Quantum Information, the Ambiguity of the Past, and the Birth ... - PiTP
Quantum Information, the Ambiguity of the Past, and the Birth ... - PiTP
Quantum Information, the Ambiguity of the Past, and the Birth ... - PiTP
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<strong>Information</strong> budget for r<strong>and</strong>om permutations <strong>and</strong> unitaries<br />
p known<br />
bits<br />
g garbage<br />
bits<br />
d unknown<br />
data bits<br />
Κnown<br />
R<strong>and</strong>om<br />
Permutation<br />
on strings <strong>of</strong><br />
p+g+d<br />
= a+i bits<br />
a accessible<br />
bits<br />
Classical<br />
Decoder<br />
i inaccessible bits<br />
Input data can be faithfully<br />
recovered iff a > g+d.<br />
Decoder output is uncorrelated<br />
with input data iff<br />
a < g.<br />
s qubits with<br />
saved purification<br />
p pure qubits<br />
g garbage<br />
qubits with<br />
lost purification<br />
d data<br />
qubits<br />
we wish<br />
to recover<br />
s<br />
p<br />
g<br />
d<br />
Known<br />
R<strong>and</strong>om<br />
Unitary<br />
s+p+g+d<br />
=a+m+i<br />
s<br />
a accessible<br />
m<br />
measured<br />
i inaccessible<br />
d<br />
<strong>Quantum</strong><br />
Decoder<br />
Input data can be coherently<br />
recovered iff<br />
s+a > i+g+d.<br />
Decoder output is uncorrelated<br />
with data<br />
iff s+a < i+g.<br />
[S. Lloyd <strong>the</strong>sis, HLW quant-ph/0407049, ADHW quantph/0606225),<br />
HP 0708.4025,…, Graeme Smith <strong>and</strong> CHB in prep.]
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