## Quantum communication moves into the unknown

By David Deutsch and Artur Ekert

**Information** is physical and any processing of information is always performed by physical means - an innocent-sounding statement, but its consequences are anything but trivial, In the last few years there has been an explosion of theoretical and experimental innovations which, their discoverers claim, are creating a fundamental new discipline: a distinctively quantum theory of information.

Quantum physics allows the construction of qualitatively new types of logic gates, absolutely secure cryptosystems (systems that combine communications and cryptography), the cramming of two bits of information into one physical bit and, as has just been proposed, a sort of "teleportation", Here we describe the last two "miracles".

Classical information theory agrees with everyday intuition: if you want to send a message using an object which can be put into one of *N* distinguishable states, the maximum number of different messages that you can send is *N*. For example, a single photon can have only two distinguishable polarisation states, say "left-handed" and "right-handed". So if you send a message by preparing the polarisation of a single photon and transmitting it, it is obvious that you can send no more than two distinguishable messages, i.e, one bit of information. Obvious, but false.

The state of a classical system can be specified by specifying the states of all its constituent systems. But in quantum theory a combined system can have additional properties, in which case the constituent systems can be said to be "entangled" with one another. Entangled states were first investigated in the famous paper of Einstein, Podolsky and Rosen (EPR). Quantum mechanics is also nonlocal, in that distant and non-interacting systems may be entangled. Last year Charles Bennett of the IBM Thomas J Watson Research Center, Yorktown Heights, New York, and Stephen Wiesner used non-locality to devise a hypothetical quantum communication system in which the receiver reads a two-bit message from two physical bits, but only one of those bits - the transmitted bit - has physically come from the sender of the message (Phys. Rev. Lett. (1992) 69 2881). The other - the reference bit - never leaves the receiver (see *(a)* in the figure).

Strangely, it is the receiver, Bob, who makes the first move. He prepares two photons, or two spin-half particles (which exist in one of two states - spin up or spin down), jointly in an "entangled" state. He stores one particle and sends the other one to the sender, "Alice", who stores it. To ensure that the entanglement is maintained, each particle must be kept isolated from its surroundings. When it is time to send a message, Alice performs one of four special operations on her stored particle before transmitting it back to Bob. For the spin-half particles these four unitary operations, performed by the quantum gate *U*, are equivalent to: doing nothing (unit operation), or rotating the spin by 180 degrees about the x, y or z axes; for photons these operations correspond to polarisation rotations. The operations have to be unitary to maintain the quantum mechanical coherence of the particle.

These operations, although performed only on one particle, affect the joint (entangled) quantum state of the two particles. This cannot be verified by measurements on the two particles separately. But by measuring both of them jointly, using the quantum gate *M*, Bob can determine which of the four operations Alice performed, and so receive one of the four messages. Thus the technique effectively doubles the peak capacity of an information channel.

The other miracle, "quantum teleportation", is also based on quantum nonlocality. In classical physics, the teleportation machines of science fiction present no problem of principle. One simply measures the state of every atom of the object to be teleported, transmits that information, and any number of copies of the object can be reconstructed by any receiver. But quantum physics fundamentally limits the accuracy of any such process because one cannot experimentally determine an unknown state. At most one can distinguish between *N* mutually orthogonal states, provided one already knows which *N* states those are. *N* is determined by the system being used for photons and spinhalf particles, for example, *N=2*.

Cloning (accurately copying) an unknown quantum state would be equivalent to a simultaneous sharp measurement of all observables of the system, including non-commuting ones, which is forbidden by the uncertainty principle. Thus, suppose Alice is given an object in an unknown quantum state Psi. Until recently, it was thought that the only way she could cause Bob to possess an object in that same state, Psi, would be either to send the object itself to Bob, or to transfer its state characteristics to another particle and send that (and irretrievably alter the state of the original object). In either case, the transmission would have to be along a channel that maintains quantum coherence, which requires the complete isolation of the transmitted object.

Bennett, Brassard, Crépeau, Jozsa, Peres and Wootters have now shown how an unknown quantum state can be "teleported" from one place to another (Phys. Rev. Lett. (1993) 70 1895). As in the previous example, Alice and Bob are each given one particle of the entangled EPR pair (see *(b)* in the figure). Then Alice brings together her particle and the particle in an unknown state, and performs jointly on those two particles a special measurement using the quantum gate M. This measurement has four possible outcomes - it is, in fact, the same measurement that is performed at the end of the two-bit communication process. Alice then communicates the result to Bob, by any ordinary channel, such as a telephone or radio transmitter, According to this result, Bob, who has the other member of the EPR pair, performs one of four operations on his particle (the same four operations that were used in the communication scheme) using the quantum gate *U*. The effect is to leave Bob's particle in exactly the same state that Alice's particle was originally in.

So far neither of these miracles is yet practical. Quantum gates such as *U* can be built, but the operation performed by the gate *M*, sometimes called a "Bell measurement", is beyond present technology. Harald Weinfirter and Anton Zeilinger from the University of lnnsbruck in Austria have designed optical experiments, using so-called "parametric down-conversion and a simple photodetection scheme, which would allow communication with more than one bit of information per physical bit. They are developing techniques that might allow quantum teleportation too. But the theoretical results, whether they are practicable or not, are already of considerable importance, because they force us to fundamentally revise our concept of information in physics.

**Figure** *(a)* Two bits for the price of one: starting from the bottom, Bob sends one particle of an entangled (EPR) pair to Alice who performs one of four operations on it with the quantum gate *M* Alice then returns the particle to Bob who measures the state of the joint (and still entangled) system with the quantum gate *M* to receive one of four possible messages (two bits of information), although only one particle (which can exist in only one of two states, i.e. carry only one bit of information) has been sent. Ouantum communication channels are represented by thin lines, classical channels by thick lines. *(b)* Ouantum teleportation: again Bob sends one particle of an entangled state to Alice who measures the joint state of this with the unknown state Psi. She then transmits (classically) this result to Bob. This information can be used to put Bob's remaining particle (the other half of the entangled pair) in the state Psi.

Extract from Physics World, June 1993