Quantum Information Put into Practice
Allowing information to be carried by physical systems described by the rules of quantum physics led to a deep questioning of the theory of information. While many questions remain open, the emerging field of quantum information already led to several rem
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Quantum Information Put into Practice
Allowing information to be carried by physical systems described by the rules of quantum physics led to a deep questioning of the theory of information. While many questions remain open, the emerging field of quantum information already led to several remarkably concrete applications which would not exist otherwise. Here we present a modest contribution to the analysis of the security of quantum key distribution (QKD), as well as a protocol which can be used to question a database with some level of security.
8.1 Memoryless Attack on the 6-State QKD Protocol Quantum key distribution (QKD) allows two parties who share an initial secret key of finite size, to increase its size by exchanging quantum and classical signals through an untrusted environment. The new key generated in this way can then be used for any cryptographic application [1], such as secure transmission of a secret message, a task which is not known to be possible by classical means. Standard security proofs for QKD protocols aim at relying on the weakest possible assumptions. For instance, it is usually admitted that a possible eavesdropper is not constrained by technological limitations but only by the laws of physics. Such assumptions allow one to derive strong security bounds. However, if a particular circumstance happens to restrict further the possible action of an eavesdropper, more refined security analyses taking these limitations into account can allow the trusted parties to improve the efficiency of their protocol. Motivated by the effort put in several groups worldwide [2–5] to implement quantum memories preserving coherence and population over more than several miliseconds, we consider the case in which the eavesdropper has no access to a long-lasting quantum memory. Security proofs applicable in this scenario have been presented in [6] for the BB84 protocol, and more recently for the BB84, SARG and 6-state QKD protocols
J.-D. Bancal, On the Device-Independent Approach to Quantum Physics, Springer Theses, DOI: 10.1007/978-3-319-01183-7_8, © Springer International Publishing Switzerland 2014
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8 Quantum Information Put into Practice
[7]. Here we give a tighter bound than [7] for the achievable secure key-rate of the prepare-and-measure 6-state protocol when the eavesdropper has no access to any quantum memory.
8.1.1 The 6-State Protocol The 6-state protocol for quantum key distribution [8] runs in 4 parts. Distribution: Alice prepares one of the six qubit states ρi = |ψi ψi | chosen uniformly at random within |0 + |1 |0 − |1 , |ψ4 = √ , √ 2 2 |0 + i|1 |0 − i|1 , |ψ6 = |ψ5 = . √ √ 2 2
|ψ1 = |0, |ψ2 = |1, |ψ3 =
(8.1.1)
She remembers the basis b A = i−1 2 corresponding to this state as well as the bit X = i − 1 mod 2. Alice sends this state to Bob through a public quantum channel. Upon receival of the system from Alice, Bob measures it in either the x, y, or z basis. He remembers his choice of basis b B = 0, 1, 2 as well as the result of his measurement Y = 0, 1
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