Two-Way Communication with a Single Quantum Particle

In this Letter we show that communication when restricted to a single information carrier (i.e., single particle) and finite speed of propagation is fundamentally limited for classical systems. On the other hand, quantum systems can surpass this limitation. We show that communication bounded to the exchange of a single quantum particle (in superposition of different spatial locations) can result in “two-way signaling,” which is impossible in classical physics. We quantify the discrepancy between classical and quantum scenarios by the probability of winning a game played by distant players. We generalize our result to an arbitrary number of parties and we show that the probability of success is asymptotically decreasing to zero as the number of parties grows, for all classical strategies. In contrast, quantum strategy allows players to win the game with certainty.

Figure 1

(a) Space-time diagram. Within the time window $\tau$ either $A$ signals to $B$ or $B$ to $A$. (b) Causal diagram. There are two possible causal relations between variables $x$, $y$, $a$, $b$; i.e., either $x$ influences $a$ and $b$, $a$ influences $b$ (in general, $a$ can be generated in past of $b$, i.e., at time $t=0$), whereas $y$ influences $b$ only (left) or vice versa (right).

Figure 2

Communication with a single quantum particle. The particle is prepared in superposition of two spatial locations $A$ and $B$. At time $t=0$ Alice and Bob encode their inputs and send their “parts of the particle” to the partner. On the way, the particle hits the unitary device (e.g., potential barrier) and gets half-reflected and half-transmitted in a coherent way (see main text). (a) If the parity of inputs is $s=0$, the transformation $U$ deterministically guides the particle to Alice’s location. (b) An analogous situation where $s=1$ and the particle deterministically ends at Bob’s location.