Quantum teleportation (Bennett
et al., Phys. Rev. Lett. 70, 1895
(1993))
has been celebrated - not
least in the secondary science media - as one of the weirdest and most
sensational recent
discoveries in quantum theory. Although indeed an interesting
application of quantum
nonlocality, it is often
entirely
misunderstood because of its very inappropriate name.
The "teleportation" protocol consists of three steps:
1. the preparation of an appropriate nonlocal Bell state,
2. the measurement of another (local) Bell state by Alice, who then
sends a
message containing the outcome to Bob, and
3. a unitary transformation performed locally by Bob.
It is evidently the crucial last step that reproduces the (possibly
unknown) spinor
state, which was destroyed at Alice's place, at Bob's place. The
first two steps are only required to inform Bob
about what to do precisely among a small set of formal possibilities
without knowing the state that is to be reproduced.
This may be more dramatically illustrated by means of a complex
physical state to be teleported - such as
Captain Kirk (CK) – instead of a spinor. According to the protocol, Bob
would need a device
that allows him to physically transform any superposition of (a
specific quantum state of) CK and his relative vacuum, a|CK> +
b|NoCK> as
a new version of Schrödinger's cat, into any other such
superposition –
including a transformation of the vacuum into the state representing
Captain Kirk. This macroscopically unrealistic, though in quantum
theory formally
conceivable device would
now evidently have to contain all the information about CK's
physical state. Bob would thus have to be able
to reconstruct Captain Kirk
when physically realizing the unitary
transformation, while the quantum aspect of the protocol (used in the
first
two
steps) only serves to circumvent the no-cloning theorem in the case of
an unknown initial superposition at Alice's place (here in the
two-dimensional Hilbert
space) if it is this that is to be "teleported".
Even for this first part of the protocol, no teleportation need be
involved, although this conclusion may depend on one's interpretation
of
quantum
mechanics – in particular on whether one assumes a quantum state to
have
ontic or epistemic meaning. Before traveling to their final positions
by
ordinary means, Alice and Bob have to prepare an appropriate Bell
state (for spinors or Captain Kirk occupation number states 0 and 1),
and then take their now entangled
subsystems with them, thereby
carefully shielding them against the environment in order to avoid
decoherence. If such a
nonlocal Bell state represents a state of reality, it contains already
a component in which Bob's
subsystem is in the state
that later is to be unitarily transformed into the required one. So
this quantum state (and the whole information it represents) is
physically at
Bob's place before the "teleportation" experiment
proper
begins. Decoherence between different outcomes of Alice's Bell state
measurement
then leads to four dynamically separate Everett branches (or four
possible
outcomes of a collapse of the wave function). They are correlated with
Bob's subsystem that was part of the initial nonlocal Bell state. Bob
himself
becomes
entangled with Alice's measurment result
when he
receives her message. Therefore, he can perform different unitary
transformations in the four different branches, which would then all
lead to the
same intended final state (Joos et al., Decoherence and the Appearance of a
Classical World, Springer 2003, p. 172).
Since according to
EPR's or Bell's analysis, for example, entanglement cannot be
understood as a
statistical
correlation between local variables (depending on incomplete
information about them), any attempt of an epistemic
interpretation in local terms must in fact assume some "spooky action
at a
distance" or telekinesis, that would have to create a certain local state to be
used by Bob in order to apply his specific unitary transformation. A
similar
conclusion would apply to an ontic interpretation in the case of an
intantaneous
dynamical collapse induced by Alice's measurement. Nonetheless, the
local
"quantum phenomenon" thereby caused at Bob's
place could no more than accidentally
create the intended state, such as |CK>; in general the
crucial final
unitary
transformation must be nontrivial.
Of course, one may deny the validity of quantum theory for
macroscopic systems (such as CK) according to Niels Bohr's philosophy –
then
one would
trivially not be able to quantum teleport them (but the same
conclusion
may be drawn in practice within a universal quantum theory from their
unavoidable
decoherence).
The experiment might then still be envisaged with mesoscopic systems,
such as
fullerenes.
Performing it in reality for such a system would demonstrate the
skills
of
future experimentalists, but not offer
any
novel insights unless it demonstrated that quantum unitarity breaks
down universally (that is, not just locally because of entanglement
with the environment) under
certain conditions.
However, the universal
validity of quantum theory is strongly supported, for example, by
the (chaotic) environmental entanglement that explains the ubiquitous
phenomenon of decoherence.
To conclude, one may say that the "quantum teleportation" protocol
allows one neither
to
teleport
physical objects, nor the information
needed to reconstruct them (even by
technically
unrestricted means).
Another, also recently invented drastic misnomer is the term quantum
eraser,
as it would imply
that the essential element of this procedure, which is claimed to
recover coherence
between different measurement results, is a
mere destruction of
information about this result. However, any physical loss of
information
(for
example, its deterministic transformation into heat, as in the
"reset" of a
memory device – see Bennett, Sci. Amer. 257(5), 108) would enforce
irreversible decoherence rather than cause the expected recoherence.
