A larger quantum alphabet

John C. Howell, Curtis J. Broadbent, Irfan Ali Khan

Quantum communication usually employs qubits to relay information. However, there has a recent effort to utilize the larger state spaces of many quantum particles. There have been successful efforts to generate qutrits and even qudits up to d=11 [1]. This talk will report on an experiment in which we generated quantum keys with alphabets well over 100. It will also be shown that there is no upper bound on the size of the alphabet with near future realizations expected to exceed 1000.

Irfan Ali-Khan, Curtis J. Broadbent, John C. Howell

We present a protocol for large-alphabet quantum key distribution (QKD) using energy-time entangled biphotons. Binned, high-resolution timing measurements are used to generate a large-alphabet key with over 10 bits of information per photon pair, albeit with large noise. QKD with 5% bit error rate is demonstrated with 4 bits of information per photon pair, where the security of the quantum channel is determined by the visibility of Franson interference fringes. The protocol is easily generalizable to even larger alphabets, and utilizes energy-time entanglement which is robust to transmission over large distances in fiber.

Hao Chen

Andrew K. Tan, Matthew H. Ho, Isaac L. Chuang

We present two new positive results for reliable computation using formulas over physical alphabets of size$q \gt 2$. First, we show that for logical alphabets of size$\ell = q$the threshold for denoising using gates subject to q-ary symmetric noise with error probability$\varepsilon $is strictly larger than that for Boolean computation, and we show that reliable computation is possible as long as signals remain distinguishable, i.e.$\epsilon \lt (q - 1) / q$, in the limit of large fan-in$k \rightarrow \infty $. We also determine the point at which generalized majority gates with bounded fan-in fail, and show in particular that reliable computation is possible for$\epsilon \lt (q - 1) / (q (q + 1))$in the case of q prime and fan-in$k = 3$. Secondly, we provide an example where$\ell \lt q$, showing that reliable Boolean computation,$\ell = 2$, can be performed using 2-input ternary,$q = 3$, logic gates subject to symmetric ternary noise of strength$\varepsilon \lt 1/6$by using the additional alphabet element for error signaling.

Giuliano G. La Guardia