Quantum circuit for optimal eavesdropping in quantum key distribution using phase-time coding
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LECULES, OPTICS
Quantum Circuit for Optimal Eavesdropping in Quantum Key Distribution Using Phase–Time Coding D. A. Kronbergc and S. N. Molotkova, b, c a
Institute of SolidState Physics, Russian Academy of Sciences, Chernogolovka, Moscow oblast, 142432 Russia b Academy of Cryptography of the Russian Federation, Moscow, 121552 Russia c Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119899 Russia email: [email protected] Received December 28, 2009
Abstract—A quantum circuit is constructed for optimal eavesdropping on quantum key distribution proto cols using phase–time coding, and its physical implementation based on linear and nonlinear fiberoptic components is proposed. DOI: 10.1134/S1063776110070046
initial state |A〉 E (see Fig. 1). The ancilla is coupled to each signal state |ψ〉 B transmitted from Alice to Bob over a quantum communication channel. The evolu tion of the coupled system (ancilla + signal) is described by a unitary operator UBE:
1. INTRODUCTION Quantum key distribution (QKD) systems are designed for exchanging secret keys over public chan nels open to any modification. Whereas the security of key distribution systems using classical signals is based on computational complexity (as in RSAtype public key cryptosystems [1]) or technological limitations of an eavesdropper (Eve), both eavesdropping detection and the security of the final key in QKD protocols are guaranteed by fundamental laws of quantum mechan ics (provided that the error rate on the receiver side does not exceed a certain maximum tolerable value) [2–4]. Any measurement on a quantum signal state changes the state being measured, causing errors detected by the receiver (Bob). Therefore, Eve should try to gain the maximum information (conditioned on Bob’s error rate) that can be extracted from signal states under the limitations imposed by fundamental principles of quantum mechanics. In the past years, it was realized and rigorously proved (e.g., see [5] and references therein) that col lective attack is the strongest type of eavesdropping attack on the quantum channel1 in QKD protocols where each signal state is prepared by the sender (Alice) independently [5, 7, 8]. In an attack of this type,2 Eve prepares an auxiliary system (ancilla) in an
U BE ( |ψ〉 B ⊗ |A〉 E ) = |Ψ〉 BE .
(1)
The result is an entangled state of the signal and the ancilla, |Ψ〉 BE ≠ |ψ〉 B ⊗ |A〉 E (see Fig. 1). Eve forwards the modified signal to Bob and stores the ancilla state in a quantum memory.3 After the transmission of quantum states and Bob’s measurements have been completed, Alice and Bob use a public classical com munication channel (see Fig. 1) to reconcile their bases, correct errors, and compress the sifted key by privacy amplification. Finally, Eve performs measure ments on her stored states, using information exchanged over the classical channel. The amount of private information accessible to Eve can be maxi mized by performing collective measurements on all states stored in her quantum memory; i
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