Figure 1

(a) From left to right, Alice's sequential measurements at times $t_1<t_2<t_3$, respectively. At each $t_k$, Alice performs a measurement, either $x_k$ or ${\overline{x}}_k$. Each measurement has two possible outcomes: 0 and 1. Alice's measurements are such that the state of the two qubits after her measurement is always entangled. (b) From left to right, possible reduced states of Bob's qubit after Alice's measurements at $t_1<t_2<t_3$, respectively. States are represented by nonunit arrows in the equatorial plane of the Bloch sphere. For example, $\overline{1}$ denotes the state when Alice measured ${\overline{x}}_1$ at $t_1$ and obtained outcome 1; $\overline{1}0$ denotes the state when Alice measured ${\overline{x}}_1$ at $t_1$ and $x_2$ at $t_2$ and obtained outcomes 1 and 0, respectively. Bob's states highlighted in purple are those produced in the particular sequence of Alice's measurements and outcomes shown in (a).