Abstract
A constraint on two complementary knowledge excesses by maximal violation of Bell inequalities for a single copy of any mixed state of two qubits
S,M
is analyzed. The complementary knowledge excesses
ΔK(
Π
M
→
Π
S
)
and
ΔK(
Π
′
M
→
Π
′
S
)
quantify an enhancement of ability to predict results of the complementary projective measurements
Π
S
,
Π
′
S
on the qubit
S
from the projective measurements
Π
M
,
Π
′
M
performed on the qubit
M
. For any state
ρ
SM
and for arbitrary
Π
S
,
Π
′
S
and
Π
M
,
Π
′
M
, the knowledge excesses satisfy the following inequality
ΔK
2
(
Π
M
→
Π
S
)+
ΔK
2
(
Π
′
M
→
Π
′
S
)≤(
B
max
/2
)
2
, where
B
max
is maximum of violation of Bell inequalities under single-copy local operations (local filtering and unitary transformations). Particularly, for the Bell-diagonal states only an appropriate choice of the measurements
Π
S
,
Π
′
S
and
Π
M
,
Π
′
M
are sufficient to saturate the inequality.