Jos Bergervoet
2021-10-01 21:48:53 UTC
A "classical channel", or more general the concept of
"classical transport" is often used in Quantum Mechanics-
related experiments, or thought experiments. But it is
usually not entirely clear how it is defined.
If we assume that quantum mechanics is our theory, then
classical transport can only be quantum mechanical transport
of a special kind, since everything has to be described
by quantum mechanics. So what is special about it? And how
can we model it as something happening entirely within the
framework of quantum mechanics, for instance to describe
quantum teleportation completely within quantum mechanics?
Let us assume we have one qubit and we are asked to do
classical transport. Possible definitions/implementations
are:
1) It first has to be measured, meaning that it will
become entangled with at least one other qubit in our
system (that's measurement, quantum mechanically!) and
then we send this other qubit by classical transport (so
we haven't gained much in terms of a definition..)
2) Just transport the qubit quantum mechanically, but
assume that along the way it gets entangled with at
least one external-world qubit. (This seems not clear
enough unless we also specifically preserve some
information along a chosen axis..)
3) Just transport the qubit quantum mechanically, but
assume the phase relation between its 2 components gets
lost, i.e. adding a random phase to the components but
maintaining their magnitudes. (Requires a preferred
axis, as it should, but requires "throwing dice" which
I'd like to avoid since it cannot happen in unitary
time evolution.)
4) As in 3), but in addition to losing the phase now
also assume that the magnitudes are lost, by collapsing
them, to [1, 0] or [0, 1], presumably both still with a
random phase applied to it. (This requires even more dice
throwing and involves a collapse of the state, so it cannot
happen in quantum mechanics. Collapse is only "apparent".)
So what should we do to describe quantum mechanically
what people mean with classical transport?
"classical transport" is often used in Quantum Mechanics-
related experiments, or thought experiments. But it is
usually not entirely clear how it is defined.
If we assume that quantum mechanics is our theory, then
classical transport can only be quantum mechanical transport
of a special kind, since everything has to be described
by quantum mechanics. So what is special about it? And how
can we model it as something happening entirely within the
framework of quantum mechanics, for instance to describe
quantum teleportation completely within quantum mechanics?
Let us assume we have one qubit and we are asked to do
classical transport. Possible definitions/implementations
are:
1) It first has to be measured, meaning that it will
become entangled with at least one other qubit in our
system (that's measurement, quantum mechanically!) and
then we send this other qubit by classical transport (so
we haven't gained much in terms of a definition..)
2) Just transport the qubit quantum mechanically, but
assume that along the way it gets entangled with at
least one external-world qubit. (This seems not clear
enough unless we also specifically preserve some
information along a chosen axis..)
3) Just transport the qubit quantum mechanically, but
assume the phase relation between its 2 components gets
lost, i.e. adding a random phase to the components but
maintaining their magnitudes. (Requires a preferred
axis, as it should, but requires "throwing dice" which
I'd like to avoid since it cannot happen in unitary
time evolution.)
4) As in 3), but in addition to losing the phase now
also assume that the magnitudes are lost, by collapsing
them, to [1, 0] or [0, 1], presumably both still with a
random phase applied to it. (This requires even more dice
throwing and involves a collapse of the state, so it cannot
happen in quantum mechanics. Collapse is only "apparent".)
So what should we do to describe quantum mechanically
what people mean with classical transport?
--
Jos
Jos