Deterministic Entanglement Swapping in a Superconducting Circuit

Entanglement swapping, the process to entangle two particles without coupling them in any way, is one of the most striking manifestations of the quantum-mechanical nonlocal characteristic. Besides fundamental interest, this process has applications in complex entanglement manipulation and quantum communication. Here we report a high-fidelity, unconditional entanglement swapping experiment in a superconducting circuit. The measured concurrence characterizing the qubit-qubit entanglement produced by swapping is above 0.75, confirming most of the entanglement of one qubit with its partner is deterministically transferred to another qubit that has never interacted with it. We further realize delayed-choice entanglement swapping, showing whether two qubits previously behaved as in an entangled state or as in a separable state is determined by a later choice of the type of measurement on their partners. This is the first demonstration of entanglement-separability duality in a deterministic way.

Figure 1

Sketch of entanglement swapping. Initially, $Q_1$ is entangled with $Q_2$ in a Bell state, and $Q_3$ with $Q_4$, but there is no correlation between $Q_1$ and $Q_4$. A joint measurement on $Q_2$ and $Q_3$ in the Bell basis will project $Q_1$ and $Q_4$ to one of four possible Bell states depending on the outcome of the $Q_2\text{−}{Q}_3$ measurement.

Figure 2

Device schematic and pulse sequence. (a) Device schematic. Five superconducting Xmon qubits (labeled from $Q_1$ to $Q_5$) are capacitively coupled to a bus resonator $R$. The frequency of each qubit can be adjusted quickly, enabling the relevant qubit-resonator interaction as well as the resonator-induced qubit-qubit couplings to be effectively switched on and off. (b) Optical image of the device. (c) Experimental sequence. The procedure consists of three parts: Generation of Bell states for qubit pairs $Q_1\text{−}{Q}_2$ and $Q_3\text{−}{Q}_4$ via resonator-mediated $\sqrt{i\mathrm{SWAP}}$ gates following $\pi$ pulses applied to $Q_1$ and $Q_3$; complete Bell state measurement on $Q_2$ and $Q_3$, achieved by subsequentially applying a dressed-state phase gate on $Q_2$ and $Q_3$ and performing a joint detection in the basis $\{|0_2⟩|0_3⟩,|0_2⟩|1_3⟩,|1_2⟩|0_3⟩,|1_2⟩|1_3⟩\}$; 2-qubit quantum state tomography for $Q_1$ and $Q_4$. The detailed pulse sequence is shown in Fig. S3(a) of the Supplemental Material [32].

Figure 3

Measured $Q_1\text{−}{Q}_4$ density matrices conditional on the four $Q_2\text{−}{Q}_3$ measurement outcomes: (a) $|0_2⟩|0_3⟩$; (b) $|0_2⟩|1_3⟩$; (c) $|1_2⟩|0_3⟩$; (d) $|1_2⟩|1_3⟩$. The results are obtained with the experiment sequence shown in Fig. 2. Each matrix element is characterized by two color bars, one for the real part and the other for the imaginary part. The black wire frames denote the matrix elements of the ideal output states.

Figure 4

Measured $Q_1\text{−}{Q}_4$ density matrices conditional on outcomes of delayed-choice $Q_2\text{−}{Q}_3$ measurement. (a)–(d) Results obtained from the four subsets of data correlated with the outcomes $\{|0_2⟩|0_3⟩,|0_2⟩|1_3⟩,|1_2⟩|0_3⟩,|1_2⟩|1_3⟩\}$ of $Q_2\text{−}{Q}_3$ measurement performed after the dressed-state phase gate. Compared with Fig. 2, the temporal orders of $Q_2\text{−}{Q}_3$ Bell measurement and $Q_1\text{−}{Q}_4$ joint state tomography are inverted, with the experimental pulse sequence shown in the Supplemental Material [32]. (e)–(h) Results obtained from the four subsets of data correlated with the outcomes of the later $Q_2\text{−}{Q}_3$ measurement without the dressed-state phase gate.