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Journal of Modern Optics

Quantum Cryptography with Photon Pairs

B. Hüttner, Asher Peres

Published Dec 1, 1994• 14 citations
Publisher

Abstract

Photons, randomly prepared in one of two non-orthogonal quantum states, are used for a cryptographic key distribution. If the receiver tests them one by one, he may either identify their state, or get an inconclusive (useless) result. If he tests them pairwise, he may also obtain information about their parity (whether or not they have the same state), without identifying each signal separately. While this procedure does not give a higher rate of information transmission, the parity-generated bits are more sensitive to attacks by an eavesdropper than bits obtained from single photons.

DOI
10.1080/09500349414552241

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Photons, randomly prepared in one of two non-orthogonal quantum states, are used for a cryptographic key distribution. If the receiver tests them one by one, he may either identify their state, or get an inconclusive (useless) result. If he tests them pairwise, he may also obtain information about their parity (whether or not they have the same state), without identifying each signal separately. While this procedure does not give a higher rate of information transmission, the parity-generated bits are more sensitive to attacks by an eavesdropper than bits obtained from single photons.
The secure distribution of the secret random bit sequences known as {open_quotes}key{close_quotes} material, is an essential precursor to their use for the encryption and decryption of confidential communications. Quantum cryptography is an emerging technology for secure key distribution with single-photon transmissions, nor evade detection (eavesdropping raises the key error rate above a threshold value). We have developed experimental quantum cryptography systems based on the transmission of non-orthogonal single-photon states to generate shared key material over multi-kilometer optical fiber paths and over line-of-sight links. In both cases, key material is built up using the transmission of a single-photon per bit of an initial secret random sequence. A quantum-mechanically random subset of this sequence is identified, becoming the key material after a data reconciliation stage with the sender. In our optical fiber experiment we have performed quantum key distribution over 24-km of underground optical fiber using single-photon interference states, demonstrating that secure, real-time key generation over {open_quotes}open{close_quotes} multi-km node-to-node optical fiber communications links is possible. We have also constructed a quantum key distribution system for free-space, line-of-sight transmission using single-photon polarization states, which is currently undergoing laboratory testing. 7 figs.
When single photons are used to code for individual bits, security can be guaranteed by exploiting Heisenberg's uncertainty principle. Binary information can be coded into two orthogonal states, such as polarization or relative phase (in an interferometer). To receive this information we require an analyzer able to discriminate between the two states in an error-free way. In a linear-polarization system a polarizing beam splitter is used with its axes aligned to the two possible polarization directions. However, using a polarizer at 45° to these directions will ensure a random output uncorrelated to the single-photon-coded bit stream. The principle of secure key sharing, or quantum cryptography, is that a random bit stream is encoded onto individual photons while randomly switching the coding basis between the 0° and 45° polarization bases (in general, any non-orthogonal measurement bases). The receiver also randomly switches between these basis, and information is shared only when a photon is received and the same basis is used for coding and for measurement. An initial experiment of this type was carried out by using faint pulses of polarized visible light over a 40-cm transmission distance.1
By realizing a quantum cryptography system based on polarization entangled photon pairs we establish highly secure keys, because a single photon source is approximated and the inherent randomness of quantum measurements is exploited. We implement a novel key distribution scheme using Wigner's inequality to test the security of the quantum channel, and, alternatively, realize a variant of the BB84 protocol. Our system has two completely independent users separated by 360 m, and generates raw keys at rates of 400-800 bits/s with bit error rates around 3%.
The secure distribution of the secret random bit sequences known as `key' material, is an essential precursor to their use for the encryption and decryption of confidential communications. Quantum cryptography is an emerging technology for secure key distribution with single-photon transmissions: Heisenburg's uncertainty principle ensures that an adversary can neither successfully tap the key transmissions, nor evade detection (eavesdropping raises the key error rate above a threshold value). We have developed experimental quantum cryptography systems based on the transmission of non-orthogonal single-photon states to generate shared key material over multi-kilometer optical fiber paths and over line-of-sight links. In both cases, key material is built up using the transmission of a single- photon per bit of an initial secret random sequence. A quantum-mechanically random subset of this sequence is identified, becoming the key material after a data reconciliation stage with the sender. In our optical fiber experiment we have performed quantum key distribution over 24-km of underground optical fiber using single-photon interference states, demonstrating that secure, real-time key generation over `open' multi-km node-to-node optical fiber communications links is possible.
Real sources of entangled photon pairs (like parametric down conversion) are not perfect. They produce quantum states that contain more than only one photon pair with some probability. In this paper it is discussed what happens if such states are used for the purpose of quantum key distribution. It is shown that the presence of "multi-pair" signals (together with low detection efficiencies) causes errors in transmission even if there is no eavesdropper. Moreover, it is shown that even the eavesdropping, that draws information only from these "multi-pair" signals, increases the error rate. Information, that can be obtained by an eavesdropper from these signals, is calculated.
Pairs of entangled photons can be employed for quantum key distribution. For each bit exactly one pair of photons is needed. Unfortunately, the quantum states produced by real sources, like a parametric down conversion, contain also terms with more than only one photon pair. We discuss several aspects of the use of such states for quantum key distribution. It is shown that the presence of multi-pair signals (together with low detection efficiencies) causes errors in transmission even in the absence of al1 eavesdropper. However, the most important result is that an individual eavesdropping on multi-pair signals increases the error rate. This fact represents the important advantage of the entanglement-based quantum key distribution.