Exceeding the Classical Capacity Limit in a Quantum Optical Channel

The amount of information transmissible through a communications channel is determined by the noise characteristics of the channel and by the quantities of available transmission resources. In classical information theory, the amount of transmissible information can be increased twice at most when the transmission resource is doubled for fixed noise characteristics. In quantum information theory, however, the amount of information transmitted can increase even more than twice. We present a proof-of-principle demonstration of this superadditivity of classical capacity of a quantum channel by using the ternary symmetric states of a single photon, and by event selection from a weak coherent light source. We also show how the superadditive coding gain, even in a small code length, can boost the communication performance of the conventional coding technique.

Figure 1

Geometrical representation of the code word (dotted arrows) and decoding (solid arrows) state vectors in a real three dimensional space.

Figure 2

(a) Encoding and decoding circuits. The angles of the HWPs, ${\theta }_0$, ${\theta }_1$, and ${\theta }_2$ are chosen as described in the text, and ${\varphi }_A=-\gamma /2=-9.74°$ and ${\varphi }_B=-45°$. (b) Quantum circuit to realize the collective decoding by $\{|{\Pi }_{yy}⟩\}$, which can be applied to any physical qubits. A received code word state is first transformed by the five controlled gates and is then detected by a standard von Neumann measurement on each letter. The open circle indicates conditioning on the control qubit being set to zero, and $\widehat{Q}(\phi )={\widehat{R}}_y(\phi ){\widehat{\sigma }}_z$, and $\gamma =19.47°$. Other nomenclature follows Ref. 13. (c) Circuit for separable (classical) decoding for $C_1$.

Figure 3

Top: histogram of photon counts for the channel matrix elements $P(yy|xx)$ corresponding to the maximum mutual information. Bottom: measured (diamonds) and theoretical (solid curve) mutual information as a function of the offset angle of the code word state set $\{|{\Psi }_{xx}⟩\}$ from the decoder state set $\{|{\Pi }_{yy}⟩\}$ around the vertical axis in Fig. 1. The dotted curve is just a guide for the eyes. The theoretical $C_1$ and accessible information $I_{\mathrm{A}\mathrm{c}\mathrm{c}}$ are shown by the dashed and one-dotted lines, respectively [10]. The square represents the experimental $C_1$.