(Web essay: www.zeh-hd.de  -- June 2007, last revised Oct 2007)

"Quantum Teleportation" and other Quantum Misnomers

H. D. Zeh

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.

Various kinds of quantum fluctuations (in particular vacuum fluctuations, depicted in terms of so-called virtual particles) are also used to circumscribe specific quantum properties, for example the entanglement that exists in the ground state of interacting fields (their physical vacuum). Subsystems have then to be objectively represented by a "mixed" reduced density matrix. A simple example is a free field in the presence of an accelerated mirror. Even a thermal equilibrium is quantum mechanically described by a density matrix that can be represented by an ensemble of time-independent energy eigenstates. In classical theory, a system in thermal equilibrium would require an ensemble that is based on incomplete information or coarse graining, which are in turn often justified by time-averaging over some chaotic motion (using ergodic theory). This classical picture seems to have given rise to the quite inadaquate misnomer of "quantum fluctuations", although it represents exactly time-independent quantum states.

                        The paradox is only a conflict between reality and your feeling what reality ought to be. – R.P. Feynman

see also   The wave function: it or bit?
                Roots and Fruits of Decoherence
                Wave function branching as a spacetime process

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