We present an algebraic approach to quantum information theory and its application to quantum cryptography. Therefore, we model the measurement process in terms of an algebraic object: a partition of unity. The POVM associated to such a partition describes the measurement results and the completely positive map associated to it the disturbance of the state. This approach leads to a compact description of quantum cryptography in which general measurements, noisy channels as well as measurement apparatus of the receiver that are out of sync with those of the sender can be described.We present an algebraic approach to quantum information theory and its application to quantum cryptography. Therefore, we model the measurement process in terms of an algebraic object: a partition of unity. The POVM associated to such a partition describes the measurement results and the completely positive map associated to it the disturbance of the state. This approach leads to a compact description of quantum cryptography in which general measurements, noisy channels as well as measurement apparatus of the receiver that are out of sync with those of the sender can be described.

IEEE International Symposium on Information Theory (ISIT)Jun 25, 20031 citation

Position Based Cryptography

Nishanth Chandran, Vipul Goyal, Ryan Moriarty +1 more

Lecture notes in computer scienceJan 1, 2009154 citations

Bell–Clauser–Horne–Shimony–Holt Behavior Under Quantum Loss and Decoherence

O. Hanyecz, András Bodor, Петер Адам +1 more

We present a detailed analysis of the effect of quantum loss and decoherence in the Bell-CHSH scenario. Adopting a device-independent approach, we study the change in the bipartite conditional probability distribution, i.e., the behavior of the realized nonlocal box pair when the elements of the entangled qubit pair subjected to independent noisy quantum channels modeled by completely positive maps. As the verification of Bell inequalities is crucial in device-independent quantum cryptography, our considerations are instructive from the perspective of quantum realizations of nonlocal box pairs. We find that the impact of quantum channels cannot be described by an equivalent classical noise channel.We present a detailed analysis of the effect of quantum loss and decoherence in the Bell-CHSH scenario. Adopting a device-independent approach, we study the change in the bipartite conditional probability distribution, i.e., the behavior of the realized nonlocal box pair when the elements of the entangled qubit pair subjected to independent noisy quantum channels modeled by completely positive maps. As the verification of Bell inequalities is crucial in device-independent quantum cryptography, our considerations are instructive from the perspective of quantum realizations of nonlocal box pairs. We find that the impact of quantum channels cannot be described by an equivalent classical noise channel.

CryptographyApr 23, 20250 citations

Position-Based Cryptography and Multiparty Communication Complexity

Joshua Brody, Stefan Dziembowski, Sebastian Faust +1 more

Lecture notes in computer scienceJan 1, 20176 citations

Quantum Cryptography in Noisy Channels

Hoi‐Kwong Lo, H. F. Chau

We provide a complete proof of the security of quantum cryptography against any eavesdropping attack including coherent measurements even in the presence of noise. Polarization-based cryptographic schemes are shown to be equivalent to EPR-based schemes. We also show that the performance of a noisy channel approaches that of a noiseless one as the error rate tends to zero. (i.e., the secrecy capacity $C_s (ε) \to C_s (0)$ as $ε\to 0$ .) One implication of our results is that one can {\it double} the efficiency of a most well-known quantum cryptographic scheme proposed by Bennett and Brassard simply by assigning vastly different probabilities to the two conjugate bases.We provide a complete proof of the security of quantum cryptography against any eavesdropping attack including coherent measurements even in the presence of noise. Polarization-based cryptographic schemes are shown to be equivalent to EPR-based schemes. We also show that the performance of a noisy channel approaches that of a noiseless one as the error rate tends to zero. (i.e., the secrecy capacity $C_s (ε) \to C_s (0)$ as $ε\to 0$.) One implication of our results is that one can {\it double} the efficiency of a most well-known quantum cryptographic scheme proposed by Bennett and Brassard simply by assigning vastly different probabilities to the two conjugate bases.

arXiv:quant-ph/9511025Nov 20, 19953 citations

C_s (ε) \to C_s (0)

ε\to 0

.) One implication of our results is that one can {\it double} the efficiency of a most well-known quantum cryptographic scheme proposed by Bennett and Brassard simply by assigning vastly different probabilities to the two conjugate bases.