then [mathjaxinline]\sum _ k M_ k = I[/mathjaxinline].</text>
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<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_M1L2-cq-qop-meas" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_M1L2-cq-qop-meas">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
</div>
</div>
<div class="problem-action-buttons-wrapper">
<span class="problem-action-button-wrapper">
<button type="button" class="save problem-action-btn btn-default btn-small" data-value="Save">
<span class="icon fa fa-floppy-o" aria-hidden="true"></span>
<span aria-hidden="true">Save</span>
<span class="sr">Save your answer</span>
</button>
</span>
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is-hidden"
tabindex="-1">
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<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
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<div class="notification warning notification-save
is-hidden"
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data-graded="True">
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</div>
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</div>
<div class="vert vert-1" data-id="block-v1:MITx+8.371.1x+2T2018+type@html+block@html_site_search_box3">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-runtime-class="LmsRuntime" data-usage-id="block-v1:MITx+8.371.1x+2T2018+type@html+block@html_site_search_box3" data-init="XBlockToXModuleShim" data-runtime-version="1" data-course-id="course-v1:MITx+8.371.1x+2T2018" data-block-type="html" data-has-score="False" data-graded="True" data-request-token="1f1aea20fe3111ee9b7e16fff75c5923">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<span><a href="/asset-v1:MITx+8.371.1x+2T2018+type@asset+block/NONE" id="dummy_course_static_link" style="display:none"/><a href="/courses/course-v1:MITx+8.371.1x+2T2018/jump_to_id/NONE" id="dummy_jump_link" style="display:none"/><script type="text/javascript">
var add_site_search = function(){
course_static_url = $('#dummy_course_static_link').attr('href').replace('/NONE', '');
jump_to_url = $('#dummy_jump_link').attr('href').replace('/NONE', '');
if (typeof String.prototype.startsWith != 'function') {
// see below for better implementation!
String.prototype.startsWith = function (str){
return this.indexOf(str) === 0;
};
}
if(typeof(String.prototype.trim) === "undefined")
{
String.prototype.trim = function()
{
return String(this).replace(/^\s+|\s+$/g, '');
};
}
var lb = String.fromCharCode(60);
var rb = String.fromCharCode(62);
var amp = String.fromCharCode(38);
var rlb = rb + lb;
var mke = function(x){ return lb + x + rb; }
var search_module_url = "";
var get_search_module_ficus = function(){
var cid = $('div.xblock').data('course-id');
if (cid){
console.log("cid = ", cid);
// search_module_url = "/courses/course-v1:MITx+8.371.1x+2T2018/" + cid + "/courseware/welcome/Search_this_course/";
search_module_url = "/courses/course-v1:MITx+8.371.1x+2T2018/courseware/welcome/Search_this_course/"; // automatically rewritten
console.log("3. search_module_url = ", search_module_url);
return;
}
var course_root_link = $('span.nav-item-course').find('a').attr('href');
if (course_root_link){
console.log("course_root_link = ", course_root_link);
search_module_url = course_root_link.replace("course/", "courseware/welcome/Search_this_course/");
console.log("2. search_module_url = ", search_module_url);
return
}
console.log("cannot determine search module url");
}
var get_search_module = function(){
// find search this module link
if (!($('div.course-index').length)){
return get_search_module_ficus();
}
$('div.course-index').find('nav').find('a').each(function(){
if ($(this).text().trim().startsWith("Search this course")){
search_module_url = $(this).attr('href');
console.log("search_module_url = ", search_module_url);
}
});
}
var go_to_search = function(){
get_search_module();
var sterm = $('#site-search-box').val();
// new_url = jump_to_url + "/Search_this_module/?q=" + sterm;
new_url = search_module_url + "?q=" + sterm;
console.log("sterm = ", sterm, " ; going to ", new_url);
window.location.href = new_url;
}
if (!$('#site-search-box').length){
$("nav.courseware").find("ol").append(lb + "section style='float:right'" + rlb + "input size='20'"
+ " id='site-search-box'"
+ rlb + "img src='" + course_static_url
+ "/images_search_glass.png'/" + rlb + "/input" + rlb + "/section" + rb);
}
$("#site-search-box").keypress(function(event) {
if (event.which == 13) {
event.preventDefault();
go_to_search();
}
});
// $('#site-search-box').bind("enterKey", go_to_search);
var get = function(x){
return eval(x);
}
return {'course_static_url': course_static_url,
'jump_to_url': jump_to_url,
'go_to_search': go_to_search,
'get_search_module': get_search_module,
'get_search_module_ficus': get_search_module_ficus,
'get': get,
}
}
var the_site_search = add_site_search();
var add_fix_transcript = function(){
if ($('div.wrap-instructor-info').length==0){
return;
}
$('div.xblock-student_view-video').each(function(key, vblock_e){
var vblock = $(vblock_e);
var vuid = vblock.data('usage-id').split('@');
var vid;
if (vuid.length==1){
vuid = vblock.data('usage-id').split(';_')
vid = vuid[5];
}else{
vid = vuid[2];
}
var mfnpre = vid.split("_video",1)[0];
var mfnid = mfnpre; // no periods
mfnpre = mfnpre.replace('8_370', '8.370'); // periods in gh filename
var lb = String.fromCharCode(60);
var rb = String.fromCharCode(62);
var mke = function(x){ return lb + x + rb; }
var ftid = "fix_transcript_" + mfnid;
if (!$('#' + ftid).length){
var html = lb + "span id='" + ftid + "' style='float:right'" + rb + lb + "a href='#'" + rb;
html += "contribute transcript fix" + mke("/a") + mke("/span");
console.log("html = ", html);
vblock.after(html)
}
$('#' + ftid).click(function(){
var cst = $('ol.subtitles').find('li.current');
var cindex = Number(cst.data('index'));
var gurl;
if (mfnpre.endsWith('_cq_sol')){
gurl = "https://github.com/mitocw/content-mit-8370x-cq-sol-subtitles/blob/master/";
}else{
gurl = "https://github.com/mitocw/content-mit-8370x-subtitles/blob/master/";
}
gurl += mfnpre + ".txt#L" + String(cindex + 10 + 1);
console.log("going to ", gurl);
window.open(gurl, "MITx 8.370x subtitle source");
});
});
}
try{
add_fix_transcript();
}
catch(err){
console.log(err);
}
try{
var rb = String.fromCharCode(62);
setTimeout(function(){ $('.math' + rb + 'span').css("border-left-color","transparent"); }, 3000);
setTimeout(function(){ $('.math' + rb + 'span').css("border-left-color","transparent"); }, 8000);
}
catch(err){
console.log(err);
}
</script></span>
</div>
</div>
</div>
</div>
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