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2. NANOMEMS PHYSICS: Quantum Wave-Particle Phenomena 69

2.4.1.1 Einstein-Podolsky-Rosen (EPR) State

In a system with two noninteracting qubits, the global state may be
expressed as [108],

ψ = c 1 00 + c 2 01 + c 3 10 + c 4 11 , (71)

where ¦ c i 2 = 1 and each term is the tensor product of the components of
i
the corresponding qubits. When c = c = 0 , and c = c = 1 2 , the
1 4 2 3
resulting state,

( 01 + 10 )
ψ = , (72)
EPR
2

is called an EPR state [108]. The EPR state is not a tensor product of the
vector states, therefore, it represents an entangled state; it does not belong to
any of the individual vector spaces, but is a combination of them. Associated
with an EPR state is the so-called Bell-state basis [108], which embodies the
possible states that can result upon measuring two-state quantum systems. In
particular, if 0 , 1 represent the two states of particle 1, and 0 , 1
1 1 2 2
represent two states of particle 2, then the measurement of their EPR pair
state may result in one of four state vectors, namely,

( 0 0 ± 1 1 )
Ψ ± = 1 2 1 2 , (73)
2

and

( 0 1 ± 1 0 )
Φ ± = 1 2 1 2 . (74)
2

One of the most transparent demonstrations of entanglement and its
implications was the experiment by Kwiat et al. [107], see Figure 2-11
below. This experiment exploited the principle of type-II parametric down
conversion to produce directed beams of polarization entangled photons. In
type-II parametric down conversion [107] an incident laser beam pump
passes through a crystal, such as beta barium borate, and can spontaneously