Fig. 1. Quantum information transfer between a two-level and a four-level quantum systems. (a) Quantum information transfer from a four-level system B to a two-level system A. (b) Quantum information transfer from a two-level system A to a four-level system B.

Fig. 2. Schematic diagrams for quantum information transfer. (a) The quantum information transfer from one qubit to another. The CX gate entangles qubit A, which initially contains no quantum information, and qubit B, which initially contains one qubit of unknown quantum information. The projective measurement on B removes quantum information from B, thus transferring the one qubit of quantum information to A. After the feedforward unitary operation, the quantum information originally stored in B is restored in A, thus completing the quantum information transfer. (b) The quantum information transfer from a ququart to a qubit. The initial state of ququart B contains two qubits of unknown quantum information, while qubit A initially contains no quantum information. After entangling A and B using a CX4 gate, where X4 swaps |0⟩ and |2⟩ (|1⟩ and |3⟩), a projective measurement is applied on B to measure whether it is in the subspace spanned by |0⟩ and |1⟩ or the subspace spanned by |2⟩ and |3⟩. Based on the measurement result, feedforward unitary operations are applied on A and B, and the final state of A and B contains the two qubits of quantum information originally stored in B, thus completing the quantum information transfer from ququart B to qubit A. (c) The quantum information transfer from a qubit to a ququart. Two qubits of unknown quantum information are initially distributed over qubit A and ququart B. After applying a CX4 gate on A and B, a projective measurement is applied on A and a feedforward unitary operation based on the measurement result is applied on B. The final state of B contains the two qubits of quantum information originally distributed over both A and B, thus completing the quantum information transfer from qubit A to ququart B.

Fig. 3. Experimental layout for quantum information transfer between a qubit and a ququart. (a) Optical CX4 gate. Two photons a1 and a2 are used to encode qubit A, where |0⟩A=|H⟩a1|H⟩a2 and |1⟩A=|V⟩a1|V⟩a2. Photon b is used to encode ququart B, where |0⟩B=|H0⟩b, |1⟩B=|H1⟩b, |2⟩B=|V0⟩b, and |3⟩B=|V1⟩b. H0 (H1) denotes photon in the upper (lower) spatial mode with horizontal polarization and V0 (V1) denotes photon in upper (lower) spatial mode with vertical polarization. A CX4 gate between the control qubit A and the target ququart B is decomposed into a CX02 gate and a CX13 gate. The CX02 (CX13) gate is equivalent to a polarization CNOT gate operating on photon a1 (a2) and photon b in the upper (lower) path. (b) Experimental setup. A pulsed ultraviolet (UV) laser is focused on two beta-barium borate (BBO) crystals and produces two photon pairs a1–a2 and b−t. By tuning HWP1 and QWP1, the first photon pair, a1–a2, is prepared at ϵ|H⟩a1|H⟩a2+ζ|V⟩a1|V⟩a2, which serves as the initial state of system A. BD1 and its surrounding waveplates (HWP2, QWP2, HWP3, QWP3, HWP4 and QWP4) prepare photon b at η|H0⟩b+κ|H1⟩b+λ|V0⟩b+μ|V1⟩b, which serves as the initial state of system B. The two polarization CNOT gates based on PPBS are used to implement the optical CX4 on system A and system B. BD2 and its surrounding waveplates (QWP5, HWP5, HWP at 0°, HWP at 45°, QWP6 and HWP6) are used to analyze the ququart state.

Fig. 4. Experimental results for the quantum information transfer from ququart B to qubit A. (a)–(e) Measurement results of the final state of A and B for the initial states |ϕ1⟩B, |ϕ2⟩B,…, and |ϕ5⟩B. Here |±⟩=12(|0⟩±|1⟩) and |±i⟩=12(|0⟩±i|1⟩). (f) Summary of the fidelities of the partial quantum state transfer for the five initial states. The average achieved fidelity of 0.7897±0.0109 overcomes the classical bound of 2/3. The error bars (SD) are calculated according to propagated Poissonian counting statistics of the raw detection events.

Fig. 5. Experimental results for the quantum information transfer from qubit A to ququart B. (a)–(i) Measurement results of the final state of B for the initial states |ψ1⟩AB, |ψ2⟩AB,…, and |ψ9⟩AB. Here |±⟩=12(|0⟩±|1⟩) and |±i⟩=12(|0⟩±i|1⟩). (j) Summary of the fidelities of the general quantum state transfer for the nine initial states. The average achieved fidelity of 0.8151±0.0074 overcomes the classical bound of 2/3. The error bars (SD) are calculated according to propagated Poissonian counting statistics of the raw detection events.

Fig. 6. Experimental setup for generating two photon pairs.

Fig. 7. HOM interference at the PPBS for an |HH⟩ input. In case of perfect interference, the count rate should drop down to 20%, leading to a theoretically achievable dip visibility of 80%.

Fig. 8. CX4 gate with linear optics. (a) The standard optical CX4 gate. (b) The simplified optical CX4 gate.

Fig. 9. State analyzer for a single-photon ququart state with both polarization and spatial degrees of freedom.

Fig. 10. (a) The Merge operation. The quantum circuit for merging the quantum information of a qubit and a d-dimensional qudit into a 2d-dimensional qudit. (b) The Split operation. The quantum circuit for splitting the quantum information of a 2d-dimensional qudit to a qubit and a d-dimensional qudit. (c) Implementing a three-qubit quantum gate using Merge and Split operations.