<?xml version="1.0" encoding="UTF-8" standalone="yes"?><oembed><version><![CDATA[1.0]]></version><provider_name><![CDATA[Azimuth]]></provider_name><provider_url><![CDATA[https://johncarlosbaez.wordpress.com]]></provider_url><author_name><![CDATA[John Baez]]></author_name><author_url><![CDATA[https://johncarlosbaez.wordpress.com/author/johncarlosbaez/]]></author_url><title><![CDATA[Quantum Steganography]]></title><type><![CDATA[link]]></type><html><![CDATA[<p>Besides talking about environmental issues, I&#8217;d also like to use this blog to talk about my day job at the <a href="http://www.quantumlah.org/">Centre for Quantum Technologies</a>.  I hope this isn&#8217;t too distracting&#8230; </p>
<p>I&#8217;d like to try live-blogging a talk here.  Today there&#8217;s a talk by Bilal Shaw of the University of Southern California about a paper he wrote with Todd Brun on <a href="http://arxiv.org/abs/1006.1934">Quantum Steganography</a>.  </p>
<p>&#8220;Steganography&#8221; is the art of hiding information by embedding it in a seemingly innocent message.  In case you&#8217;re wondering &#8211; and I&#8217;ve got the kind of mind that can&#8217;t help wondering &#8211; the word &#8220;steganography&#8221; <i>actually is</i> etymologically related to the word &#8220;stegosaurus&#8221;. They both go back to words meaning &#8220;cover&#8221; or &#8220;roof&#8221;.  Some other words with the same root are &#8220;thatch&#8221;, &#8220;deck&#8221; -and even &#8220;detect&#8221;, which is like &#8220;de-deck&#8221;: to take the lid off something!</p>
<p>Steganography is an <a href="http://en.wikipedia.org/wiki/Steganography#Ancient_steganography">ancient art</a>, still <a href="http://en.wikipedia.org/wiki/Steganography#Digital_steganography">thriving today</a>.  For example, that Russian spy ring they just caught were <a href="http://www.wired.com/dangerroom/2010/06/alleged-spies-hid-secret-messages-on-public-websites/">embedding secret data in publicly visible websites</a>. The advantage of steganography over ordinary cryptography is that if you do it right, it doesn&#8217;t draw attention to itself.  See this picture?</p>
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<img src="https://i0.wp.com/upload.wikimedia.org/wikipedia/commons/4/4e/StenographyOriginal.png" alt="" />
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<p>Remove all but the two least significant bits of each color component and you&#8217;ll get a picture that&#8217;s almost black. But then make that picture 85 times brighter and here&#8217;s what you&#8217;ll see:</p>
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<img src="https://i1.wp.com/upload.wikimedia.org/wikipedia/commons/1/1b/StenographyRecovered.png" alt="" />
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<p>All this is purely classical, of course.  But what fiendish tricks can we play using quantum mechanics?  Can we hide Schr&ouml;dinger&#8217;s cat in a seemingly innocent tree?</p>
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<img width="250" src="https://i1.wp.com/www.victorianweb.org/art/illustration/tenniel/alice/6.5.jpg" alt="" />
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<p>Bilal&#8217;s <a href="http://arxiv.org/abs/1006.1934">paper</a> describes a few recipes for quantum steganography.   Alas, I&#8217;m not good enough at cryptography and live-blogging to beautifully deliver an instant summary of how they work. But roughly, the idea is to fake the effects of mildly &#8220;depolarizing&#8221; channel, one that introduces some errors into the qubits you&#8217;re transmitting, pushing pure states closer to the center of the <a href="http://en.wikipedia.org/wiki/Bloch_sphere">Bloch sphere</a>, where pure noise lives.  You can&#8217;t introduce <i>too</i> many errors, since this would make the error rate suspiciously high to someone spying on our transmissions.  So, there&#8217;s a kind of tradeoff here&#8230;</p>
<p>I&#8217;d be happy for an expert to give a better description!</p>
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