Decoherence (required for the quasi-classical outcome of a "real"
measurement,
for example) is precisely defined by the transfer of
"information" into uncontrollable entanglement with the environment
(that is, the
irreversible
dislocalization of the corresponding superpositions). This information
is thus lost in practice; the typical
decoherence-producing environment can not be regarded as an informed
"witness" of the decohered
quantity. In a causal world, redundant genuine information usually exists
about
macroscopic quantities, which in this way form an objective (that is,
documented) "history" – see The
Direction of Time.
Only in
the case of
a
reversible
("virtual") measurement of a microscopic system by another one, when
factorizing
components have not yet evolved into dynamically autonomous "branches"
of the wave function, can
the conjugate
variable still be measured (then irreversibly) by simultaneously
eliminating
the original virtual
measurement result. (This experiment was first
and
very appropriately described by Edward Jaynes in Foundation of Radiation Theory and Quantum
Electronics, A. Barut, edt., Plenum 1980 – see here, item 38).
It is a shame – if not a scandal – that such inappropriate and
often sensationalist terminology is so readily accepted by the
physics
media, while contributions which appropriately criticize these and
similar
pseudo-concepts, such as the inconsistent ("dualistic") standard
interpretation of quantum mechanics in terms of "complementary"
classical
concepts, usually meet strong reservations by the editors.
Similar arguments as valid for the quantum erasor apply to the
Afshar
experiment (see here
and Bill Unruh's
comments),
which, when
analyzed consistently by means of quantum concepts, demonstrates once
more how Bohr's complementarity
concept is simply used in a phenomenological way to
distinguish, in effect, between different "pointer bases" (branch
modes)
that would characterize different measurement devices. However, a
pointer
basis is physically
determined by decoherence (unavoidable entanglement
with a normal
environment) – it does not have to be
chosen ad hoc corresponding to some
presumed classical
property of the quantum object. None of the so-called
Welcher-Weg
measurements registers the classical Weg
(path) of a particle, but
rather a partial single-particle wave function
(a component that leaves one
of the
slits only, for example). A
particle may ultimately seem
to be observed with the final click of the
counter, but this phenomenon is
again
described
by a decoherence process that leads to several branches
containing differently localized wave
packets of the detector variable (the "pointer") – correlated with
corresponding wave
packets of the "particle" if this is not absorbed. A
particle has in fact never
been
observed (see also here and here). Even the
concept of particle number
has recently (rather unintentionally) been confirmed experimentally for
photons as representing no more than the number of nodes in the wave
functional (P. Bertet
et al., Phys. Rev. Lett. 89, 200402 (2002); V. Parigi et al., Science
317, 1890
(2007)). I am convinced that this explanation applies to other
"particles" as well.
So it may seem
that Ernst Mach resigned too early from his doubts in the existence of
atoms (as particles, that is)!
The misconception underlying most of this inappropriate nomenclature is related to the presently perhaps even more popular (and thus even more misleading) misnomer or misconception of quantum information, which is used to circumscribe the fundamental quantum mechanical property of entanglement. The latter is known to characterize individual and completely defined real states (such as Bell states or generic many-particle states, e.g. total angular momentum eigenstates). Entanglement does not merely describe statistical correlations, which would have to be facilitated by incomplete knowledge or information, although it may be dynamically transformed into apparent ensembles by means of decoherence (further entanglement) – in particular during irreversible measurements. Accepting the physical reality of nonlocal entangled quantum states eliminates any need for spooky action at a distance, and in particular for any advanced action that seems to occur in a delayed choice experiment. This delayed choice simply determines which property of the controllably entangled wave function that has unitarily arisen in a virtual "measurement" is finally irreversibly ("really") measured. Paradoxes arise only if one attempts to describe quantum physics exclusively in local terms.
Other quantum misnomers which are based on an inappropriate
application
of classical concepts have become established tradition. Examples are
the
pseudo-concepts of quantum
uncertainty and quantum
fluctuations. If a quantum state is completely defined (pure),
this means
that it is "certain". The "uncertainty relations" can then well be
understood in terms of the Fourier theorem applied to wave packets –
provided momentum and energy are consistently defined as wave number
and frequency, respectively, just rescaled by means of Planck's
constant. Nonetheless, uncertain initial conditions, assumed to hold
for classical position and momentum variables, are often misused in a
pseudo-argument to
justify the observed dynamical
quantum indeterminism. However, such probabilistic
quantum "events",
formulated as jumps between quantum states, would require a stochastic
modification of the deterministic Schrödinger equation (the
collapse of the wave function or a corresponding branching). This
dynamical
indeterminism has thus nothing to do with the uncertainty relations.
see also The
wave function: it or bit?
Roots
and
Fruits
of Decoherence
Wave function branching as a spacetime
process