7 pages, 2 figures, LaTeX, Equation 6 corrected, nomenclature in equations 14-17, and eqn. 19 modified for clarity. Equation 18 added for clarity. Conclusions expanded for clarity and reference 26 added. Some minor grammatical corrections
Many quantum key distribution analyses examine the link security in a subset of the full Hilbert space that is available to describe the system. In reality, information about the photon state can be embedded in correlations between the polarization space and other dimensions of the Hilbert space in such a way that Eve can determine the polarization of a photon without affecting it. This paper uses the concept of suitability to quantify the available information for Eve, and then describe a systematic way to calculate and measure these possibilities.
Quantum key distribution (QKD) allows two remote users to establish a secret key in the presence of an eavesdropper. The users share quantum states prepared in two mutually-unbiased bases: one to generate the key while the other monitors the presence of the eavesdropper. Here, we show that a general $d$-dimension QKD system can be secured by transmitting only a subset of the monitoring states. In particular, we find that there is no loss in the secure key rate when dropping one of the monitoring states. Furthermore, it is possible to use only a single monitoring state if the quantum bit error …
Franson interferometers are increasingly being proposed as a means of securing high-dimensional energy-time entanglement-based quantum key distribution (QKD) systems. Heuristic arguments have been proposed that purport to demonstrate the security of these schemes. We show, however, that such systems are vulnerable to attacks that localize the photons to several temporally separate locations. This demonstrates that a single pair of Franson interferometers is not a practical approach to securing high-dimensional energy-time entanglement based QKD. This observations leads us to investigate the se…
This paper presents the feasibility study of deploying Quantum Key Distribution (QKD) from High Altitude Platforms (HAPs), as a way of securing future communications applications and services. The paper provides a thorough review of the state of the art HAP technologies and summarises the benefits that HAPs can bring to the QKD services. A detailed link budget analysis is presented in the paper to evaluate the feasibility of delivering QKD from stratospheric HAPs flying at 20 km altitude. The results show a generous link budget under most operating conditions which brings the possibility of us…
Theoretical quantum key distribution (QKD) protocols commonly rely on the use of qubits (quantum bits). In reality, however, due to practical limitations, the legitimate users are forced to employ a larger quantum (Hilbert) space, say a quhexit (quantum six-dimensional) space, or even a much larger quantum Hilbert space. Various specific attacks exploit of these limitations. Although security can still be proved in some very special cases, a general framework that considers such realistic QKD protocols, as well as} attacks on such protocols, is still missing. We describe a general method of at…
Proving the unconditional security of a quantum key distribution (QKD) scheme is a highly challenging task as one needs to determine the most efficient attack compatible with experimental data. This task is even more demanding for continuous-variable QKD as the Hilbert space where the protocol is described is infinite dimensional. A very natural way to address this problem is to make an extensive use of the symmetries of the protocols. In this article, we investigate a symmetry in phase space that is particularly relevant to continuous-variable QKD, and explore the way towards a new quantum de…
An increase in the dimension of state space for quantum key distribution (QKD) can decrease its fidelity requirements while also increasing its bandwidth. A significant obstacle for QKD with qudits (d>2) has been an efficient and practical quantum state sorter for photons whose complex fields are modulated in both amplitude and phase. We propose such a sorter based on a multiplexed thick hologram, constructed e.g. from photo-thermal refractive (PTR) glass. We validate this approach using coupled-mode theory with parameters consistent with PTR glass to simulate a holographic sorter. The model a…
Finite key analysis of quantum key distribution (QKD) is an important tool for any QKD implementation. While much work has been done on the framework of finite key analysis, the application to individual protocols often relies on the the specific protocol being simple or highly symmetric as well as represented in small finite-dimensional Hilbert spaces. In this work, we extend our pre-existing reliable, efficient, tight, and generic numerical method for calculating the asymptotic key rate of device-dependent QKD protocols in finite-dimensional Hilbert spaces to the finite key regime using the …
