Connection between entanglement and the speed of quantum evolution

It has been recently pointed out [V. Giovannetti, S. Lloyd, and L. Maccone, Europhys. Lett. 62, 615 (2003)] that, for certain classes of states, quantum entanglement enhances the “speed” of evolution of composite quantum systems, as measured by the time a given initial state requires to evolve to an orthogonal state. We provide here a systematic study of this effect for pure states of bipartite systems of low dimensionality, considering both distinguishable (two-qubits) subsystems, and systems constituted of two indistinguishable particles.

Figure 1

Curves in the $(C,\tau ∕T_{\mathit{min}})$ plane corresponding, for each value of $C$, to the states of two (distinguishable) qubits with maximum and minimun $\tau ∕T_{\mathit{min}}$. The points represent randomly generated individual states that evolve to an orthogonal state. All depicted quantities are dimensionless.

Figure 2

Curves in the $(C,\tau ∕T_{\mathit{min}})$ plane corresponding, for each value of $C$, to the states of two bosons with maximum and minimun $\tau ∕T_{\mathit{min}}$. The points represent randomly generated individual states that evolve to an orthogonal state. All depicted quantities are dimensionless.

Figure 3

Randomly generated states of two fermions that evolve to an orthogonal state. Each point corresponds to one of those states as represented in the $(C,\tau ∕T_{\mathit{min}})$ plane. It transpires from the figure that for each value of the concurrence $C$ the time $\tau ∕T_{\mathit{min}}$ needed to reach an orthogonal state may adopt any value, from $\frac{1}{3}\sqrt{10}$ up to a maximum equal to 2. All depicted quantities are dimensionless.