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Multiple choice
By Schumacher's quantum source coding theorem, a memoryless quantum source with density operator
ρ
\rho
ρ
can be faithfully compressed (fidelity approaching 1) to
R
R
R
qubits per signal exactly when:
R
R
R
is greater than zero, since any nonzero rate suffices
R
R
R
is greater than
log
2
(
d
)
\log_2(d)
lo
g
2
(
d
)
for a
d
d
d
-dimensional system
R
R
R
is greater than the von Neumann entropy
S
(
ρ
)
S(\rho)
S
(
ρ
)
R
R
R
is greater than the Shannon entropy
H
H
H
of the label probabilities
{
p
x
}
\{p_x\}
{
p
x
}
, regardless of
S
(
ρ
)
S(\rho)
S
(
ρ
)
Check answer