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# Saving Space with Quantum Information

Physics 7, 106
A technique that packs the full content of three bits of quantum information into two may be a space saver for quantum computers.

If quantum computers are to become practical devices, they need to handle large amounts of data. Now researchers demonstrate the compression of quantum data by reducing the number of quantum bits (qubits) needed to store a given amount of information. In this first experiment they compressed three qubits into two, but they say the results can lead to larger numbers of qubits in the future.

To minimize data storage and transmission requirements for traditional computers, computer scientists have devised data compression techniques for the ones and zeros that make up digital data. Think of a data record containing a long string of identical bits—N zeros, for example. Rather than physically allocating the value “zero” to N distinct bits of memory, it’s more economical to store a single zero, along with the instruction to read it N times. Both convey the same information, but the “compressed” statement takes up less space.

Quantum information is carried in the form of “qubits”—superpositions of quantum states that can be both one and zero in different proportions at the same time. Reading—that is, measuring—a qubit converts it into a classical bit with a definite one or zero value, no longer in a combination state. Reading a set of N identical qubits that are equal parts one and zero, for example, would produce roughly N/2 ones and N/2 zeros. But taking a single such qubit and reading it N times would produce the same answer over and over, because after the first reading, the qubit becomes classical. In other words, the N-qubit state contains more information than the classical reading procedure can convey, so the classical compression method will not work.

However, a mathematical argument shows that the information contained in a set of N identical qubits can in principle be carried by many fewer qubits; the number is approximately the logarithm of N [1]. Lee Rozema of the University of Toronto and his colleagues have now devised a way to put this method of qubit compression into practice.

In the simplest case, the compression method puts the information contained in three identical qubits into two qubits that are not identical. Information common to all three qubits is encoded only once in the pair instead of redundantly in all three. Physically, compressing the qubits means making them interact to generate two new qubits with the properties prescribed by the mathematical recipe. Figuring out how to do this was the hard part of the problem, says Rozema. As in any manipulation of quantum information, the challenge was to perform actions on the qubits without destroying their quantum nature.

Rozema and his colleagues used two independent properties of a photon to encode qubits, so in principle each photon could hold two qubits. The two properties were polarization (horizontal or vertical orientation of the photon’s electric field) and position in an interferometer (traveling along one path or the other through the experimental setup). The team began by creating three identical qubits with two photons, carried by the polarization and path of one photon and by the polarization of a second. They then compressed the three qubits into two by passing both photons through a complex optical system that caused the photons to interact. At the end of the process, one photon carried two nonidentical qubits containing the information of the original three identical qubits.

To read the compressed data, the researchers needed a classical bit that they obtained by making a certain measurement on the second photon. The result of this measurement determined the procedure (measurements) that could extract the original three qubits from the two compressed qubits. The extra classical bit from the second photon is akin to the instruction, in classical compression, that says how many times to duplicate the single stored bit.

Mark Wilde of Louisiana State University in Baton Rouge calls the work “a clever implementation of the quantum compression algorithm” and says it could be useful for “shuffling around quantum data in future quantum computation and communication devices.” But scaling the process up to larger numbers of qubits will likely be hard, he says. Rozema agrees but says that the new work is a proof-of-principle demonstration, and besides, scaling up remains a challenge for all quantum information operations.

This research is published in Physical Review Letters.

Correction (20 October 2014): An earlier version of this story incorrectly stated that Mark Wilde is at the University of Louisiana. He is at Louisiana State University.

–David Lindley

David Lindley is a freelance science writer in Alexandria, Virginia.

## References

1. D. Bacon, I. L. Chuang, and A. W. Harrow, “Efficient Quantum Circuits for Schur and Clebsch-Gordan Transforms,” Phys. Rev. Lett. 97, 170502 (2006); M. Plesch and V. Buzek, “Efficient Compression of Quantum Information,” Phys. Rev. A 81, 032317 (2010)

## Subject Areas

Quantum Information

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