The entropy photon-number inequality is a lower bound on the effective photon number associated with the von
Neumann entropy of two independently prepared bosonic inputs after passive mixing.
Put 
for 
,
with 
.
This increasing function has inverse 
.
For 
modes and finite natural-base von
Neumann entropy 
, define the effective number by 
. For input 
and output modes 
, the assertion is
 |
Here 
and 
are the Fock space annihilation operators. The reduced
output 
is obtained by tracing out the other mixed modes.
Modes within each input may be entangled; independence is required between the two inputs.
