## QUANTUM INFORMATION PROCESSING

### QUANTUM TELEPORTATION

Entanglement is central to the phenomenon of quantum teleportation. It is the process by which quantum information (e.g. the exact state of an atom or photon) is transmitted, exactly, using classical communication channel from one location to another, with the help of previously shared quantum entanglement between the sending and receiving locations.

 Figure 14: Quantum Teleportation. Source: IBM Research.

Anybody who has watched Star-Trek is familiar with the idea of teleportation where an object or person is made to “disappear” in one place while a perfect replica emerges somewhere else (“apparate” for Harry Potter fans). The science behind teleportation is usually not explained by science fiction writers, but the effect they portray is dramatic. Information from the original object is “extracted” and transmitted to the receiving end which is then used to construct the replica. The replica does not contain actual material of the original, but is invariably created from the same kinds of atoms, their arrangement modeled in exactly in the same way as the original. Think of a fax machine that works on 3-dimensional objects as well as documents, but produces an exact copy instead of an approximate facsimile, destroying the original during the process of “scanning”.

Quantum teleportation is a much more realistic and subtler effect where information is transferred between entangled quantum states. The idea of teleporting quantum particles emerged from purely theoretical considerations of a young researcher named William Wootters, who, in 1980, wrote his Ph.D. thesis centered on the question: from what principles can Born’s rule in quantum theory be derived? Important to his considerations was a task known as quantum state tomography. Since measurement of a quantum state results in its modification, obtaining a complete characterization of a quantum state requires measurements on many identical copies of itself. Quantum state tomography is the process by which a quantum state is reconstructed using measurements on an ensemble of identical quantum states. In the fall of 1989, Asher Peres found strong numerical evidence showing joint measurements on a pair of systems yielded superior tomography than the separate measurements. It seemed, therefore, that if a pair of similarly prepared particles was separated in space, an experimenter would be less likely to identify their state than if they were together. After attending a seminar delivered by Wootters in 1992, Charlie Bennett of IBM Research Division, T.J. Watson Research Center, started to ponder whether the inherent nonlocality associated with spatially separated entangled systems could achieve the same quality of quantum state tomography as opposed to the case when they were in contact.

In 1993, Bennett and an international group of six scientists including Wootters, showed that the quantum state of a system could indeed be transferred from one party to distant party using only local operations and classical communication, provided the original is destroyed, and in so doing were able to circumvent the no-cloning theorem. The trick was dubbed “quantum teleportation” by its authors. The abstract of their paper, published in Physical Review Letters reads: “An unknown quantum state $\mid\phi\rangle$ can be disassembled into, then later reconstructed from, purely classical information and purely nonclassical Einstein-Podolsky-Rosen (EPR) correlations. To do so the sender Alice, and the receiver Bob, must prearrange the sharing of an EPR-correlated pair of particles. Alice makes a joint measurement on her EPR particle and the unknown quantum system, and sends the classical result of this measurement. Knowing this, Bob can convert the state of his EPR particle into an exact replica of the unknown state $\mid\phi\rangle$ which Alice destroyed.”

 Figure 15: Scientists reported that they were able to teleport quantum information reliably across a distance of about 10 feet. Source: New York Times.

In a conventional facsimile transmission, the original object is practically unscathed after the scanning process is complete, although scanning in this case is capable of extracting only partial information about the object. The scanned information is then transmitted to the receiving station, where it is imprinted on paper (or on some other surface) to produce an approximate copy of the original. In contrast, two entangled objects B and C (Figure 12) that were originally in contact, are separated in quantum teleportation—object B is brought to the sending station, while object C is transmitted to the receiving station. A, the original object to be teleported, is scanned together with object B at the sending station. This process is irreversible as it disrupts the states of both A and B. The scanned information is accepted by the receiving station, where it is used to “select one of several treatments” to be applied to object C. This makes C as an exact replica of A. The information is considered teleported because the original object A never travels the distance between the two locations.

In subsequent years, various groups have demonstrated teleportation experimentally in a variety of systems, including single photons, coherent light fields, nuclear spins, and trapped ions. Quantum teleportation has the immense promise as it can facilitate long range quantum communications. One day it could also be the enabling technology for a “quantum internet”.

In 2014, physicists from the Kavli Institute of Nanoscience at the Delft University of Technology in the Netherlands, reported successful transmission of quantum data involving the spin state of an electron to another electron about 10 feet away (Figure 13). Successful experiments with quantum teleportation has been reported in the past, but the results of the Delft University study have an unprecedented replication rate of 100 percent for their studied distance.

In 2016, researchers at the National Institute of Standards and Technology (Valivarthi, et al., 2016) were able to teleport quantum information carried by photons over 6.2 kilometers (km) of optical fiber, four times farther than the previous record. The researchers used a variation of the method described above: here three observers participate rather than the conventional two. Bob and Alice each make measurements of an entangled state and another photon, about 8 kilometers from each other. Their results are then sent to Charlie, who combines the two results to achieve quantum teleportation. This method assures that the experiment extended beyond a single lab location, and it was done using existing dark fiber and wavelengths of light commonly used in current fiber internet.