We address the question of how much entanglement can be certified from the observed correlations and the knowledge of the Hilbert space dimension of the measured systems. We focus on the case in which both systems are known to be qubits. For several correlations (though not for all), one can certify the same amount of entanglement as with state tomography, but with fewer assumptions, since nothing is assumed about the measurements. We also present security proofs of quantum key distribution without any assumption on the measurements. We discuss how both the amount of entanglement and the secur…
Quantum Key Distribution (QKD) provides an efficient means to exchange information in an unconditionally secure way. Historically, QKD protocols have been based on binary signal formats, such as two polarisation states, and the transmitted information efficiency of the quantum key is intrinsically limited to 1 bit/photon. Here we propose and experimentally demonstrate, for the first time, a high-dimensional QKD protocol based on space division multiplexing in multicore fiber using silicon photonic integrated lightwave circuits. We successfully realized three mutually unbiased bases in a four-d…
The faraday mirror (FM) plays a very important role in maintaining the stability of two way plug-and-play quantum key distribution (QKD) system. However, the practical FM is imperfect, which will not only introduce additional quantum bit error rate (QBER) but also leave a loophole for Eve to spy the secret key. In this paper, we propose a passive faraday mirror attack in two way QKD system based on the imperfection of FM. Our analysis shows that, if the FM is imperfect, the dimension of Hilbert space spanned by the four states sent by Alice is three instead of two. Thus Eve can distinguish the…
Quantum key distribution (QKD) offers the promise of absolutely secure communications. However, proofs of absolute security often assume perfect implementation from theory to experiment. Thus, existing systems may be prone to insidious side-channel attacks that rely on flaws in experimental implementation. Here we replace all real channels with virtual channels in a QKD protocol, making the relevant detectors and settings inside private spaces inaccessible while simultaneously acting as a Hilbert space filter to eliminate side-channel attacks. By using a quantum memory we find that we are able…
We present security proofs for a protocol for Quantum Key Distribution (QKD) based on encoding in finite high-dimensional Hilbert spaces. This protocol is an extension of Bennett's and Brassard's basic protocol from two bases, two state encoding to a multi bases, multi state encoding. We analyze the mutual information between the legitimate parties and the eavesdropper, and the error rate, as function of the dimension of the Hilbert space, while considering optimal incoherent and coherent eavesdropping attacks. We obtain the upper limit for the legitimate party error rate to ensure uncondition…
A photon with a modulated wavefront can produce a quantum communication channel in a larger Hilbert space. For example, higher dimensional quantum key distribution (HD-QKD) can encode information in the transverse linear momentum (LM) or orbital angular momentum (OAM) modes of a photon. This is markedly different than using the intrinsic polarization of a photon. HD-QKD has advantages for free space QKD since it can increase the communication channelÕs tolerance to bit error rate (BER) while maintaining or increasing the channels bandwidth. We describe an efficient numerical simulation of the …
Quantum Key Distribution (QKD) guarantees the security of communication with quantum physics. Most of widely adopted QKD protocols currently encode the key information with binary signal format---qubit, such as the polarization states. Therefore the transmitted information efficiency of the quantum key is intrinsically upper bounded by 1 bit per photon. High dimensional quantum system is a potential candidate for increasing the capacity of single photon. However, due to the difficulty in manipulating and measuring high dimensional quantum systems, the experimental high dimensional QKD is still…
Recently, Chau introduced an experimentally feasible qudit-based quantum-key-distribution (QKD) scheme. In that scheme, one bit of information is phase encoded in the prepared state in a $2^n$-dimensional Hilbert space in the form $(|i\rangle\pm|j\rangle)/\sqrt{2}$ with $n\ge 2$. For each qudit prepared and measured in the same two-dimensional Hilbert subspace, one bit of raw secret key is obtained in the absence of transmission error. Here we show that by modifying the basis announcement procedure, the same experimental setup can generate $n$ bits of raw key for each qudit prepared and measur…
