Ebook: Quantum Cryptography and Computing

This book contains a selection of papers invited and presented at the NATO sponsored Advanced Research Workshop on “Quantum Cryptography and Computing: Theory and Implementation” held at the University of Gdansk, Poland from September 9^th to 12th 2009. The purpose of the workshop was to assess the state of the art in the subject areas and identify the most pressing research goals.

The workshop was an opportunity for about 38 experts from USA, Europe and the countries of the former Soviet Union republics to discuss theoretical and applied aspects of quantum cryptography and computing.

We wish to thank the NATO Public Diplomacy Division, Science for Peace and Security section (SPS) and more specifically Dr. Chris De Wispelaere, Program Director of Information and Communication Security, for the generous financial support of the workshop.

Special thanks are due to the University of Gdansk administration represented by the Rektor, Prof. Bernard Lammek, for making all meeting facilities available free of charge.

The Workshop Office was skillfully run by Elżbieta Bandura and Malgorzata Chrustowska. An important workshop publicity and communication job was well done by Piotr Arlukowicz. Several other people helped in various ways to make the workshop successful. They are: Rafał Demkowicz-Dobrzański, Andrzej Grudka, Michał Horodecki, Jarosław Korbicz, Łukasz Pankowski and Marcin Pawłowski. We also express our sincere thanks to several persons who helped edit the NATO ARW proceedings book. They are: Jarek Korbicz, Wiesław Laskowski and Marcin Pawłowski.

Above all we are deeply grateful to the workshop participants, especially those who contributed papers to this book.

R. Horodecki

S. Ya. Kilin

J. Kowalik

The problem of looking for the optimal local operations assisted by classical communication (LOCC) is investigated. A method based on semi-definite programming is presented providing the optimal solutions or in worst case the upper bounds. The method is applied successfully to two problems: local cloning of entangled states and local eavesdropping on secret sharing protocols.

Since 1997 Senetas Corporation Limited has designed and manufactured network encryption hardware that allows high speed voice, video and data networks to operate securely when data is in transmission. Senetas has its encryptors deployed to secure the world’s most critical information networks for governments, military, foreign agencies, banking and financial institutions in over 40 countries. Taking developments from the labs of the University of Geneva and idQuantique, Senetas jointly created the world’s first, and fastest, commercial quantum encryption solution in 2007. Since then Senetas has quantum-enabled its globally-accredited classic encryption hardware to future-proof customers, and continues to work with idQuantique and the University of Geneva to add further functionality to the high speed quantum encryption solution, now deployed on four continents – Africa, Asia, North America and Europe.

We describe a scheme for quantum anonymous voting of n participants based on the single nitrogen-vacancy centers in diamond. The scheme requires a bipartite entanglement creation between the electronic spins of the two distant NV centers, unitary operation of NV electronic spin together with n nearby nuclear spins of carbon isotopes, and one projective measurement of the electronic spin state - optical readout. As a result, the quantum anonymous voting protocol can be realized, making any attempt of the tallyman to learn who voted which way detectable.

Quantum Communication Protocols, such as Quantum Key Distribution, are typically described in the language of abstract qubits. For implementations, on the other hand, we use light pulses where the signals are described as elements of the infinite dimensional Hilbert space of optical modes. In this contribution I discuss how those two pictures fit together, especially in a cryptographic scenario.

A cryptographic analysis is presented of a new quantum key distribution protocol using phase-time coding. An upper bound is obtained for the error rate that guarantees secure key distribution. When no counts are detected in the control time slot, the protocol guarantees secure key distribution if the bit error rate in the sifted key does not exceed 50%. This protocol partially discriminates between errors due to system defects (e.g., imbalance of a fiber-optic interferometer) and eavesdropping. In the absence of eavesdropping, the counts detected in the control time slot are not caused by interferometer imbalance, which reduces the requirements for interferometer stability.

Devices and protocols for information processing are often required to work for arbitrary inputs. For example, in channel coding theory, one demands that a coding scheme transmits any possible input state reliably over a given noisy channel. Similarly, in quantum cryptography, security of a protocol should hold independently of the inputs, even if they are chosen maliciously. In this short paper, we review the Post-Selection Technique introduced in (Phys. Rev. Lett. 102:020504, 2009). Its main purpose is to simplify the analysis of information processing schemes so that only one single input needs to be considered. If a scheme satisfies a desired criterion when acting on this particular input, then—under certain symmetry conditions—the same criterion is automatically met for arbitrary inputs. We illustrate the Post-Selection Technique at the example of quantum cryptography. Here, it can be used to show that security of a Quantum Key Distribution scheme against general attacks—somewhat surprisingly—follows from its security against one specific attack. This not only simplifies security proofs, but also has other remarkable implications, e.g., that no randomness is needed for privacy amplification.

I review the ideas and main results in the derivation of security bounds in quantum key distribution for keys of finite length. In particular, all the detailed studies on specific protocols and implementations indicate that no secret key can be extracted if the number of processed signals per run is smaller than 10⁵ − 10⁶. I show how these numbers can be recovered from very basic estimates.

We review the current state of research in qudit-based quantum key distribution with an emphasis on experimental techniques used for state preparation and measurements. The question of practical usefulness of this schemes and of qudit-based QKD in general is addressed.

