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The Quantum Physics of Teleportation

John G. Cramer

Alternate View Column AV-62
Keywords: quantum nonlocality entangled states recreation communication
Published in the December-1993 issue of Analog Science Fiction & Fact Magazine;
This column was written and submitted 5/17/93 and is copyrighted ©1993 by John G. Cramer.
All rights reserved. No part may be reproduced in any form without the explicit permission of the author.

    Teleportation is familiar idea in science fiction. It permeated the SF literature of the Golden Age, providing the basis for SF classics like Van Vogt's World of Null-A (1945), Budry's Rogue Moon(1960), and many others. The Star Trek series' transporter has also "beamed" the concept of teleportation to our pop culture. But modern hard-SF has largely abandoned teleportation as a concept that has more to do with fantasy and parapsychology than with real science.

    Imagine my surprise then, to discover an article on the subject of teleportation in the March 29, 1993 issue of Physical Review Letters, that "hot-news" flagship physics journal of the American Institute of Physics. The article, by an international collaboration of physicists hereafter designated by the initials BBCJPW, does not provide a plan for constructing a transporter. Instead it describes an in-principle procedure for copying and transporting a quantum state from one location and one observer to another by a process that is characterized as teleportation. The BBCJPW scheme exploits some of the peculiarities of quantum physics and reveals some of the rules of the game in that exotic domain. Let us begin by discussing these rules.

    First, we will focus on the quantum state vector (also known as the wave function). Any quantum system, for example an electron with the characteristics of position, energy, momentum, and a spin vector pointing in some direction, is completely described by the state vector, as denoted by the symbol |y>. Anything that is knowable about the electron is mathematically encoded within |y>. An essential rule of the quantum world is that the state vector can never be completely known because no measurement can determine it completely (except in the special case that it has been prepared in some particular state or some member of a known "basis" group of states in advance). In general, the quantum state coded within |y> can only be "glimpsed" by a measurement of one of the properties of the quantum system. In the act of pinning down one particular property of |y>, the measurement destroys any opportunity to determine some of the other properties of the quantum state. The quantum state can be preserved unchanged only by refraining from making any measurements of its properties. This frustrating aspect of quantum mechanics is the essence of Heisenberg's uncertainty principle.

    A second ground rule of quantum mechanics is that a pair of spatially separated quantum sub-systems that are parts of an overall quantum system can be "entangled". This bizarre property of quantum systems was discovered in the formalism of quantum mechanics by Albert Einstein and his coworkers Podolsky and Rosen and is known as EPR non-locality. A measurement on one of the entangled sub-systems not only forces it into a particular state but also, across space-time and even backwards in time, forces the sub-system with which it is entangled into a corresponding state. For example, measuring the polarization of one of a pair of entangled photons precipitates the other photon, which may be light years away, into the same state of polarization as that which was measured for its entangled twin.

    The state vector, however, does not have to describe a microscopic system like a photon or an electron. It can describe large collections of atoms: chemical compounds, human beings, planets, stars, galaxies. There have even been recent papers in quantum cosmology by Stephen Hawking and others in which the properties of the state vector of the entire universe are discussed.

    But what has this to do with teleportation? The basic operation of teleportation can be described as determining the total quantum state of some largish system, transmitting this state information from one place to another, and making a perfect reconstruction of the system at the new location. However, since it is not even in-principle possible to measure the complete state vector of even a very simple quantum system because of the uncertainty principle, as discussed above, this would seem to rule out teleportation on even small quantum systems as physically impossible.

    "Not so!" say BBCJPW. There is a way around this quantum roadblock which exploits the peculiarities of EPR nonlocality to transmit the complete description of the state of a quantum system over nature's privileged communication channel without performing measurements that extract a complete description of the state vector as information. They propose a multistep procedure by which any quantum state |y> can be teleported intact from one location to another (but only at a transmission speed that is less than or equal to the velocity of light). The BBCJPW procedure goes like this:

Step 1: Prepare a pair of quantum sub-systems |a> and |b> in an entangled state, so that they are linked by EPR non-locality.

Step 2: Transport one of these entangled quantum subsystems (|a>) to the location of the teleport transmitter (the authors call the transmitter operator Alice) and the other subsystem (|b>) to the location of the teleport receiver (the authors call the receiver operator Bob). These two subsystems are correlated by nonlocality, but at this point contain no information about the quantum state |y> to be teleported. In a sense, they represent an open quantum channel that is ready to transmit.

Step 3: Alice brings the teleported state |y> into contact with the entangled state |a> and performs a quantum measurement on the combined system (|y> |a>). The details of the measurement have been previously agreed upon by Bob and Alice.

Step 4: Using a conventional communication channel, Alice transmits to Bob a complete description of the outcome of measurement she has performed.

Step 5: Bob subjects his quantum subsystem to a set of linear transformations (for example rotations through 90o.) that are dictated by the outcome of Alice's measurement. After these transformations, Bob's quantum subsystem is no longer in state |b> and is now in a state identical to the original quantum state |y>, which has in effect been teleported from Alice to Bob.

