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arXiv:quant-ph/9912105 · Physical Review Letters

Entangled State Quantum Cryptography: Eavesdropping on the Ekert Protocol

D. Naik, Charles G. Peterson, Andrew G. White, Andrew J. Berglund, Paul G. Kwiat

Published May 15, 2000• 390 citations
arXivHTMLPDF

Abstract

Using polarization-entangled photons from spontaneous parametric down-conversion, we have implemented Ekert's quantum cryptography protocol. The near-perfect correlations of the photons allow the sharing of a secret key between two parties. The presence of an eavesdropper is continually checked by measuring Bell's inequalities. We investigated several possible eavesdropper strategies, including pseudo-quantum-nondemolition measurements. In all cases, the eavesdropper's presence was readily apparent. We discuss a procedure to increase her detectability.

DOI
10.1103/physrevlett.84.4733

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Using polarization-entangled photons from spontaneous parametric down-conversion, we have implemented Ekert's quantum cryptography protocol. The near-perfect correlations of the photons allow the sharing of a secret key between two parties. The presence of an eavesdropper is continually checked by measuring Bell's inequalities. We investigated several possible eavesdropper strategies, including pseudo-quantum-nondemolition measurements. In all cases, the eavesdropper's presence was readily apparent. We discuss a procedure to increase her detectability.
Summary form only given. Quantum cryptography uses single photons to allow secure distribution of secret key material to sender and receiver, without the possibility of an undetected eavesdropper. In the protocol suggested by Ekert, each photon of a quantum-mechanically entangled pair is sent to the sender and receiver, who randomly measure the polarization in various bases. If the bases are the same, then sender and receiver will have completely correlated measurement results, which become the shared secret key. Other combinations of measurements are used to test Bell's inequalities, which limit the possible correlations achievable with any local realistic theory. The presence of an intermediate eavesdropper can be readily detected by an inability to violate Bell's inequality. Using the polarization-entangled photon pairs from a novel spontaneous parametric down-conversion source, we have experimentally implemented. Ekert's proposal.
In single-qubit quantum secret sharing, a secret is shared between NNN parties via manipulation and measurement of one qubit at a time. Each qubit is sent to all NNN parties in sequence; the secret is encoded in the first participant's preparation of the qubit state and the subsequent participants' choices of state rotation or measurement basis. We present a protocol for single-qubit quantum secret sharing using polarization entanglement of photon pairs produced in type-I spontaneous parametric downconversion. We investigate the protocol's security against eavesdropping attack under common experimental conditions: a lossy channel for photon transmission, and imperfect preparation of the initial qubit state. A protocol which exploits entanglement between photons, rather than simply polarization correlation, is more robustly secure. We implement the entanglement-based secret-sharing protocol with 87% secret-sharing fidelity, limited by the purity of the entangled state produced by our present apparatus. We demonstrate a photon-number splitting eavesdropping attack, which achieves no success against the entanglement-based protocol while showing the predicted rate of success against a correlation-based protocol.
We have implemented the 'six-state' quantum cryptography protocol using polarization-entangled photon pairs, in which the polarization of each photon of a pair is measured in one of three randomly chosen bases. For a given amount of eavesdropping, this protocol results in a larger error rate than in four- or two-state protocols, but reduces the number of key-producing events. We have experimentally investigated several incoherent eavesdropping strategies, and verified the predicted enhancement in error rate. However, we demonstrate that for low error rates, the efficiency for secret key generation is higher when using the four-state protocol.
We propose a double-entanglement-based quantum cryptography protocol that is both efficient and deterministic. The proposal uses photon pairs with entanglement both in polarization and in time degrees of freedom; each measurement in which both of the two communicating parties register a photon can establish one and only one perfect correlation, and thus deterministically create a key bit. Eavesdropping can be detected by violation of local realism. A variation of the protocol shows a higher security, similar to the six-state protocol, under individual attacks. Our scheme allows a robust implementation under the current technology.
We present a mathematical physics analysis of entangled translucent eavesdropping in quantum cryptography, based on the recent work of Ekert, Huttner, Palma, and Peres. The key generation procedure involves the transmission, interception, and reception of two nonorthogonal photon polarization states. At the receiving end, a positive operator valued measure (POVM) is employed in the measurement process. The eavesdropping involves an information-maximizing von Neumann-type projective measurement. We propose a new design for a receiver that is an all-optical realization of the POVM, using a Wollaston prism, a mirror, two beam splitters, a polarization rotator, and three photodetectors. We present a quantitative analysis of the receiver. We obtain closed-form algebraic expressions for the error rates and mutual information, expressed in terms of the POVM-receiver error rate and the angle between the carrier polarization states. We also prove a significant result, namely, that in the entangled translucent eavesdropping approach, the unsafe error rate based on standard mutual information comparisons is equivalent to the maximum allowable error rate based on perfect mutual information for the eavesdropper. In this case, the above unsafe error rate is in fact not overly conservative.
The recent application of the principles of quantum mechanics to cryptography has led to a remarkable new dimension in secret communication.Quantum Cryptography uses the principles of Quantum Mechanics to implement a cryptographic system.The key problem which is solved by using quantum techniques is that of eavesdropping detection.Conventional secret-key cryptography techniques require the communication of a secret key prior to message exchange.Quantum principles can be used to detect eavesdropping probabilistically when it occurs.The bits are represented as qubits, physically modeled by photons, and communicated over a quantum channel.The polarization states of photons represent 0's and 1's.As a result of these new developments, it is now possible to construct cryptographic communication systems which detect unauthorized eavesdropping should it occur, and which give a guarantee of no eavesdropping should it not occur.