Page 83 - Principles and Applications of NanoMEMS Physics

70 Chapter 2

UV-Pump
UV-Pump

BBO-Crystal
BBO-Crystal
Cones
Cones
Figure 2-11. Entangled photons via type-II parametric down conversion. (After [107].)

decay into two photons of lower energy, one polarized vertically and one
polarized horizontally, for instance. In particular, each photon can be emitted
along a cone in such a way that two photons of a pair are found opposite to
each other on the respective cones. If it occurs that the photons travel along
the cone intersections, however, then neither photon is in a definite
polarization state, but their relative polarizations are complementary, i.e.,
they are entangled. Taking the state of the photons along the intersecting
cones as entangled, i.e.,

( H V − V H )
Φ − = 1 2 1 2 , (75)
2

we see that, because the polarization relationship of complementarity must
be maintained, whenever photon 1 is measured and found to have vertical
polarization, the polarization of photon 2 will be horizontal, and vice versa.
This means that no matter the state in which photon 1 is found, the state of
photon 2 can be predicted to be in the orthogonal state when measured.
Entanglement, therefore, enables a strong correlation among the photons.
This is a general property among entangled particles. By appropriately
controlling the evolution of aggregates of particles, it is possible to induced
them into entangled states. The agents that control the evolution of states are
called quantum gates.

2.4.1.2 Quantum Gates
Given a qubit prepared in the initial state ψ () , its state at a
t
0
ψ
subsequent time t is given by ψ () t = U ( ,tt ) ( ) , where U is the
t
0 0
qubit’s transition matrix[60] Unitary reversible matrices U prescribing the
evolution of qubits are called quantum logic gates [102], [111]. Thus, a