(a) Schematic diagram of PM-QKD. Alice generates a coherent state, | √ µae 2πiκa/d , where κa ∈ {0, 1,. .. , d − 1}. Similarly, Bob generates | √ µ b e 2πiκ b /d. Alice and Bob send the two coherent states which interfere at an untrusted measurement site. (b) Schematic diagram of PM-QKD with d = 2 plus phase randomization. Alice prepares | √ µae i(φa+πκa) and Bob prepares | √ µ b e i(φ b +πκ b ). The two coherent states interfere at an untrusted measurement site. If the phase difference |(φa + πκa) − (φ b + πκ b )| is 0, detector L clicks; if the phase difference is π, detector R clicks. After Eve announces her measurement result, Alice and Bob publicly announce φa and φ b. (c) Equivalent scenario for the postselected signals with φa = φ b. A trusted party (Charlie) prepares |Ψ C , splits it and sends it to both Alice and Bob. Without loss of generality, we consider the case where Alice and Bob both modulate this by the same phase 0 or π to create the systems A and B. If |Ψ C only contains odd-or even-photon number components, we can see that |Ψ0 = |Ψπ.

Contexts in source publication

Context 1

... the two communication parties, Alice and Bob, generate coherent state pulses independently. For a d-phase PM-QKD protocol, Alice and Bob encode their key information κ a , κ b ∈ {0, 1, . . . , d − 1}, into the phases of the coherent states, respectively, and send them to an untrusted measurement site that could be con- trolled by Eve, as shown in Fig. 1(a). Eve is expected to perform interference detection. Define a successful de- tection as the case where one and only one of the two detectors clicks, denoted by L click and R click. This in- terference measurement would match the phases of Alice and Bob's signals. Conditioned on Eve's announcement, Alice and Bob's key information is ...

Context 2

... focus on PM-QKD with d = 2 and phase randomization. That is, Alice and Bob add extra random phases on their coherent state pulses be- fore sending these pulses to Eve. After Eve's announce- ment, Alice and Bob announce the extra random phases and postselect the signals based on the random phases. This PM-QKD scheme is detailed below and shown in Fig. 1(b). For simplicity, by using the name "PM-QKD" in the text below, we refer to the case of d = 2 plus phase ...

Context 3

... provide an intuitive understanding of the manner in which PM-QKD works, we demonstrate its security by considering an equivalent scenario shown in Fig. 1(c). Here, a trusted party (Charlie) prepares a pure state |Ψ C , splits it using a 50-50 beam splitter, and sends it to Alice and Bob separately. Alice and Bob encode their key information κ a and κ b into systems A and B by modulating the phases, and then they send these to Eve who is supposed to tell whether |κ a − κ b | = 0 or 1. Thus, ...

Context 4

... The phase sifting condition φ a = φ b = φ is equivalent to imagining that Charlie em- ploys a source state of |Ψ C = | √ µe iφ C in Fig. 1(b). For a phase-randomized state | √ µe iφ C , it is equivalent ...

Context 5

... the equivalent scenario considered above, shown in Fig. 1(b), a trusted party Charlie is introduced. We need to emphasize that the virtual Charlie will be removed in the real implementation in Sec. IV. If Charlie does exist, Eve may inject some probes after Charlie's out- puts, and then she measures them at the output of Al- ice and Bob to learn their operations. This is the main problem of ...

Context 6

... that the virtual Charlie will be removed in the real implementation in Sec. IV. If Charlie does exist, Eve may inject some probes after Charlie's out- puts, and then she measures them at the output of Al- ice and Bob to learn their operations. This is the main problem of detection-device-independent QKD [26,27]. In the PM-QKD protocol shown in Fig. 1(a), Alice and Bob can simply isolate their light source and modulators in an optical circulator to prevent such Trojan-horse- like attacks. Hence, the PM-QKD scheme, like other MDI-QKD schemes, is secure against Trojan-horse-like ...

Context 7

... we address a few practical issues. In the protocol shown in Fig. 1, Alice and Bob only retain their signals when their announced phases, φ a and φ b are either ex- actly the same or with a π difference. However, since the announced phases are continuous, the successful sifting probability tends to zero. Moreover, we assume that Al- ice's and Bob's laser sources are perfectly locked, such that their ...

Context 8

... are a few interesting directions on PM-QKD. First, it is interesting to work out the security of the general d-phase PM-QKD protocol shown in Fig. 1(a) with and without phase randomization. Meanwhile, in the above discussions, PM-QKD in Fig. 1(b) is treated as a single-basis scheme with phase randomization. In a dual viewpoint, we can regard the different global phases φ a , φ b as different bases and naturally treat the phase- sifting step as basis-sifting. This is interesting, ...

Context 9

... are a few interesting directions on PM-QKD. First, it is interesting to work out the security of the general d-phase PM-QKD protocol shown in Fig. 1(a) with and without phase randomization. Meanwhile, in the above discussions, PM-QKD in Fig. 1(b) is treated as a single-basis scheme with phase randomization. In a dual viewpoint, we can regard the different global phases φ a , φ b as different bases and naturally treat the phase- sifting step as basis-sifting. This is interesting, since it shows the advantage of QKD using multi-nonorthogonal bases. Moreover, this multibases ...

Context 10

... two random bits κ a , β a as the key and the random choice of the X or Y basis, respectively, and then generates a coherent pulse | µ/2e i(πκa+πβa/2) A . Similarly, Bob generates | µ/2e i(πκ b +πβ b /2) B . They send their coherent pulses to Eve, who is supposed to perform an interference mea- surement and announce the detection results [ Fig. 10(a)]. After Eve's announcement, Alice and Bob announce the basis information β a , β b and perform basis ...

Context 11

... encoding QKD protocol, namely TF-QKD [16]. As shown in Fig. 10(b), Alice generates two random bits κ a , β a as the key, chooses randomly the X or Y basis, and modulates another random phase φ a for the phase randomization in the decoy-state method. She generates a coherent pulse | µ/2e i(πκa+πβa/2+φa) A . Similarly, Bob generates a coherent pulse | µ/2e i(πκ b +πβ b /2+φ b ) B . They send their ...