The invention relates generally to quantum communication (QC). In particular, this invention relates to quantum key distribution using weak measurement of sequentially emitted photons.
Secure communication involves exchange of information between intended communicants, e.g., Alice and Bob, without an eavesdropper, e.g., Eve, from unauthorized interception of the information message. Quantum cryptography represents an example of this process. Such methods include development of conventional quantum key distribution (QKD) protocol. Separately, weak measurements of quantum states have been investigated for various purposes.
The earliest conventional QKD protocol involves a method of securely communicating a private key from one party to another for use in onetime pad encryption. This procedure is documented by Charles Bennett and Gilles Brassard in “Quantum Cryptography: Public Key Distribution and Coin Tossing”, at the International Conference on Computers, Systems & Signal Processing, December 1984, and commonly referred to as BB84. See http://www.research.ibm.com/people/b/bennetc/bennettc198469790513.pdf for details.
The weak value of an observable of a quantum system at an intermediate time is equally determined by both the initial state of the system and the state resulting from a final projective measurement. In this manner, the weak value contains a signature of the correlations between past and future states of the system. The time-symmetric formulation of quantum mechanics first introduced the concepts of weak measurement and weak values. See Y. Aharonov et al. “How . . . measurement . . . ”, Phys. Rev. Ltrs., 60 (1988) 1351; Y. Aharonov et al., “Properties of a quantum system . . . ” Phys. Rev. A, 41 (1990) 11; B. Reznik et al., “On the time symmetric formulation . . . ”, Phys. Rev. A, 52 (1995) 2538. While debate continues over the meaning of weak values, their utility has been experimentally demonstrated in many areas, particularly in relation to Hardy's Paradox. See Y. Aharonov et al., “Revisiting Hardy's Paradox . . . ”, Phys. Ltrs. A, 301 (2002) 130; K. Yokota et al., “Direct observation . . . ”, New J. of Phys., 11 (2009) 033011; J. Lundeen et al., “Experimental Joint Weak Measurement . . . ”, Phys. Rev. Ltrs., 102 (2009) 020404; D. Starling et al., “Precision frequency measurements”, Phys. Rev. A, 82 (2010) 062822; and N. Brunner et al., “Measuring small longitudinal phase shifts . . . ”, Phys. Rev. Ltrs., 105 (2010) 010405.