-
Notifications
You must be signed in to change notification settings - Fork 0
/
TheWorldofQuantum04.html
483 lines (407 loc) · 19.8 KB
/
TheWorldofQuantum04.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="generator" content="Docutils 0.17.1: http://docutils.sourceforge.net/" />
<title>5. Entanglement — World of Tech</title>
<link href="_static/css/theme.css" rel="stylesheet">
<link href="_static/css/index.ff1ffe594081f20da1ef19478df9384b.css" rel="stylesheet">
<link rel="stylesheet"
href="_static/vendor/fontawesome/5.13.0/css/all.min.css">
<link rel="preload" as="font" type="font/woff2" crossorigin
href="_static/vendor/fontawesome/5.13.0/webfonts/fa-solid-900.woff2">
<link rel="preload" as="font" type="font/woff2" crossorigin
href="_static/vendor/fontawesome/5.13.0/webfonts/fa-brands-400.woff2">
<link rel="stylesheet" type="text/css" href="_static/pygments.css" />
<link rel="stylesheet" type="text/css" href="_static/sphinx-book-theme.css?digest=c3fdc42140077d1ad13ad2f1588a4309" />
<link rel="stylesheet" type="text/css" href="_static/togglebutton.css" />
<link rel="stylesheet" type="text/css" href="_static/copybutton.css" />
<link rel="stylesheet" type="text/css" href="_static/mystnb.css" />
<link rel="stylesheet" type="text/css" href="_static/sphinx-thebe.css" />
<link rel="stylesheet" type="text/css" href="_static/panels-main.c949a650a448cc0ae9fd3441c0e17fb0.css" />
<link rel="stylesheet" type="text/css" href="_static/panels-variables.06eb56fa6e07937060861dad626602ad.css" />
<link rel="preload" as="script" href="_static/js/index.be7d3bbb2ef33a8344ce.js">
<script data-url_root="./" id="documentation_options" src="_static/documentation_options.js"></script>
<script src="_static/jquery.js"></script>
<script src="_static/underscore.js"></script>
<script src="_static/doctools.js"></script>
<script src="_static/clipboard.min.js"></script>
<script src="_static/copybutton.js"></script>
<script>let toggleHintShow = 'Click to show';</script>
<script>let toggleHintHide = 'Click to hide';</script>
<script>let toggleOpenOnPrint = 'true';</script>
<script src="_static/togglebutton.js"></script>
<script>var togglebuttonSelector = '.toggle, .admonition.dropdown, .tag_hide_input div.cell_input, .tag_hide-input div.cell_input, .tag_hide_output div.cell_output, .tag_hide-output div.cell_output, .tag_hide_cell.cell, .tag_hide-cell.cell';</script>
<script src="_static/sphinx-book-theme.d59cb220de22ca1c485ebbdc042f0030.js"></script>
<script>const THEBE_JS_URL = "https://unpkg.com/thebe@0.8.2/lib/index.js"
const thebe_selector = ".thebe,.cell"
const thebe_selector_input = "pre"
const thebe_selector_output = ".output, .cell_output"
</script>
<script async="async" src="_static/sphinx-thebe.js"></script>
<link rel="author" title="About these documents" href="about.html" />
<link rel="index" title="Index" href="genindex.html" />
<link rel="search" title="Search" href="search.html" />
<link rel="next" title="What is Quantum Computing?" href="QuantumComputing01.html" />
<link rel="prev" title="4. Wave-Function Collapse" href="TheWorldofQuantum05.html" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<meta name="docsearch:language" content="None">
<!-- Google Analytics -->
</head>
<body data-spy="scroll" data-target="#bd-toc-nav" data-offset="80">
<div class="container-fluid" id="banner"></div>
<div class="container-xl">
<div class="row">
<div class="col-12 col-md-3 bd-sidebar site-navigation show" id="site-navigation">
<div class="navbar-brand-box">
<a class="navbar-brand text-wrap" href="index.html">
<!-- `logo` is deprecated in Sphinx 4.0, so remove this when we stop supporting 3 -->
<img src="_static/logo.png" class="logo" alt="logo">
<h1 class="site-logo" id="site-title">World of Tech</h1>
</a>
</div><form class="bd-search d-flex align-items-center" action="search.html" method="get">
<i class="icon fas fa-search"></i>
<input type="search" class="form-control" name="q" id="search-input" placeholder="Search this book..." aria-label="Search this book..." autocomplete="off" >
</form><nav class="bd-links" id="bd-docs-nav" aria-label="Main">
<div class="bd-toc-item active">
<ul class="nav bd-sidenav">
<li class="toctree-l1">
<a class="reference internal" href="introqc.html">
The Quantum World
</a>
</li>
</ul>
<p aria-level="2" class="caption" role="heading">
<span class="caption-text">
Quantum vs. Classical
</span>
</p>
<ul class="current nav bd-sidenav">
<li class="toctree-l1">
<a class="reference internal" href="TheWorldofQuantum00.html">
<strong>
The Quantum vs. Classical World
</strong>
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="TheWorldofQuantum01.html">
1. Introduction to the Quantum World: A Video
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="TheWorldofQuantum02.html">
2. Wave-Particle Duality
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="TheWorldofQuantum03.html">
3. Superposition
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="TheWorldofQuantum05.html">
4. Wave-Function Collapse
</a>
</li>
<li class="toctree-l1 current active">
<a class="current reference internal" href="#">
5. Entanglement
</a>
</li>
</ul>
<p aria-level="2" class="caption" role="heading">
<span class="caption-text">
Quantum Computing
</span>
</p>
<ul class="nav bd-sidenav">
<li class="toctree-l1">
<a class="reference internal" href="QuantumComputing01.html">
<strong>
What is Quantum Computing?
