Quantum information

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.... -[[User:Jono|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]]