Ebook: Quantum Communication and Security

This volume contains a selection of papers invited and presented at the NATO sponsored Advanced Research Workshop on “Quantum Communication and Security” held at the Gdańsk University in Gdańsk, Poland from September 10th to 13th, 2006.

The purpose of the workshop was to assess the state of the art in the workshop subject area and identify new research challenges.

The workshop was an opportunity for many experts from Western Europe, USA and former Soviet Union Republics for discussing theoretical and applied aspects of quantum communication and cryptography.

We wish to thank the NATO Security Through Science Division and more specifically Dr. Hadassa Jakobovits, Director of Information and Communication Security Program for the generous support of the workshop.

Special thanks are due to the Gdańsk University administration officials, Rector, Prof. Andrzej Ceynowa and Dean, Prof. Andrzej Kowalski who made available all workshop facilities at no cost. Without any reservation, we say that Gdańsk University was the highest quality host of this NATO workshop.

There are several persons who contributed directly to the success of the workshop. They provided an excellent office and technical support. They include Prof. Wiesław Miklaszewski, Mrs Elżbieta Bandura, Mrs Anita Charkot, Mr Tomasz Paterek, and Mr Wiesław Laskowski.

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

Marek Żukowski, Sergei Kilin and Janusz Kowalik

We briefly present three topics in quantum communication. First of all a method, called error filtration, to reduce errors during quantum communication. We apply this method to quantum cryptography in a noisy environment, and describe an experimental realisation thereof. Second we describe an experimental realisation of quantum string flipping, in which two parties that do not trust each other want to generate a string of random bits. Finally we present the experimental realisation of a source of photon pairs at telecommunication wavelengths based on parametric fluorescence in periodically poled twin hole fibers.

We discuss the importance of entanglement creation for successful eavesdropping in quantum cryptography. We give a definition of asymmetric universal entangling machine which entangles a system in an unknown state to a specially prepared ancilla. We describe explicitly such a machine for any quantum system having finite number of levels and prove its optimality. We show that the asymmetric universal entangling machine is a device, required for optimal individual eavesdropping on the 6-state protocol of quantum cryptography.

We present simple and practical quantum solution for secure multiparty communication protocols, the secret sharing and the communication complexity and their proof-of-principle experimental realizations. In the secret sharing protocol, a secret is split among several parties in a way that its reconstruction requires the collaboration of the participating parties. In the communication complexity problem, the goal is to maximize the success probability of the partners for solving for giving communication resources some N partner communication complexity tasks. Our quantum solution is based on sequential transformations on a single qubit. In contrast with recently proposed schemes involving multiparticle GHZ states.

Whereas quantum cryptography ensures security by virtue of complete indistinguishability of nonorthogonal quantum states, attenuation in quantum communication channels and unavailability of single-photon sources present major problems. Since the restrictions imposed by non-relativistic quantum mechanics and used to formulate key distribution protocols are largely exhausted, new principle is required. The fundamental relativistic causality principle in quantum cryptography can be used to propose a new approach to ensuring unconditional security of quantum cryptography that eliminates these difficulties. Photons represent truly relativistic massless particles (the massless quantized field states) which travel at a maximum permissible speed. That is why in the development and realization of quantum cryptography in open space it would be unnatural to take no advantage of the additional possibilities offered by nature.

We investigate the use of photon number states to identify eavesdropping attacks on quantum key distribution (QKD) schemes. The technique is based on the fact that different photon numbers traverse a channel with different transmittivity. We then describe a QKD scheme utilizing this method, which overcomes the upper limit on the key generation rate imposed by the dead time of detectors when using a heralded source of photons.

A crucial assumption in the security proof of standard Quantum Key Distribution protocols is that the honest parties know how their devices work. However, it is possible to construct schemes whose security proof requires almost no assumption on the devices, but the minimal ones. We present some of these protocols together with the security analysis against individual attacks. All these schemes are based on the existence of non-local correlations, namely correlations that cannot be described by a local model.

We show that under coarse-grained measurements there is no observational difference between a quantum superposition of macroscopically distinct states (“Scrödinger-cat states”) and a classical mixture of these states. Since normally our observations in every-day life are of limited accuracy, no quantum features can be observed. Remarkably, the information gain in such classical coarse-grained measurements is only half of the maximal information gain in sharp quantum measurements. This suggests a novel approach to macroscopic realism and classical physics within quantum theory.

We developed an approach to a quantitative characterization of entanglement properties of, possibly mixed, bi- and multipartite quantum states of arbitrary finite dimension. Particular emphasis was given to: 1) the derivation of reliable estimates which allow for an efficient evaluation of entanglement measures, 2) construction of measures of entanglement useful in the monitoring of the time evolution of multipartite correlations under incoherent environment coupling and experimental production of entangled states, 3) construction of quantities characterizing entanglement which are directly measurable (defined in terms of physically realizable operators). To this end we proposed generalizations of concurrence for multipartite quantum systems that can distinguish qualitatively distinct quantum correlations (generalized multipartite and multidimensional concurrences). We derived a lower bound for the concurrence of mixed quantum states valid in arbitrary dimensions. As a corollary, a weaker, purely algebraic estimate was found, which can be used to detect mixed entangled states with a positive partial transpose. We discussed also the monotonicity of the constructed quantities under local operations and classical communication (LOCC). We provided a condition for the monotonicity of generalized multipartite concurrences which qualifies them as legitimate entanglement measures. The constructed quantities can be, in principle, accessible in experiments to directly quantify the pure-state entanglement via a measurement of a physical observable.

