Just as classical information is the amount of classical communication needed to convey a classical message, '''quantum information'''
can be defined as the amount of quantum communication needed to convey unknown quantum states.
Imagine that a party is given a sequence of unknown quantum states chosen randomly from some distribution denoted by the
density matrix $\backslash rho$. Then Ben Schumacher showed that the number of qubits needed to faithfully transmit
these states is given by von Neumann entropy
$S(\backslash rho)=-Tr\backslash rho\backslash log\backslash rho$.
Essentially, given a sample of $n$ such states, one can compress the states, so that they reside on a smaller Hilbert space of dimension just over $2^\{nS(\backslash rho)\}$.
Note that the compression works even though one doesn't know what the states are, nor from what ensemble they are chosen from.
One only knows the density matrix $\backslash rho$. An elegent way to think of this is to think of $\backslash rho$ to be on
system $A$, and consider its purification, on a reference system $R$, such that one has the pure state
$|\backslash psi\backslash rangle\_\{AR\}$. Faithful compression of $\backslash rho$ will then produce a state which
has high fidelity with $|\backslash psi\backslash rangle\_\{AR\}$.
The protocol for Schumacher's compression scheme is as follows: ....someone to insert....
-Jono 23:18, 9 Dec 2005 (GMT)
==References==
Schumacher, B. [http://prola.aps.org/abstract/PRA/v51/i4/p2738_1 Quantum coding]. Phys. Rev. A 51, 2738–-2747 (1995).
==See also==
Partial quantum information
Category:Quantum Information Theory
Category:Handbook of Quantum Information

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Monday, October 26, 2015 - 17:56