A quantum cryptography scheme based on entanglement between a single particle state and a vacuum state is proposed. The scheme utilizes linear optics devices to detect the superposition of the vacuum and single particle states. Existence of an eavesdropper can be detected by using a variant of Bell's inequality.Entanglement could be exploited in many interesting applications, including quantum teleportation [1, 2] and quantum cryptography [3]. Discussion on the nonlocal nature (entanglement) of quantum systems was initiated by Einstein, Podolsky and Rosen (EPR) [4] and later extended by Bell [5][6][7]. Since then many authors have studied the physical meaning of the nonlocality of a single particle [8][9][10][11][12][13][14][15]. Generally, quantum cryptography schemes based on entanglement (EPR-based schemes) use two or more spatially separated particles possessing correlated properties as the source of entanglement. However, recent developments in experimental techniques [16][17][18] for generating and manipulating single photons have made quantum information processing utilizing single particle entanglement feasible. Here, single particle entanglement refers to entanglement of a single particle state and the vacuum state [19].In the present study, we developed a quantum cryptography scheme based on single particle entanglement. The propopsed scheme utilizes linear optics to detect a superposition of the vacuum state and a single photon state. A variant of Bell's inequality suggested by Peres [20] is used for the detection of eavesdropping. In fact, the idea of quantum cryptography using single particle entanglement is not new. Examples of other approaches that can be considered as quantum cryptography schemes using single particle entanglement are the phase coding scheme of Bennett [21] and Ardehali's scheme based on the delayed choice experiment [22], which uses interferometers. In these double-rail schemes, detection of a particle state is performed by a single observer at a given site. A characteristic feature of our single rail scheme is that both of two space-like separated parties, whom we call Alice and Bob, detect either a single particle or no particle at their respective sites. This characteristic makes our scheme more compatible with the original meaning of quantum nonlocality.We begin with a description of our scheme, which is depicted in Fig. 1. The setup consists of a single photon source (S) and a lossless 50/50 beam splitter (BS 0 ), which generate the single particle entanglement state, and two identical non-deterministic projective measurement devices belonging to Alice and Bob, respectively. Each projective measurement device shown in detail in Fig. 2 itself consists of a lossless 50/50 beam splitter (BS A or BS B ) with a probe state γ|0 + δ|1 and two photon detectors (D Aa , D Ab or D Ba , D Bb ). We assume that every beam splitter induces a sign change in a transmitted beam incident on the black side (Eq. (2)).
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