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arXiv:quant-ph/0511163 · New Journal of Physics

Experimental quantum cryptography with qutrits

Simon Gröblacher, Thomas D. Jennewein, Alipasha Vaziri, Gregor Weihs, Anton Zeilinger

Published May 26, 2006• 415 citations
arXivHTMLPDF

Abstract

We produce two identical keys using, for the first time, entangled trinary quantum systems (qutrits) for quantum key distribution. The advantage of qutrits over the normally used binary quantum systems is an increased coding density and a higher security margin. The qutrits are encoded into the orbital angular momentum of photons, namely Laguerre–Gaussian modes with azimuthal index l + 1, 0 and −1, respectively. The orbital angular momentum is controlled with phase holograms. In an Ekert-type protocol the violation of a three-dimensional Bell inequality verifies the security of the generated keys. A key is obtained with a qutrit error rate of approximately 10%.

DOI
10.1088/1367-2630/8/5/075

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We produce two identical keys using, for the first time, entangled trinary quantum systems (qutrits) for quantum key distribution. The advantage of qutrits over the normally used binary quantum systems is an increased coding density and a higher security margin. The qutrits are encoded into the orbital angular momentum of photons, namely Laguerre–Gaussian modes with azimuthal index l + 1, 0 and −1, respectively. The orbital angular momentum is controlled with phase holograms. In an Ekert-type protocol the violation of a three-dimensional Bell inequality verifies the security of the generated keys. A key is obtained with a qutrit error rate of approximately 10%.
We try to create the cryptographic scheme of producing two identical keys using, for the first time, entangled trinary quantum systems for quantum key distribution. The advantage of trinary quantum systems over the normally used binary quantum systems is an increased coding density and a higher security margin. The trinary quantum systems are encoded into the orbital angular momentum of photons, namely Laguerre -Gaussian modes with azimuthally index 1 +1, 0 and -1, respectively. The orbital angular momentum is controlled with phase holograms. In an Ekert-type protocol the violation of a three-dimensional Bell inequality verifies the security of the generated keys. A key is obtained with a trinary quantum system error rate of approximately 10%.
The best qubit one-way quantum-key-distribution (QKD) protocol can tolerate up to 14.6% in the error rate. It has been shown how this rate can be increased by using larger quantum systems. The polarization state of a biphoton can encode a three-level quantum system---a qutrit. The realization of a QKD system with biphotons encounters several problems in generating, manipulating, and detecting such photon states. We define those limitations and find within them a few protocols that perform almost as well as the ideal qutrit protocol. One advantage is that these protocols can be implemented with minor modifications into existing single photon systems. The security of one protocol is proved for the most general coherent attacks and the largest acceptable error rate for this protocol is found to be around 17.7%. For comparison, the security of the best possible qutrit protocol of four mutually unbiased bases was also rigorously analyzed against general attacks, with a proven bound on the acceptable error rate of 21.1%.
We experimentally demonstrate a quantum key distribution protocol using entangled photon pairs in orbital angular momentum (OAM). Here Alice uses a fixed phase hologram to modulate her OAM state on one photon with a spatial light modulator (SLM), while Bob uses the designed N different phase holograms for his N-based keys on the other photon with his SLM. With coincidences, Alice can fully retrieve the keys sent by Bob without reconciliation. We report the experiment results with N = 3 and OAM eigenmodes |ℓ = ±1〉, and discuss the security from the light path and typical attacks.
Abstract. We have developed a scheme to generate, control, transmit and measure entangled photonic qutrits (two photons each of dimension d = 3). A Bell test of this source has previously been reported elsewhere [1], therefore, here we focus on how the control of the system is realized. Motivated by these results, we outline how the scheme can be used for two specific quantum protocols, namely key distribution and coin tossing and discuss some of their advantages and disadvantages. Performing quantum communication with high-dimensional systems would appear to be an obvious and straightforward extension to many of the qubit protocols that have driven quantum information science in recent years. There have been theoretical proposals for Quantum Key Distribution (QKD) [2] with greater security [3] as well as specific proposals for qutrits such as quantum coin tossing [4]. Fundamentally, high-dimensional Bell inequalities have revealed greater violations of non-locality [5] while increasing the dimensions of the entangled systems has been shown to facilitate closing the detection loop-hole [6] for such tests. Optics has been able to provide a realistic test-bed for these proposals with several different schemes being realized for generating high-dimensional entanglement [7, 8] as well as the scheme presented here [1, 9]. This source of entangled qutrits is analogous to the energy-time qubit arrangement of Franson [10]. The experimental scheme has been developed for telecom wavelengths and with proven long distance quantum communication architecture [11, 12] to optimise the usefulness of this high dimensional entanglement resource. We have already performed
The Ekert quantum key distribution protocol uses pairs of entangled qubits and performs checks based on a Bell inequality to detect eavesdropping. The 3DEB protocol uses instead pairs of entangled qutrits to achieve better noise resistance than the Ekert protocol. It performs checks based on a Bell inequality for qutrits named CHSH-3. In this paper, we present a new protocol, which also uses pairs of entangled qutrits, but achieves even better noise resistance than 3DEB. This gain of performance is obtained by using another inequality called here hCHSH-3. As the hCHSH3 inequality involve products of observables which become incompatible when using quantum states, we show how the parties running the protocol can measure the violation of hCHSH3 in the presence of noise, to ensure the secrecy of the key.