Experimental detection of qubit-environment entanglement without accessing the environment

Decoherence is an unavoidable effect of the quantum system coupled to an environment, which leads to the system evolving from a pure state to a mixed one. A critical issue here is that the reduction of purity is quantum or classical, which corresponds to whether or not entanglement is generated between the system and environment. We report a proof-of-principle experimental investigation of such entanglement in a simple but paradigmatic case, in which a qubit system interacts with a pure dephasing channel. The pure dephasing process is realized in a linear photonic system, and the experiment is a validation in a very controlled setting. By adopting previous methods to detect qubit-environment entanglement, we prove that such entanglement can be detected by performing local measurements on only one subsystem, even when the other subsystem in the pair cannot be detected. Our experiment paves the way for investigating features of open quantum system dynamics.

Figure 1

Illustration of detection of QEE generated during pure dephasing. (a) A qubit (Q) interacts with environment (E) for time $\tau$. The task is to detect whether QEE is generated at time $\tau$. (b) The initial qubit is prepared as $|+\rangle$, and measurements are performed on both the qubit and the environment. QEE can be detected by the concurrence, which is obtained by the reconstructed states of the qubit and the environment. (c) The initial qubit is prepared as $|0\rangle$ or $|1\rangle$, and measurement is implemented only to the environment. QEE can be detected by a change in the state of the environment. (d) The initial qubit is prepared as $|0\rangle$ or $|1\rangle$, and then transformed into $|+\rangle$. After extra time $t_1$, the measurement is implemented only to the qubit. QEE is detected by a change in the qubit state. (e) The qubit is initially prepared as $|0\rangle$ or $|1\rangle$, and then transformed into $|0\rangle$ after time $\tau$. After extra time $t_0$, the state is transformed into $|+\rangle$. After time $t_1$, the measurement is implemented only to the qubit. QEE can be detected via a change of the qubit state even for the special environment state.

Figure 2

Experimental setup for the method to detect QEE generated during pure dephasing based on the comparison of qubit states, including state preparation, evolution $U\left(\tau \right)$, qubit rotation, extra evolution $U\left(t_1\right)$, and measurement of qubits. Evolution of the qubit and environment is implemented via rotating the polarizations of the photons in different spatial modes. Qubit rotation is realized by swap operations for basis transformation (between the polarizations and spatial modes of the photons) and a rotation on the polarizations of the photons. Measurements of the qubit state are projective measurement on the spatial modes of photons, which are realized by a swap operation for basis transformation from the spatial modes to polarizations and projective measurements on the polarizations of photons via wave plates and a BD. For methods based on entanglement monotone and comparing environment state, the measurement device in the inset (a) is performed after evolution $U\left(\tau \right)$. The inset (b) shows the details for the swap operation.

Figure 3

Experimental results. Detection of QEE through three estimates: Concurrence (red pentagons), the distance between two states of environment (yellow squares), and the distance between two qubit states (blue triangles). (a) QEE estimate vs the evolution time $\tau$. The initial state of environment is $|+\rangle$. (b) QEE estimate vs the parameter of the initial state of environment. The evolution time is fixed, $\tau =\pi /4$. All quantities plotted are dimensionless. Error bars (too small to show) indicate the statistical uncertainty and are estimated via assuming the Poissonian statistics.

Figure 4

Experimental results. (a) QEE detection through comparing qubit states for different time $t_1$. In this case, we fix the evolution time $\tau =3\pi /4$ and choose two different initial states of the environment: A pure state $|+\rangle$ (blue triangles) and a maximal mixed state (black stars). (b) QEE detection through comparing qubit states with additional evolution $U\left(t_0\right)$ after the evolution $U\left(\tau \right)$. In this case, we fix the evolution time $\tau =\pi /4$ and the extra time $t_1=\pi /4$, and choose two different initial states of the environment: A pure state $|0\rangle$ (blue triangles) and a maximal mixed state (black stars). All plotted quantities are dimensionless. Error bars indicate the statistical uncertainty and are estimated via assuming the Poissonian statistics.