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IEEE Journal of Selected Topics in Quantum Electronics

The Error Tolerance Bound for Secure Multi-Qubit QKD Against Incoherent Attack

Kyongchun Lim, Heasin Ko, Kiung Kim, Changho Suh, June‐Koo Kevin Rhee

Published Nov 12, 2014• 5 citations
Publisher

Abstract

The tolerance bound for quantum symbol error rate in a multi-qubit quantum key distribution system is derived in consideration of an incoherent attack on a single-photon quantum channel, where multi-qubit encoding and measurement can be applied to a single photon in combination of polarization, phase, and frequency modulations. This paper presents a solid theoretical evidence of a multiqubit gain in secrecy performance.

DOI
10.1109/jstqe.2014.2369498

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The tolerance bound for quantum symbol error rate in a multi-qubit quantum key distribution system is derived in consideration of an incoherent attack on a single-photon quantum channel, where multi-qubit encoding and measurement can be applied to a single photon in combination of polarization, phase, and frequency modulations. This paper presents a solid theoretical evidence of a multiqubit gain in secrecy performance.
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We propose an extension of quantum key distribution based on encoding the key into quNits, i.e. quantum states in an N -dimensional Hilbert space. We estimate both the mutual information between the legitimate parties and the eavesdropper, and the error rate, as a function of the dimension of the Hilbert space. We derive the information gained by an eavesdropper using optimal incoherent attacks and an upper bound on the legitimate party error rate that ensures unconditional security when the eavesdropper uses finite coherent eavesdropping attacks. We also consider realistic systems where we assume that the detector dark count probability is not negligible.
We propose an extension of quantum key distribution based on encoding the key into quNits, i.e. quantum states in an N-dimensional Hilbert space. We estimate both the mutual information between the legitimate parties and the eavesdropper, and the error rate, as a function of the dimension of the Hilbert space. We derive the information gained by an eavesdropper using optimal incoherent attacks and an upper bound on the legitimate party error rate that ensures unconditional security when the eavesdropper uses finite coherent eavesdropping attacks. We also consider realistic systems where we assume that the detector dark count probability is not negligible. PACS numbers: 03.67.Dd, 03.67.Hk, 03.67.−a, 03.65.Ta 1.
Quantum key distribution (QKD) enables information-theoretic secure communication, yet its ultimate tolerance to noise and achievable transmission distance remain fundamentally constrained. We establish the maximum quantum bit error rate (QBER) compatible with secure QKD and derive corresponding upper bounds on communication distance. Our results follow from a fundamental capacity threshold for qubit Pauli channels and apply to protocols based on two or more mutually unbiased bases, using either single-photon or weak coherent sources. By connecting information-theoretic limits to realistic physical noise models, we obtain universal bounds on achievable distances in fiber and free-space links, including diffraction-limited constraints relevant to deep-space quantum communications. These findings clarify the ultimate noise robustness of QKD and delineate the fundamental boundaries of secure quantum communication.
This paper presents an investigation of practical quantum secure communication using multi-photon tolerant protocols. Multi-photon tolerant protocols loosen the limit on the number of photons imposed by currently used quantum key distribution protocols. The multi-photon tolerant protocols investigated in this paper are multi-stage protocols that do not require any prior agreement between a sender Alice and a receiver Bob. The security of such protocols stems from the fact that the optimal detection strategies between the legitimate users and the eavesdropper are asymmetrical, allowing Bob to obtain measurement results deterministically while imposing unavoidable quantum noise to the eavesdropper Eve's measurement. Multi-photon tolerant protocols are based on the use of transformations known only to the communicating party applying them i.e. either Alice or Bob. In this paper multi-photon tolerant protocols are used in order to share a key or a message between a sender Alice and a receiver Bob. Thus such protocols can be either used as quantum key distribution (QKD) protocols or quantum communication protocols. In addition, multi-stage protocols can be used to share a key between Alice and Bob, followed by the shared key used as a seed key to a single-stage protocol, called the braiding concept. This paper presents a practical study of multi-photon tolerant multi-stage protocols. Security aspects as well as challenges to the practical implementation are discussed. In addition, secret raw key generation rates are calculated with respect to both losses and distances over a fiber optical channel. It is well-known that raw key generation rates decreases with the increase in channel losses and distances. In this paper, coherent non-decoying quantum states are used to transfer the encoded bits from Alice to Bob. Raw key generation rates are calculated for different average photon numbers µ and compared with the case of µ=0.1, which is the average number of photons used in most single-photon based QKD protocols. Furthermore, an optimal average number of photons to be used within the secure region of the multi-photon tolerant protocols is calculated. It is worth noting that, with the increased key generation rates and distances of communication offered by the multi-photon tolerant protocols, quantum secure communication need not be restricted to quantum key distribution; it can be elevated to attain direct quantum secure communication.
Quantum key distribution introduces a new way of key exchange through a public quantum channel between two communicating nodes. However, the first introduced BB84 protocol was theoretically verifying security based on single photon sources. At this time, it was hard to achieve such device. Therefore, it was a challenging aspect to prove the security of QKD system using coherent light sources or “multi emitting photon source”, which introduces Photon number splitting attacks. We are interested to simulate and investigate the QKD system using coherent laser sources and study the PNS attack. The idea involves that; Eve can crash a beam of light, absorbing some photons using QND measurement and transmit the others. Such attack can make Eve dominant to the situation and gain much information of the key without the fear of getting exposed to the communicating parties. Herein, this paper discusses some useful solution to detect such attack and proves the security of QKD even with weak laser sources.