Abstract
We present a protocol for quantum key distribution using discrete modulation of coherent states of light. Information is encoded in the variable phase of coherent states which can be chosen from a regular discrete set ranging from binary to continuous modulation similar to phase-shift keying in classical communication. Information is decoded by simultaneous homodyne measurement of both quadratures and requires no active choice of basis. The protocol utilizes either direct or reverse reconciliation both with and without postselection. We analyze the security of the protocol and show how to enhance it by the optimal choice of all variable parameters of the quantum signal.
Highlights
Quantum key distribution (QKD) is a procedure of information exchange between two parties, the sender Alice and the receiver Bob, which allows one to distribute absolutely secure data between them (Dusek et al 2006, Gisin et al 2002, Scarani et al 2009)
The distinctive part of QKD with respect to classical communication is the use of a quantum information channel, where the signal is protected from unauthorized duplication Bennett and Brassard 1984, Dieks 1982, Ekert 1991, Wooters and Zurek 1982)
The information signal can be described by discrete variables (DV) or by continuous variables (CV) (Cerf et al 2007), physically the signal can be of various kinds: single photons (Bennett and Brassard 1984), weak coherent pulses (Bennett 1992), squeezed states (Hillery 2000, Ralph 1999) and other systems where a signal possesses essentially quantum properties
Summary
Quantum key distribution (QKD) is a procedure of information exchange between two parties, the sender Alice and the receiver Bob, which allows one to distribute absolutely secure data between them (Dusek et al 2006, Gisin et al 2002, Scarani et al 2009). The further enhancement can be done with help of two-way communication (Pirandola et al 2008) Another interesting option for improving characteristics of QKD is to consider discrete alphabets (Heid and Lütkenhaus 2006, Namiki and Hirano 2003) instead of Gaussian ones. Having in mind the idea of improving the properties of DV QKD by use of more symmetric alphabets with higher number of letters (Sych et al 2005), we present a new CV QKD protocol which generalizes previous ones with discrete modulation (Heid and Lütkenhaus 2006, Lorenz et al 2004, Namiki and Hirano 2003). The protocol employs an alphabet with N coherent states |αk = |aei(2π/N)k which have relative phases (2π/N )k and a fixed amplitude a In classical communication, this type of encoding is known as phase-shift keying (PSK). We perform a security analysis of the proposed protocol for lossy but noiseless quantum channels, providing full optimization of all parameters of the protocol, and show how the number of letters affect the key rate
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