</strong>
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="QuantumComputing01b.html">
<strong>
What is a Qubit?
</strong>
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="QuantumComputing02.html">
<strong>
How does Quantum Computing work?
</strong>
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="QuantumComputing02b.html">
<strong>
Types of Quantum Computers
</strong>
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="QuantumComputing03.html">
<strong>
Why is Quantum Computing important?
</strong>
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="quantum03.html">
<strong>
How to become a Quantum Scientist
</strong>
</a>
</li>
</ul>
<p aria-level="2" class="caption" role="heading">
<span class="caption-text">
Quantum Programming
</span>
</p>
<ul class="nav bd-sidenav">
<li class="toctree-l1">
<a class="reference internal" href="Tutorial00.html">
<strong>
An Introduction to Quantum Programming
</strong>
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="Tutorial01.html">
Tutorial A : Single Qubit Operations and Visualization of the Qubit State
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="Tutorial02.html">
Tutorial B: More Single Qubit Gates
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="comingsoon.html">
Tutorial C: Multiple Qubit Operations and Quantum Circuits
</a>
</li>
</ul>
<p aria-level="2" class="caption" role="heading">
<span class="caption-text">
Back Matter
</span>
</p>
<ul class="nav bd-sidenav">
<li class="toctree-l1">
<a class="reference internal" href="QuantumGlossary.html">
<strong>
A Quantum Glossary
</strong>
</a>
</li>
<li class="toctree-l1">
<a class="reference internal" href="about.html">
<strong>
About the Author
</strong>
</a>
</li>
</ul>
</div>
</nav> <!-- To handle the deprecated key -->
<div class="navbar_extra_footer">
Powered by <a href="https://jupyterbook.org">Jupyter Book</a>
</div>
</div>
<main class="col py-md-3 pl-md-4 bd-content overflow-auto" role="main">
<div class="topbar container-xl fixed-top">
<div class="topbar-contents row">
<div class="col-12 col-md-3 bd-topbar-whitespace site-navigation show"></div>
<div class="col pl-md-4 topbar-main">
<button id="navbar-toggler" class="navbar-toggler ml-0" type="button" data-toggle="collapse"
data-toggle="tooltip" data-placement="bottom" data-target=".site-navigation" aria-controls="navbar-menu"
aria-expanded="true" aria-label="Toggle navigation" aria-controls="site-navigation"
title="Toggle navigation" data-toggle="tooltip" data-placement="left">
<i class="fas fa-bars"></i>
<i class="fas fa-arrow-left"></i>
<i class="fas fa-arrow-up"></i>
</button>
<div class="dropdown-buttons-trigger">
<button id="dropdown-buttons-trigger" class="btn btn-secondary topbarbtn" aria-label="Download this page"><i
class="fas fa-download"></i></button>
<div class="dropdown-buttons">
<!-- ipynb file if we had a myst markdown file -->
<!-- Download raw file -->
<a class="dropdown-buttons" href="_sources/TheWorldofQuantum04.ipynb"><button type="button"
class="btn btn-secondary topbarbtn" title="Download source file" data-toggle="tooltip"
data-placement="left">.ipynb</button></a>
<!-- Download PDF via print -->
<button type="button" id="download-print" class="btn btn-secondary topbarbtn" title="Print to PDF"
onclick="printPdf(this)" data-toggle="tooltip" data-placement="left">.pdf</button>
</div>
</div>
<!-- Source interaction buttons -->
<div class="dropdown-buttons-trigger">
<button id="dropdown-buttons-trigger" class="btn btn-secondary topbarbtn"