    The BBCJPW scheme for teleportation requires both a normal sub-light-speed communication channel and a nonlocal EPR channel to send the quantum state vector from one location to another, and also requires considerable pre-arrangement of entangled states and measurement procedures to make the transfer possible. It transfers the quantum system without having completely measured its initial state. The initial state |y> is in effect destroyed at Alice's location and recreated at Bob's location.

    BBCJPW analyze the information flow implicit in the process and show that Alice's measurement does not provide any information about the quantum state |y>. All of the state information is passed by the "privileged" EPR link between the entangled states. The measurement results can be thought of as providing the code key that permits the EPR information to be decoded properly at Bob's end. And because the measurement information must travel on a conventional communications channel, the decoding cannot take place until the code key arrives, insuring that no faster-than-light teleportation is possible.

    It should be mentioned that while it is quite feasible to produced entangled quantum states of the kind needed in the BBCJPW teleportation scheme, as demonstrated by the pioneering EPR experiment of Freedman and Clauser and the subsequent experiments of Aspect and his co-workers a decade later, these states have up to now involved particles (photons) that are separating at the velocity of light and cannot be "stored until needed" as would be desirable for convenient implementation of the BBCJPW scheme.

    The BBCJPW procedure, as mentioned above, is not a design for a machine that teleports macroscopic objects, e.g., human beings, from one location to another. It is concerned with the teleportation only of quantum states of elementary particles. However, since this is a SF magazine I am permitted to indulge in some speculation on the science-fictional implications of the BBCJPW work. The key element of the scheme is the entangled quantum state that provides the nonlocal link between the transmitter and receiver. It is difficult to visualize a complex entangled sub-system that could interact properly with a macroscopic object for the purposes of teleportation. It would have to contain the same ensemble of atoms in nearly the same arrangements as the object transmitted. For physicists, that's a mere engineering detail now that the in-principle feasibility of teleportation has been demonstrated.

    So let's consider how macroscopic BBCJPW teleportation might be used in an SF context. 

Example 1: an advance terrestrial civilization sends out an exploration ship filled with macroscopic entangled state that are twins of similar states held in storage on Earth. If the ship travels at 1% of c, it will take twelve hundred years to travel the 11.9 light years to Tau Ceti. After it arrives, robots unload the ship and set up a teleport receiver unit for each entangled state. When everything is ready, the colonists step into transmitter units where they join the stay-at-home entangled states and are destructively "measured" by the transmitter. The results of the measurement are recorded and sent by radio or light beam to the receivers at Tau Ceti. The measurement information can be transmitted redundantly several times with error-correcting code to insure its integrity. Twelve years later, Earth time, the beamed information is received at Tau Ceti, the transformations on the entangled states are performed, and the colonists emerge from the receiver units. For the teleported colonists no subjective time at all has passed, and they have had a perfectly safe trip because it was known that the receiver apparatus had arrived and was fully checked out before the transmission was made. The explorers can also return to Earth, with the same 12 year gap in subjective time, using other entangled subsystems that were brought along for the trip to teleport in the opposite direction. Not, perhaps, as exciting as quicker SF trips to the stars using space-warps or hyperdrives, but a safe and efficient way of exploring the stars.

Example 2: a wormhole link has been established with a neighboring bubble universe, but it is discovered that the other universe is dominated by antimatter rather than normal matter. Is exploration within the antimatter universe possible? Sure. We know that entangled matter-antimatter subsystems can be produced, for example an electron and positron produced as a pair in an electromagnetic interaction. With macroscopic entangled subsystems that are matter-antimatter twins, the antimatter subsystem could be transported through the wormhole, after which explorers from our world might be teleported through the wormhole and converted to antimatter at the same time. A return trip with other matter-antimatter subsystems would reverse the process, converting the explorers back to matter and returning them to our universe simultaneously.

    I'm sure that there are many other possibilities for SF themes based on quantum teleportation. We now have a physics basis for teleportation. Its uses in SF are limited only by our imagination.


References:

Quantum Teleportation:

"Teleporting an Unknown Quantum State via Dual Classical and Einstein-Podolsky-Rosen Channels", C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K Wootters, Phys. Rev. Letters 70, 1895 (1993).

Entangled States and EPR Nonlocality: 

S. J. Freedman and J. F. Clauser, Phys. Rev. Letters 28, 938 (1972); 
A. Aspect, J. Dalibard, and G. Roger, Phys. Rev. Letters 49, 91 (1982); 
John G. Cramer, Reviews of Modern Physics 58, 647 (1986); 
John G. Cramer, Intl. J. Theor. Phys. 27, 227 (1988); 
C. H. Bennett and S. J. Wiesner, Phys. Rev. Letters 69, 2881 (1992).


SF Novels by John Cramer:  my two hard SF novels, Twistor and Einstein's Bridge, are newly released as eBooks by Book View Cafe and are available at : http://bookviewcafe.com/bookstore/?s=Cramer .

AV Columns Online: Electronic reprints of about 177 "The Alternate View" columns by John G. Cramer, previously published in Analog , are available online at: http://www.npl.washington.edu/av.


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