<s>
Permutationally	O
invariant	O
quantum	B-Algorithm
state	I-Algorithm
tomography	I-Algorithm
(	O
PI	O
quantum	B-Algorithm
state	I-Algorithm
tomography	I-Algorithm
)	O
is	O
a	O
method	O
for	O
the	O
partial	O
determination	O
of	O
the	O
state	O
of	O
a	O
quantum	O
system	O
consisting	O
of	O
many	O
subsystems	O
.	O
</s>
<s>
Quantum	B-Algorithm
state	I-Algorithm
tomography	I-Algorithm
is	O
a	O
method	O
to	O
determine	O
all	O
these	O
parameters	O
from	O
a	O
series	O
of	O
measurements	O
on	O
many	O
independent	O
and	O
identically	O
prepared	O
systems	O
.	O
</s>
<s>
Thus	O
,	O
in	O
the	O
case	O
of	O
full	O
quantum	B-Algorithm
state	I-Algorithm
tomography	I-Algorithm
,	O
the	O
number	O
of	O
measurements	O
needed	O
scales	O
exponentially	O
with	O
the	O
number	O
of	O
particles	O
or	O
qubits	O
.	O
</s>
<s>
Permutationally	O
invariant	O
quantum	B-Algorithm
tomography	I-Algorithm
is	O
such	O
a	O
method	O
needing	O
fewer	O
measurements	O
than	O
state	O
tomography	O
.	O
</s>
<s>
PI	O
quantum	B-Algorithm
tomography	I-Algorithm
only	O
measures	O
the	O
permutationally	O
invariant	O
part	O
of	O
the	O
density	O
matrix	O
.	O
</s>
<s>
The	O
number	O
of	O
independent	O
real	O
parameters	O
of	O
for	O
qubits	O
scales	O
as	O
The	O
number	O
of	O
local	O
measurement	O
settings	O
scales	O
as	O
Thus	O
,	O
permutationally	O
invariant	O
quantum	B-Algorithm
tomography	I-Algorithm
is	O
considered	O
manageable	O
even	O
for	O
large	O
.	O
</s>
<s>
In	O
other	O
words	O
,	O
permutationally	O
invariant	O
quantum	B-Algorithm
tomography	I-Algorithm
is	O
considered	O
scalable	O
.	O
</s>
<s>
There	O
are	O
other	O
approaches	O
for	O
tomography	O
that	O
need	O
fewer	O
measurements	O
than	O
full	O
quantum	B-Algorithm
state	I-Algorithm
tomography	I-Algorithm
.	O
</s>
<s>
Compressed	B-Algorithm
sensing	I-Algorithm
is	O
especially	O
suited	O
for	O
low	O
rank	O
states	O
.	O
</s>
<s>
Permutationally	O
invariant	O
tomography	O
can	O
be	O
combined	O
with	O
compressed	B-Algorithm
sensing	I-Algorithm
.	O
</s>
<s>
Permutationally	O
invariant	O
tomography	O
has	O
been	O
tested	O
experimentally	O
for	O
a	O
four-qubit	O
symmetric	O
Dicke	O
state	O
and	O
also	O
for	O
a	O
six-qubit	O
symmetric	O
Dicke	O
in	O
photons	O
,	O
and	O
has	O
been	O
compared	O
to	O
full	O
state	O
tomography	O
and	O
compressed	B-Algorithm
sensing	I-Algorithm
.	O
</s>
<s>
The	O
hybrid	O
method	O
combining	O
permutationally	O
invariant	O
tomography	O
and	O
compressed	B-Algorithm
sensing	I-Algorithm
has	O
also	O
been	O
tested	O
.	O
</s>
