Biomedical Engineering Reference
In-Depth Information
in a delocalized state (a superposition of exciton states located in different dots).
The resulting dephasing rate depends extremely strongly on temperature (
T
7
∼
at
D
2
as long as
the carrier wave functions overlap and logarithmic for larger distances). As a result,
the dephasing time drops from micro-seconds at temperatures of a few Kelvin to
picoseconds at 100 K [
97
].
low temperatures) and shows dependence on the inter-dot distance (
∼
9.3.4
Entanglement Decay
One of the fundamental qualities of quantum theory is the appearance of non-
classical correlations, such as entanglement [
99
,
100
]. Entanglement between two
systems manifests itself by the appearance of correlations between the results of
appropriately chosen measurements on the entangled subsystems which cannot
be accounted for by any classical (realistic and local) theory [
101
]. Furthermore,
entanglement is an important resource in quantum information processing [
102
],
and it is essential for quantum teleportation [
103
], superdense coding [
104
], and the
distribution of cryptographic keys [
105
].
Entanglement, as a non-local property of multiple quantum systems, is expected
to be more fragile than the phase coherence of individual subsystems. In order
to manifest genuinely quantum behavior resulting from entanglement a quantum
system must maintain phase relations between the components of its quantum su-
perposition state, involving different states of distinct subsystems. Keeping in mind
that the subsystems may be separated by a macroscopic distance, one may expect
such a non-local superposition state to be extremely fragile to the dephasing effect
of the environment. In fact, it has been shown (for a 2
2 system) that entanglement
between two subsystems tends to decay faster than local coherence [
19
,
21
,
106
].
As expected, the decay of entanglement is stronger, if the subsystems interact with
different environments (which might result from a large spatial separation between
them). Furthermore, certain states that show robust entanglement under collective
dephasing become disentangled by the interaction with separate environments [
21
].
It was also shown for two different classes of systems [
19
,
20
] that certain states may
become separable (completely disentangled) within a finite time under conditions
that lead to a usual, exponential decay of local coherence (this phenomenon is
known as the “sudden death” of entanglement). Since even partial entanglement of
many copies of a bipartite quantum system may be distilled to a smaller number
of maximally entangled systems [
107
], it is essential to understand whether the
influence of the environment leads to the appearance of separability in realistic
models of dephasing.
The study of entanglement requires an entanglement measure that can be
calculated from the system state. For pure states, the von Neumann entropy of one
subsystem [
108
] is a good entanglement measure, but for mixed states a unique
entanglement measure has not been found [
109
,
110
]. One choice is to use the
entanglement of formation (EOF), defined as the ensemble average of the von
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