aria-label="Connect with source repository"><i class="fab fa-github"></i></button>
<div class="dropdown-buttons sourcebuttons">
<a class="repository-button"
href="https://github.com/Jaim-gem/qc"><button type="button" class="btn btn-secondary topbarbtn"
data-toggle="tooltip" data-placement="left" title="Source repository"><i
class="fab fa-github"></i>repository</button></a>
<a class="issues-button"
href="https://github.com/Jaim-gem/qc/issues/new?title=Issue%20on%20page%20%2FTheWorldofQuantum04.html&body=Your%20issue%20content%20here."><button
type="button" class="btn btn-secondary topbarbtn" data-toggle="tooltip" data-placement="left"
title="Open an issue"><i class="fas fa-lightbulb"></i>open issue</button></a>
</div>
</div>
<!-- Full screen (wrap in <a> to have style consistency -->
<a class="full-screen-button"><button type="button" class="btn btn-secondary topbarbtn" data-toggle="tooltip"
data-placement="bottom" onclick="toggleFullScreen()" aria-label="Fullscreen mode"
title="Fullscreen mode"><i
class="fas fa-expand"></i></button></a>
<!-- Launch buttons -->
<div class="dropdown-buttons-trigger">
<button id="dropdown-buttons-trigger" class="btn btn-secondary topbarbtn"
aria-label="Launch interactive content"><i class="fas fa-rocket"></i></button>
<div class="dropdown-buttons">
<a class="binder-button" href="https://mybinder.org/v2/gh/Jaim-gem/qc/gh-pages?labpath=_sources/v2/gh/Jaim-gem/qc/gh-pages?urlpath=tree/_sources/TheWorldofQuantum04.ipynb"><button type="button"
class="btn btn-secondary topbarbtn" title="Launch Binder" data-toggle="tooltip"
data-placement="left"><img class="binder-button-logo"
src="_static/images/logo_binder.svg"
alt="Interact on binder">Binder</button></a>
<a class="colab-button" href="https://colab.research.google.com/github/Jaim-gem/qc/blob/gh-pages/_sources/TheWorldofQuantum04.ipynb"><button type="button" class="btn btn-secondary topbarbtn"
title="Launch Colab" data-toggle="tooltip" data-placement="left"><img class="colab-button-logo"
src="_static/images/logo_colab.png"
alt="Interact on Colab">Colab</button></a>
<button type="button" class="btn btn-secondary topbarbtn"
onclick="initThebeSBT()" title="Launch Thebe" data-toggle="tooltip" data-placement="left"><i
class="fas fa-play"></i><span style="margin-left: .4em;">Live Code</span></button>
</div>
</div>
</div>
<!-- Table of contents -->
<div class="d-none d-md-block col-md-2 bd-toc show noprint">
<div class="tocsection onthispage pt-5 pb-3">
<i class="fas fa-list"></i> Contents
</div>
<nav id="bd-toc-nav" aria-label="Page">
<ul class="visible nav section-nav flex-column">
<li class="toc-h2 nav-item toc-entry">
<a class="reference internal nav-link" href="#shrodinger-s-cat-in-a-box-pt-3-two-entangled-superposed-quantum-cats">
<strong>
Shrodinger’s Cat in a Box (Pt. 3) – Two Entangled Superposed Quantum Cats?
</strong>
</a>
</li>
</ul>
</nav>
</div>
</div>
</div>
<div id="main-content" class="row">
<div class="col-12 col-md-9 pl-md-3 pr-md-0">
<!-- Table of contents that is only displayed when printing the page -->
<div id="jb-print-docs-body" class="onlyprint">
<h1>5. Entanglement</h1>
<!-- Table of contents -->
<div id="print-main-content">
<div id="jb-print-toc">
<div>
<h2> Contents </h2>
</div>
<nav aria-label="Page">
<ul class="visible nav section-nav flex-column">
<li class="toc-h2 nav-item toc-entry">
<a class="reference internal nav-link" href="#shrodinger-s-cat-in-a-box-pt-3-two-entangled-superposed-quantum-cats">
<strong>
Shrodinger’s Cat in a Box (Pt. 3) – Two Entangled Superposed Quantum Cats?
