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Experimental security analysis a four-photon private state

Krzysztof Dobek, Michał Karpiński, Rafał Demkowicz-Dobrzański, Konrad Banaszek, Paweł Horodecki

Published Jan 1, 2011• 0 citations
Publisher

Abstract

We report experimental generation of a noisy entangled four-photon state that exhibits a separation between secure key contents and distillable entanglement. This difference is exposed by a detailed analysis of its privacy properties.
DOI
10.1364/cleo_at.2011.jtuf5

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We report experimental generation of a noisy entangled four-photon state that exhibits a separation between the secure key contents and distillable entanglement, a hallmark feature of the recently established quantum theory of private states. The privacy analysis, based on the full tomographic reconstruction of the prepared state, is utilized in a proof-of-principle key generation. The inferiority of distillation-based strategies to extract the key is exposed by an implementation of an entanglement distillation protocol for the produced state.
We provide a simple security proof for prepare and measure quantum key distribution protocols employing noisy processing and one-way postprocessing of the key. This is achieved by showing that the security of such a protocol is equivalent to that of an associated key distribution protocol in which, instead of the usual maximally entangled states, a more general private state is distilled. In addition to a more general target state, the usual entanglement distillation tools are employed (in particular, Calderbank-Shor-Steane-like codes), with the crucial difference that noisy processing allows some phase errors to be left uncorrected without compromising the privacy of the key.
Hereunder, we study the class of irreducible private states that are private states from which all the secret content is accessible via measuring their key part. We provide the first protocol which distills key not only from the key part, but also from the shield if only the state is reducible. We prove also a tighter upper bound on the performance of that protocol, given in terms of regularized relative entropy of entanglement instead of relative entropy of entanglement previously known. This implies in particular that the irreducible private states are all strictly irreducible if and only if the entangled but key-undistillable states ('entangled key-undistilable states') exist. In turn, all the irreducible private states of the dimension 4 ⨂ 4 are strictly irreducible, that is, after an attack on the key part they become separable. Provided the bound key states exist, we consider different subclasses of the irreducible private states and their properties. Finally we provide a lower bound on the trace norm distance between key-undistillable states and private states, in sufficiently high dimensions.