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arXiv:quant-ph/0304036 · Physical Review Letters

Experimental Demonstration of Quantum Source Coding

Yasuyoshi Mitsumori, John A. Vaccaro, Stephen Mark Barnett, Erika Andersson, Atsushi Hasegawa, Masahiro Takeoka, Masahide Sasaki

Published Nov 19, 2003• 15 citations
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Abstract

We report an experimental demonstration of Schumacher's quantum noiseless coding theorem. Our experiment employs a sequence of single photons, each of which represents three qubits in terms of eight spatial and polarization modes. We initially prepare each photon in one of a set of eight nonorthogonal code word states corresponding to the value of a block of three binary letters. We use quantum coding to compress this quantum data into a two-qubit quantum channel and then uncompress the two-qubit channel to restore the original data with a fidelity approaching the theoretical limit.

DOI
10.1103/physrevlett.91.217902

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We report an experimental demonstration of Schumacher's quantum noiseless coding theorem. Our experiment employs a sequence of single photons, each of which represents three qubits in terms of eight spatial and polarization modes. We initially prepare each photon in one of a set of eight nonorthogonal code word states corresponding to the value of a block of three binary letters. We use quantum coding to compress this quantum data into a two-qubit quantum channel and then uncompress the two-qubit channel to restore the original data with a fidelity approaching the theoretical limit.
We review our experiment on quantum source and channel codings, the most fundamental operations in quantum info-communications. For both codings, entangling letter states is essential. Our model is based on the polarization-location coding, and a quasi-single photon linear optics implementation to entangle the polarization and location degrees of freedom. Using single-photon events in a subset of possible cases, we simulate quantum coding-decoding operations for nonorthogonal states under the quasi-pure state condition. In the quantum channel coding, we double the spatial bandwidth (number of optical paths), and demonstrate the information more than double can be transmitted. In the quantum source coding, we halve the spatial bandwidth to compress the data and decompress the original data with the high fidelity approaching the theoretical limit.
The general scheme of data compression using the quantum noiseless coding theorem of Schumacher is dicussed for general quantum sources. When the Hilbert space of the quantum source is decomposable into orthogonal subspaces, one can first perform classical data compression before performing the quantum data compression for individual subspaces. For minimizing the resource in quantum coding, a general parameterization of the dimensions in the Jozsa-Schumacher quantum data compression scheme is presented.
We have devised an optical scheme for the recently proposed protocol for encoding two qubits into one qutrit. In this protocol, Alice encodes an arbitrary pure product state of two qubits into a state of one qutrit. Bob can then restore either of the two encoded qubit states error-free but not both of them simultaneously. We have successfully realized this scheme experimentally using spatial-mode encoding. Each qubit (qutrit) was represented by a single photon that could propagate through two (three) separate fibers. We theoretically propose two generalizations of the original protocol. We have found a probabilistic operation that enables us to retrieve both qubits simultaneously with average fidelity above 90% and we have proposed an extension of the original encoding transformation to encode NNN qubits into one (N+1)(N+1)(N+1)-dimensional system.
We present experimental results implementing the Quantum Schur-Weyl Transform QSWT for three qubits, allowing us to compress three quantum bits into two. In our implementation the three qubits are encoded in two photons. The first photon encodes a path and a polarization qubit, while the second photon encodes a single polarization qubit. We use the QSWT to map all of the information from the 3 qubits onto the path and polarization qubits encoded in the first photon, allowing us to discard the second photon. We characterize our compression by performing measurements on the remaining two qubits and show that they obey the statistics of a three qubit system. We expect our technique to become extremely useful in the near future, for all quantum information architectures, as few qubit quantum memories become available.