# Don't exceed speed of light

In Einstein's prophetic world, fact is stranger than fiction. In the TV show Star Trek, beam-me-up-Scotty teleportation was only possible within the range of the "transporter," but in Einstein's world, teleportation is not limited by range. It does, however, require "entangled pairs" that have to be preinstalled like Sci-Fi channel Stargates.

Teleportation is only possible if Alice keeps one half of an entangled pair at point A, while the other half is physically moved to Bob's location at point B. After that, it's as if anything goes — as long as it doesn't lead to exceeding the speed of light.

"It is hard to understand entanglement classically, because you always have to remember that nothing you do can send a message faster than the speed of light," said IBM Fellow Charles Bennett. "Entanglement may be described by saying that the two particles are in a state of sameness (or oppositeness), even though neither particle by itself has a definite state." Bennett and colleagues Gilles Brassard (University of Montreal) and Claude Crpeau (McGill University), Richard Jozsa (University of Bristol, England), Asher Peres (Technion-Israel Institute of Technology) and William Wootters (Williams College) discovered teleportation late in 1992. Their pioneering paper on it appeared in early 1993.

But it all began in 1905, when Einstein, then an obscure Swiss patent-office clerk, published his first scientific paper, explaining the dual nature of light as both wave and particle.

His second paper explained Brownian motion, thereby setting lower limits on the measurement accuracy required for teleportation, but Einstein's third paper derived his most famous result from the impossibility of exceeding the speed of light — special relativity, which maintains that time slows while mass and length increase as you approach the speed of light.

The impossibility of exceeding the speed of light is relevant to almost all of Einstein's findings — including entanglement, which he called "spooky action at a distance," even while he steadfastly maintained the impossibility of faster-than-light communication.

If such communication were possible, then Alice would merely have to disturb her half of the entangled pair to produce an immediate measurable change in Bob's particle, which could then be used, Morse code style, for faster-than-light communication.

"As it is," Bennett said, "any measurement Bob does on his particle yields a random result. The effects of entanglement only become evident in comparing his measurement results with those obtained by Alice on her particle, which cannot be done instantaneously."

Even confined to light speed, teleportation is still remarkable because it behaves as if it can squeeze precise analog information into a mere 2-bit digital channel (whereas the analog information is really being passed by entanglement).

For instance, in one version of teleportation, a single "data" photon, polarized at an arbitrary analog angle (say, with an angle theta of 10°) is given to Alice. She doesn't know theta, and by Heisenberg's famous uncertainty principle would disturb its polarization by attempting to measure it. So instead of measuring the data photon alone, she combines it with her half of the entangled pair and measures that. The effect of Alice's measurement is to project the mix of her data photon and entangled photon into one of four quadrants that reveals the relationship between their polarizations without revealing the data photon's polarization angle. But, since Bob's half of the entangled pair has the same relational state, Alice's quadrant measurement also tells her about the relation between her data photon and Bob's half of the entangled pair. In particular, it tells Alice into which quadrant the data photon and Bob's half of the entangled pair fall: the same polarization, perpendicular, complementary (add up to 90°) or supplementary (add up to 180°).

When Alice sends Bob her 2-bit quadrant measurement revealing which of these four cases she obtained, Bob can rotate his entangled photon (still without learning or measuring its polarization) into an exact replica of the polarization state the data photon had before the experiment began: 10° input at A yields 10° out at B. And yet Alice only communicated the 2-bit quadrant number to Bob.

"This might appear to allow faster-than-light communication, but before Bob receives Alice's 2-bit communication, Bob has only one chance in four of guessing Alice's message," said Bennett. "He would have four equiprobable outcomes — 10°, 100°, 90° and 170° — which is so random as to be useless in determining the correct polarization of 10°."

The bottom line: Teleportation is possible, but unlike Scotty's temperamental "transporter," quantum teleportation works over arbitrary distances and doesn't even require you to measure the properties you are trying to teleport — indeed, measuring them before the transmission would spoil the results. Instead, sharing an entangled pair enables Einstein's spooky action at a distance to pass analog information — transferring a precise value that you don't even measure, while leaving you with the simple task of projecting a simple relational property that can be classically communicated.