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arXiv:1007.2588 · Physical Review A

Experimental quantum-cryptography scheme based on orthogonal states

Alessio Avella, G. Brida, Ivo Pietro Degiovanni, Marco Genovese, Marco Gramegna, P. Traina

Published Dec 10, 2010• 39 citations
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Abstract

Since, in general, nonorthogonal states cannot be cloned, any eavesdropping attempt in a quantum-communication scheme using nonorthogonal states as carriers of information introduces some errors in the transmission, leading to the possibility of detecting the spy. Usually, orthogonal states are not used in quantum-cryptography schemes since they can be faithfully cloned without altering the transmitted data. Nevertheless, L. Goldberg and L. Vaidman [Phys. Rev. Lett. 75, 1239 (1995)] proposed a protocol in which, even if the data exchange is realized using two orthogonal states, any attempt to eavesdrop is detectable by the legal users. In this scheme the orthogonal states are superpositions of two localized wave packets traveling along separate channels. Here we present an experiment realizing this scheme.

DOI
10.1103/physreva.82.062309

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Since, in general, nonorthogonal states cannot be cloned, any eavesdropping attempt in a quantum-communication scheme using nonorthogonal states as carriers of information introduces some errors in the transmission, leading to the possibility of detecting the spy. Usually, orthogonal states are not used in quantum-cryptography schemes since they can be faithfully cloned without altering the transmitted data. Nevertheless, L. Goldberg and L. Vaidman [Phys. Rev. Lett. 75, 1239 (1995)] proposed a protocol in which, even if the data exchange is realized using two orthogonal states, any attempt to eavesdrop is detectable by the legal users. In this scheme the orthogonal states are superpositions of two localized wave packets traveling along separate channels. Here we present an experiment realizing this scheme.
Since, in general, non-orthogonal states cannot be cloned, any eavesdropping attempt in a Quantum Communication scheme using non-orthogonal states as carriers of information introduces some errors in the transmission, leading to the possibility of detecting the spy. Usually, orthogonal states are not used in Quantum Cryptography schemes since they can be faithfully cloned without altering the transmitted data. Nevertheless, L. Goldberg and L. Vaidman [Phys. Rev. Lett. 75 (7), pp. 12391243, 1995] proposed a protocol in which, even if the data exchange is realized using two orthogonal states, any attempt to eavesdrop is detectable by the legal users. In this scheme the orthogonal states are superpositions of two localized wave packets which travel along separate channels, i.e. two different paths inside a balanced Mach-Zehnder interferometer. Here we present an experiment realizing this scheme.
We report on our experimental implementation of QKD with orthogonal states. Since, in general, non-orthogonal states cannot be cloned, any eavesdropping attempt in a Quantum Communication scheme using non-orthogonal states as carriers of information introduces some errors in the transmission, leading to the possibility of detecting the spy. Usually, orthogonal states are not used in Quantum Cryptography schemes since they can be faithfully cloned without altering the transmitted data. Nevertheless, L. Goldberg and L. Vaidman proposed a protocol in which, even if the data exchange is realized using two orthogonal states, any attempt to eavesdrop is detectable by the legal users. In this scheme the orthogonal states are superpositions of two localized wave packets travelling along separate channels. Here we describe in detail the first experimental realization of a quantum cryptography system based on orthogonal states and the measures of the main parameters that quantify the quality of the system. Our results demonstrate the possibility of achieving a QKD transmission based on orthogonal state with a Quantum Bit Error Rate comparable with more common secure QKD systems. Therefore, it provides a significant hint to the discussion on the minimal quantum resources necessary for the implementation of quantum tasks overcoming classical limits.
In recent years Quantum Key Distribution (QKD) has emerged as the most paradigmatic example of Quantum technology allowing the realization of intrinsically secure communication links over hundreds of kilometers. Beyond its commercial interest QKD also has high conceptual relevance in the study of quantum information theory and the foundations of quantum mechanics. In particular, the discussion on the minimal resources needed in order to obtain absolutely secure quantum communication is yet to be concluded. Here we present an overview on our last experimental results concerning two novel quantum cryptographic schemes which do not require some of the most widely accepted conditions for realizing QKD. The first is Goldenberg-Vaidman protocol \cite{v}, in which even if only orthogonal states (that in general can be cloned without altering the state) are used, any eavesdropping attempt is detectable. The second is N09 protocol \cite{no} which, being based on the quantum counterfactual effect, does not even require any actual photon transmission in the quantum channel between the parties for the communication.
The security of quantum cryptography is guaranteed by the no-cloning theorem, which implies that an eavesdropper copying transmitted qubits in unknown states causes their disturbance. Nevertheless, in real cryptographic systems some level of disturbance has to be allowed to cover, e.g., transmission losses. An eavesdropper can attack such systems by replacing a noisy channel by a better one and by performing approximate cloning of transmitted qubits which disturb them but below the noise level assumed by legitimate users. We experimentally demonstrate such symmetric individual eavesdropping on the quantum key distribution protocols of Bennett and Brassard (BB84) and the trine-state spherical code of Renes (R04) with two-level probes prepared using a recently developed photonic multifunctional quantum cloner [Lemr et al., Phys. Rev. A 85, 050307(R) (2012)]. We demonstrated that our optimal cloning device with high-success rate makes the eavesdropping possible by hiding it in usual transmission losses. We believe that this experiment can stimulate the quest for other operational applications of quantum cloning.
Quantum cryptography protocols using entangled qubit pairs can increase the rate and security of information exchange through a quantum channel. Usually those protocols are non-deterministic, i.e. a classical bit is encoded in a quantum state, but the actual bit value cannot be determined. Therefore they request the transmission of additional information through a public channel. By contrast, the ping-pong coding scheme based on entangled photons allows for deterministic and direct key distribution. No qubit has to be discarded and information can be decoded without the need for a subsequent transmission of additional information. Communication through a public channel nevertheless is necessary to ensure asymptotical security against arbitrary eavesdropping attacks.
It is shown that maximally efficient protocols for secure direct quantum communications can be constructed using any arbitrary orthogonal basis. This establishes that no set of quantum states (e.g. GHZ states, W states, Brown states or Cluster states) has an advantage over the others, barring the relative difficulty in physical implementation. The work provides a wide choice of states for experimental realization of direct secure quantum communication protocols. We have also shown that this protocol can be generalized to a completely orthogonal-state-based protocol of Goldenberg–Vaidman (GV) type. The security of these protocols essentially arises from duality and monogamy of entanglement. This stands in contrast to protocols that employ nonorthogonal states, like Bennett–Brassard 1984 (BB84), where the security essentially comes from noncommutativity in the observable algebra.