Schematic and theory

The delayed-choice decoherence suppression scenario is schematically shown in Fig. 1a. A two-qubit entangled state, , is prepared at the time t=0 and sent to Alice and Bob with temporal delays and , respectively. At time t D , Bob’s qubit suffers from Markovian amplitude damping decoherence15, which is described by a quantum map: , where D is the magnitude of amplitude damping, and subscript S (E) refers to system (environment). As a result, the two-qubit state becomes mixed, causing reduced entanglement quantified by concurrence, C d

Figure 1: Scheme for delayed-choice decoherence suppression. (a) A two-qubit entangled state is prepared and sent to Alice and Bob. In Bob’s quantum channel, amplitude damping decoherence of strength D is present at time t D , causing reduction of entanglement between the two qubits. Bob performs the RM on his qubit after the decoherence. Alice’s decision whether to suppress the decoherence, by applying the WM on her qubit, may be made after the decoherence or even after the detection of Bob’s qubit. (b) Experimental schematic of delayed-choice decoherence suppression. BP, Brewster’s angle glass plate; BS, non-polarizing beam splitter; HWP, half-wave plate; PBS, polarizing beam splitter; Pol, polarizer; QWP, quarter-wave plate. Full size image

Bob’s reversing measurement (RM), applied immediately after the decoherence, is represented as , where and p r is strength of the RM. Alice’s decision at time t W whether to suppress the decoherence, by applying the WM on her qubit, may be made after the decoherence (t W >t D ) or even after the detection of Bob’s qubit (t W >t B ). Alice’s WM is represented as , where and p is WM strength. The reversing measurement strength is chosen to be p r =p+D(1−p) (refs 20, 21, 23). After Alice’s WM and Bob’s RM, entanglement in the two-qubit is quantified by concurrence C r (H.-T.L., J.-C.L., K.-H.H. and Y.-H.K., manuscript in preparation),

Note that C r >C d that indicates that the delayed-choice decoherence suppression scheme can successfully circumvent Markovian amplitude damping decoherence. It is worth pointing out that, since the WM and RM are both non-unitary, the success probability of our scheme is less than unity. The success probability of the delayed-choice decoherence suppression scheme is (refs 21, 23).

Experimental implementation

The experimental schematic of delayed-choice decoherence suppression is shown in Fig. 1b. The qubit is encoded in a polarization state of a single-photon: |0›≡|H›, |1›≡|V›, where |H› is horizontal polarization and |V› is vertical polarization. The initial two-qubit entangled state (|Φ› with ) is prepared by using type-I spontaneous parametric down conversion from a 6-mm thick β-BaB 2 O 4 crystal24. The photons are frequency filtered by a set of interference filters with 5 nm bandwidth. Optical delays and are implemented with single-mode fibres (SMF). Note that wave plates are used to compensate polarization rotation by SMFs at each SMF output. The Markovian amplitude damping decoherence (D) is set up with a displaced Sagnac interferometer21,23. The WM and the RM are implemented with wave plates and Brewster’s angle glass plates25. The final two-qubit state is analysed with wave plates and polarizers via two-qubit quantum state tomography23.

We implement the delayed-choice decoherence suppression scheme in two configurations, space-like separation and time-like separation, by varying the temporal delays and . The space–time diagrams for the two configurations are shown in Fig. 2. First, in Fig. 2a, we set up the temporal delays such that Alice’s WM and Bob’s decoherence events are in space-like separation. To make sure that the delayed-choice is indeed made after the decoherence itself, we need to consider the timing resolution of the detector (0.35 ns), the coincidence time window for measuring the joint detection events (2.0 ns) and the physical dimensions of the apparatus implementing WM, RM and D. The times for the photon to traverse the apparatus implementing WM, RM and D are 0.10, 0.33 and 1.0 ns, respectively. The overall timing uncertainty is thus 3.8 ns. Since Alice’s WM is made 5.3 ns after the decoherence event, it can be guaranteed that no information about Alice’s choice can be transferred to Bob at the time of decoherence. Furthermore, Alice’s WM and Bob’s decoherence are physically separated by L=2.8 m, so that the time difference between the two events is shorter than the time at which light travels between them (5.3 ns<L/c=9.3 ns). The two events are, thus, in space-like separation as neither of the events are within the forward light cones of each other, see Fig. 2a. This ensures that no causal relationship, that is, no classical communication, can be established between the two events in this setting.

Figure 2: Space–time diagrams for space-like and time-like configurations. The two-qubit entangled state generation event is marked as a red star at the origin. The spatial separation between the two events, that is, the decoherence on Bob’s qubit and WM on Alice's qubit, is L=2.8 m. The shaded regions represent forward light cones of the events. (a) The two events are space-like separated. The temporal difference between the two events (5.3 ns) is shorter than the time light travels between them (L/c=9.3 ns). The two events are thus not in a causal relation, that is, no classical communication is possible between the two events. (b) The two events are time-like separated: WM on Alice’s qubit is in the time-like future of the decoherence event on Bob’s qubit. Full size image

Second, we set up the apparatus such that Alice’s WM is in time-like future of the decoherence event on Bob, see Fig. 2b. Experimentally, we increase by inserting a 400-m fibre spool on Alice’s side to achieve . As with the space-like separation depicted in Fig. 2a, Alice’s WM is made sufficiently after the decoherence itself, hence no information about Alice’s choice can be sent back to Bob’s decoherence event. In the time-like separation, however, it is possible for Bob to send classical information about the decoherence to Alice, possibly affecting Alice’s WM.