We show that bipartite Bell inequalities based on the Einstein–Podolsky–Rosen criterion for elements of reality and derived from the properties of some hyper-entangled states: (a) Allow feasible experimental verifications of the fact that the impossibility of elements of reality grows exponentially with the size of the subsystems, and (b) significantly reduces the minimum detection efficiency required to experimentally refute elements of reality without the fair sampling assumption.

When n--k systems of an n-partite permutation-invariant state are traced out, the resulting state can be approximated by a convex combination of tensor product states. This is the quantum de Finetti theorem. In this paper, we summarise the results that we have obtained in section II of [1]: we show that an upper bound on the trace distance of this approximation is given by , where d is the dimension of the individual system, thereby improving previously known bounds. Our result follows from a more general approximation theorem for representations of the unitary group: Consider a pure state that lies in the irreducible representation of the unitary group , for highest weights μ, ν and μ+ν. Let ξ_μ be the state obtained by tracing out U_ν. Then ξ_μ is close to a convex combination of the coherent states U_μ(g)|v_μ〉, where and |v_μ〉 is the highest weight vector in U_μ.

Problem of classification of the set of all entangled states is considered. Invariance of entangled states relative to the transformations from a group of symmetry of qubit space leads to classification of all states of the system through irreducible representations from that group. Excess of entropy the of a subsystem over the entropy of the whole system indicates the presence of entaglement in the system.

I explain quantum nonlocality experiments and discuss how to optimize them. Statistical tools from missing data maximum likelihood are crucial. New results are given on CGLMP, CH and ladder inequalities. Open problems are also discussed.

We present an experimental and theoretical characterization of the symmetric four-qubit entangled Dicke state with two excitations D⁽²⁾₄. We investigate the state's violation of local realism and study its characteristic properties with respect to quantum information applications. For the experimental observation of the state we used photons obtained from parametric down conversion. This allowed, in a simple experimental set-up, quantum state tomography yielding a fidelity as high as 0.844 ± 0.008.

We discuss the security of QKD protocol with four-state system based on single spatial and frequency non-degenerate down converted photons. Simple schemes for biphoton generation and their deterministic measurements are analyzed. Three main incoherent attacks (intercept-resend, intermediate basis and optimal attack) on QKD protocol in Hilbert space with dimension D = 4 using three mutually unbiased bases were analyzed. It has been shown that QKD protocol with four-dimensional states belonging to three mutually unbiased bases provides better security against the noise and eavesdropping than protocols exploiting two bases with qubits and ququarts.

We discuss codes for protecting logical qubits carried by optical fields from the effects of amplitude damping, i.e. linear photon loss. We demonstrate that the correctability condition for one-photon loss imposes limitations on the range of manipulations than can be implemented with passive linear-optics networks.

We present recent work of our group in the field of long distance quantum communication. First, we present a feasibility experiment of a simple e-way scheme which is robust to photon number splitting attacks. Then, we show results on a rapid upconversion photon detector, which could increase the maximum rates of quantum key distribution (QKD). Finally, we present a teleportation experiment over a commercial fiber network. This would be an ingredient of a future quantum relay, which could increase the reach of QKD

For scalable applications of optical quantum information it is desirable to have a well controlled source of photons, producing single photons or entangled-pairs on-demand. The finite delay following decay of an exciton confined in a quantum dot makes them a good source of single photons, we demonstrate this, triggering the emission with a pulsed laser. Currently the most widely used techniques for generating entangled photon pairs are nonlinear optical processes, such as parametric down conversion, which produces a probabilistic number of pairs per excitation cycle. Such a source is of limited use in quantum information/processing applications where a regular stream of single entangled photon pairs is preferable. We produced such a triggered source from a semiconductor device for the first time, using the two-photon cascade from a biexciton confined in a single quantum dot. We demonstrate a fidelity of 70% for the emission from the biexciton cascade to the expected bell state. Single quantum dots could prove to be the first robust and compact triggered source of entangled photons.

We discuss the quantum memory protocol based on a polarization-sensitive control of the field and atomic spin subsystems in the process of offresonant coherent Raman scattering of light by spatially extended and optically thick atomic sample. The protocol can be adjusted for atoms, which spin angular momentum ≥ 1, and applied for deterministic quantum memory storage and retrieval schemes. The proposed protocol involves just a single pass of light through atomic ensemble without the need for elaborate pulse shaping or quantum feedback. As a practically relevant example we consider the interaction of a light pulse with hyperfine components of D₁ line of ⁸⁷Rb.

An interaction between an ensemble of two-level atoms and a classical resonance wave and two quantized modes is considered. Using the effective Hamiltonian describing a parametric down conversion process we consider the dynamics of the system when one of the modes is in coherent state and another one is in vacuum state initially. We found a regime of generation in which the both quantized modes have the macroscopic photon numbers and their state is entangled.

Quantum Key Exchange (QKE, also known as Quantum Key Distribution or QKD) allows communicating parties to securely establish cryptographic keys. It is a well-established fact that all QKE protocols require that the parties have access to an authentic channel. Without this authenticated link, QKE is vulnerable to man-in-the-middle attacks. Overlooking this fact results in exaggerated claims and/or false expectations about the potential impact of QKE. In this paper we present a systematic comparison of QKE with traditional key establishment protocols in realistic secure communication systems.