Abstract
We consider the counterfactual protocol proposed in Phys. Rev. Lett., 103, 230501 (2009) within a device independent framework and show how its security can easily be compromised. Capitalising on the fact that the protocol is based on the use of a single photon entanglement phenomenon, we propose an equivalent protocol. It can be made secure within such a pessimistic framework against a supra-quantum Eve limited only by the no-signalling principle. The equivalence the protocol demonstrates the possibility of device independent framework for counterfactual quantum cryptography.
Highlights
We consider the counterfactual protocol proposed in Phys
The single photon entanglement refers to a phenomenon of entanglement between the photon numbers in two spatially separated modes where one mode is connected to Bob as the quantum channel while the other remains with Alice[3]
We identify the essential source of insecurity and propose a modification and subsequently a proper counterfactual QKD (CQKD), which would be secure within a device independent framework
Summary
Let us begin with a review of the CQKD framework[2], which security we analyse here. It must be noted that this description is completely equivalent to the one proposed by ref. 2; though it has, to a certain extent, some simplicity in its description. The single-photon pulse passes through a 50:50 beam splitter (BS1) in which the output results in the following state (in accordance with Alice’s choice of polarisation state): ΨH=. Where 0 i denotes the vacuum state with i ∈ A, B represent the path towards Alice’s mirror M1 and Bob’s site, respectively. The pulse that travels through path B is reflected by M2 before entering the input port of the polarising beam splitter (PBS) on Bob’s site. The PBS is configured such that, if Bob’s choice of polarisation is not equal to Alice, the PBS will transmit the pulse towards BS2 and the split pulse that travels in the two modes are recombined at beam splitter, BS2. If the incoming polarisation is the same with Bob’s choice, the pulse will be reflected towards Bob’s measurement setting which consists of photon detector, D3. The raw key will be extracted from the event in which detector D2 clicks
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