We address the problem of the security of the continuous variable quantum key distribution with the coherent states in the presence of a trusted noise of different origins, e.g. preparation noise at the sender side and the detection noise at the remote receiver side. We show the essential difference between the impact of these types of noise under conditions of lossy quantum channel, available to an eavesdropper. While detection noise reduces the key rate without breaking the security, the preparation noise is destructive for the secure transmission. At the same time we show that by the state purification we can compensate for the destructive effect of the preparation noise, so that upon optimal purification its impact becomes similar to that of the detection noise. The effect is persistent also upon realistic error correction.

Security of the two-way quantum communication protocol proposed by Lucamarini and Mancini (Phys. Rev. Lett. 94 (2005) 140501) can be impaired in the case of considerable quantum channel noise. We present scheme which considers the opportunity of eavesdropping due to a separation of two procedures, namely, the verification procedure and the communication procedure.

We survey the recent sequence of algorithms for evaluating Boolean formulas consisting of NAND gates.

We ask whether there are fundamental limits on storing quantum information reliably in a bounded volume of space. To investigate this question, we study quantum error correcting codes specified by geometrically local commuting constraints on a 2D lattice of finite-dimensional quantum particles. For these 2D systems, we derive a tradeoff between the number of encoded qubits k, the distance of the code d, and the number of particles n. It is shown that kd² = O(n) where the coefficient in O(n) depends only on the locality of the constraints and dimension of the Hilbert spaces describing individual particles. We show that the analogous tradeoff for the classical information storage is k(√d) = O(n).

In a recent work [10], POULIN and one of us presented a quantum algorithm for preparing thermal Gibbs states of interacting quantum systems. This algorithm is based on Grover’s technique for quantum state engineering, and its running time is dominated by the factor (√D/[Zscr ]_β), where D and [Zscr ]_β denote the dimension of the quantum system and its partition function at inverse temperature β, respectively. We present here a modified algorithm and a more detailed analysis of the errors that arise due to imperfect simulation of Hamiltonian time evolutions and limited performance of phase estimation (finite accuracy and nonzero probability of failure). This modification together with the tighter analysis allows us to prove a better running time by the effect of these sources of error on the overall complexity. We think that the ideas underlying of our new analysis could also be used to prove a better performance of quantum Metropolis sampling by TEMME et al. [12].

Spin systems consisting of a single electronic spin of the NV center in diamond and few proximal ¹³C nuclei spins which are considered now as a candidate for a room-temperature implementation of a quantum computer register with optical access are studied by spin-Hamiltonian method using parameters of hyperfine NV-¹³C interactions taken from EPR measurements on NV ensemble and from ab initio (DFT) simulation of carbon clusters containing NV centers. Experimental data on ODMR spectra and spin echo modulation obtained on single NV+n¹³C centers are interpreted without fitting parameters.

Squeezed vacuum with large photon numbers is an example of a macroscopic system with nonclassical properties. These properties are manifested in pairwise intensity correlations, also called twin-beam squeezing. We produce squeezed vacuum in a traveling-wave pulse-pumped frequency non-degenerate optical parametric amplifier (NOPA). Twin-beam squeezing is measured via direct detection and measurement of the difference-signal variance for two balanced detectors. It is shown that the study of the intensity correlations using this method requires a collection of a large number of modes, both longitudinal and transverse.

We study classical capacity regions of quantum Gaussian multiple access channels (MAC). In classical variants of such channels, whilst some capacity superadditivity-type effects such as the so called water filling effect may be achieved, a fundamental classical additivity law can still be identified, viz. adding resources to one sender is never advantageous to other senders in sending their respective information to the receiver. Here, we show that quantum resources allow violation of this law, by providing an illustrative scheme of an experimentally feasible Gaussian MAC.

We present a procedure for the measurement of quadrature components of an electromagnetic field in the far-field as an alternative to the traditional approach based on the homodyne detection (HD) technique. For this we suggest to use coherent sources such as phase-locked lasers or optical parametric oscillators operating above threshold. Then we show how to arrange the detection procedure in the far field that is exactly or partly equivalent to the HD. Our scheme can be applied for both the classical and non-classical fields. The potential of the procedure is illustrated by an example which utilizes the pixellised sources of the non-classical light. As an integral part of our investigation we develop a theory of the pixellised source of the spatio-temporally squeezed light.

We discuss linear optical quantum teleportation in the Knill-Laflamme-Milburn scheme. We calculate the probability of faithful teleportation when one uses nonmaximally entangled states. We show that for single teleportation maximally entangled state is optimal. On the other hand for a sequence of teleportations nonmaximally entangled state is optimal. Hence, probability of faithful teleportation is nonmultiplicative. We also introduce measure of nonmultiplicativity and show that nonmultiplicativity increases with the number of teleportations.

We propose a protocol of continuous variable entanglement creation at distances of 100 km using small cross-Kerr nonlinearity χ ≥ χ_min ≈ 0.01. The protocol corresponds to the contemporary level of experimental equipment and can be used for such practical applications as quantum key distribution.

Low loss magnetic surface plasmon polariton (SPP) modes characterized by enhanced electrical field component and subwavelength confinement on the dielectric and negative-index metamaterial interface are presented. We demonstrate a possibility of storage and perfect retrieval of the low loss magnetic SPP fields by using a photon echo quantum memory on Raman atomic transition. We describe the specific properties of the proposed technique which opens a possibility for efficient nano scale multi-mode quantum memory.

We derive the local bounds for all possible linear Bell inequalities with the reduced entropy of the settings. Such bounds are important for analysis of experiments that involve sources with non identical independent distribution or resort to postselection. Since the entropy reduction can be considered as an information leakage from laboratories, our results have also nontrivial implications for quantum cryptography.