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May 31st, 2016, 09:06 PM  #1 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 240 Thanks: 23 Math Focus: Number theory  Efficiency of quantum computing
The World Wide Web contains over 10^21 bytes. At least how many qubits (binary units of quantum information) would be needed to represent it?

November 28th, 2016, 03:07 AM  #2 
Member Joined: Oct 2016 From: labenon Posts: 33 Thanks: 4 
Hi, I have read somewhere this information. I hope this will help you. "A theorem is proven for quantum information theory that is analogous to the noiseless coding theorem of classical information theory. In the quantum result, the von Neumann entropy S of the density operator describing an ensemble of pure quantum signal states is equal to the number of spin1/2 systems (‘‘quantum bits’’ or ‘‘qubits’’) necessary to represent the signal faithfully. The theorem holds whether or not the signal states are orthogonal. Related results are also presented about the fidelity of quantum coding and about representing entangled quantum states." 
November 28th, 2016, 06:10 AM  #3 
Senior Member Joined: Apr 2014 From: UK Posts: 763 Thanks: 287 
At any given time, 0 qubits are required to represent it as the result is all the bytes and is fixed. If you wanted to represent the changes over time you would need to constrain the changes to a measurable number in order to define the number of qubits needed to uniquely identify the differences. If you want to represent every possible state of every byte, you'd need 73 qubits 
November 29th, 2016, 09:36 PM  #4 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 240 Thanks: 23 Math Focus: Number theory 
I get 70 qubits; my math is rustier than my physics, though. (ln10/ln2)21~70 
December 1st, 2016, 08:19 AM  #5 
Senior Member Joined: Apr 2014 From: UK Posts: 763 Thanks: 287 
try 8*10^21 

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computing, efficiency, quantum 
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