</strong>
</a>
</li>
</ul>
</nav>
</div>
</div>
</div>
<div>
<section class="tex2jax_ignore mathjax_ignore" id="entanglement">
<h1>5. Entanglement<a class="headerlink" href="#entanglement" title="Permalink to this headline">¶</a></h1>
<p>
<img alt="entangle" src="https://cdn.mos.cms.futurecdn.net/XXvNg65B8odU3wbAi5J44D-970-80.jpg.webp" /></p>
<aside class="margin sidebar">
<p class="sidebar-title"></p>
<p>Credit: Getty Images</p>
</aside>
<p>The last thing that we’ll look at is <strong>entanglement</strong>. Entanglement is when the states of two (or more) quantum objects are <em>linked</em> to one another.</p>
<p><em>To illustrate, we’ll continue with our quantum cat thought experiment…</em></p>
<section id="shrodinger-s-cat-in-a-box-pt-3-two-entangled-superposed-quantum-cats">
<h2><strong>Shrodinger’s Cat in a Box (Pt. 3) – Two Entangled Superposed Quantum Cats?</strong><a class="headerlink" href="#shrodinger-s-cat-in-a-box-pt-3-two-entangled-superposed-quantum-cats" title="Permalink to this headline">¶</a></h2>
<p>Let’s push Schrodinger’s thought experiment a little further by saying that we now have two superposed quantum cats.<br> But this time they’re also <em>maximally entangled</em> . That means that at some point in time, these cats were most likely <em>in the same box</em>. We imagine now that the two cats (in each a different box now) have physically separated and each gone to opposite ends of the universe.</p>
<p>Now, a classical observer at the both ends decides to look into the box <em>at the same time</em> to take note of what they see. The process is repeated with similarly-prepared entangled quantum cats a sufficient number of times, then the two observers meet and compare their notes.</p>
<p><em>Can you think of what they will notice?</em> Click below to find out.</p>
<div class="toggle docutils container">
<p>For each pair of cats, they will either get the same result every time <strong>or</strong> a different result every time!
In the first possible scenario, the cats are entangled to be same all the time. That is, if you measure a dead cat on one end you will also measure a dead cat on the other end, and when you measure an alive cat on one end you will also measure the cat being alive on the next end. In the second possible scenario, the cats can be entangled to be opposite each time. That is, once you measure the cat in one state at a given end, the cat on the other end will always be in the opposite state.</p>
</div>
<p>If you are puzzled, add now the idea that the cats were initially superposed and their fates only “decided” when each observer decided to look, remembering that they looked at the exact same time.</p>
<p><em>What can that possibly mean about the physical reality of quantum mechanical objects?</em></p>
<p>From a classical perspective, and also Einstein’s perspective, <em>it would appear</em> that the cats “communicated” their final states <em>faster than the speed of light</em> at the moment of observation… which of course violates Einstein’s theory that nothing (not even information) can travel faster than light.</p>
<p>However there is <em>another way</em> to interpret this, which makes Einstein both <em>right</em> and <em>wrong</em>. Yet this way is even stranger than what we can think.</p>
<p>Suppose that Einstein is <em>right</em>… that <em>nothing</em> can travel faster than the speed of light… but suppose also that entangled quantum systems <strong>do not need to communicate anything</strong>. But in fact, entangled quantum systems (and by extension Quantum Mechanics) can be <strong>non-local</strong>, meaning that they are not confined/localized to just one particular space! And that <em>distance really means nothing</em> for two ‘linked’ quantum objects. (Now the above header image depicting two atoms connected by an invisible string appears relevant.)</p>
<p>This view of Quantum Mechanics is more accepted now as increasingly complex experimental setups confirm time and again that a <strong>local</strong> theory for quantum systems appears invalid, and that only a <strong>non-local</strong> view can explain experimental observations and calculations.</p>
</section>
</section>
<script type="text/x-thebe-config">
{
requestKernel: true,
binderOptions: {
repo: "Jaim-gem/qc",
ref: "gh-pages",
},
codeMirrorConfig: {
theme: "abcdef",
mode: "python"
},
kernelOptions: {
kernelName: "python3",
path: "./."
},
predefinedOutput: true
}
</script>
<script>kernelName = 'python3'</script>
</div>
<!-- Previous / next buttons -->
<div class='prev-next-area'>
<a class='left-prev' id="prev-link" href="TheWorldofQuantum05.html" title="previous page">
<i class="fas fa-angle-left"></i>
<div class="prev-next-info">
<p class="prev-next-subtitle">previous</p>
<p class="prev-next-title">4. Wave-Function Collapse</p>
</div>
</a>
<a class='right-next' id="next-link" href="QuantumComputing01.html" title="next page">
<div class="prev-next-info">
<p class="prev-next-subtitle">next</p>
<p class="prev-next-title"><strong>What is Quantum Computing?</strong></p>
</div>
<i class="fas fa-angle-right"></i>
</a>
</div>
</div>
</div>
<footer class="footer">
<p>
By TTLAB<br/>
© Copyright 2021.<br/>
</p>
</footer>
</main>
</div>
</div>
<script src="_static/js/index.be7d3bbb2ef33a8344ce.js"></script>
</body>
</html>