Simulations of continuum coherent states and its use in quantum cryptographic systems

Abstract

The continuum states formalism is suitable for field quantization in optical fibre; however, they are harder to use than discrete states. On the other hand, a Hermitian phase operator can be defined only in a finite dimensional space. We approximated a coherent continuum state by a finite tensor product of coherent states, each one defined in a finite dimensional space. Using this, in the correct limit, we were able to obtain some statistical properties of the photon number and phase of the continuum coherent states from the probability density functions of the individual, finite dimensional, coherent states. Then, we performed a simulation of the BB84 protocol, using the continuum coherent states, in a fibre interferometer commonly used in quantum cryptography. We observed the fluctuations of the mean photon number in the pulses that arrive at Bob, which occurs in the practical system, introduced by the statistical property of the simulation.     

Expanded quantum cryptographic entangling probe

A generalized quantum circuit and design are given for an optimal entangling probe to be used in attacking the BB84 protocol of quantum key distribution and yielding maximum information to the probe. Probe photon polarization states become optimally entangled with the BB84 signal states on their way between the legitimate transmitter and receiver. The present design generalizes an earlier one by Brandt [J. Mod. Optics 52 2177 (2005)] to include a complete range of error rates that can be induced by the probe.     

Alternative design for quantum cryptographic entangling probe

An alternative design is given for an optimized quantum cryptographic entangling probe for attacking the BB84 protocol of quantum key distribution. The initial state of the probe has a simpler analytical dependence on the set error rate to be induced by the probe than in the earlier design. The new device yields the same maximum information to the probe for a full range of induced error rates. As in the earlier design, the probe contains a single CNOT gate which produces the optimum entanglement between the BB84 signal states and the correlated probe states.     

Decoherence in quantum systems

We discuss various definitions of decoherence and how it can be measured. We compare and contrast decoherence in quantum systems with an infinite number of eigenstates (such as the free particle and the oscillator) and spin systems. In the former case, we point out the essential difference between assuming "entanglement at all times" and entanglement with the reservoir occuring at some initial time. We also discuss optimum calculational techniques in both arenas.     

Defense and attack of complex and dependent systems

A framework is constructed for how to analyze the strategic defense of an infrastructure subject to attack by a strategic attacker. Merging operations research, reliability theory, and game theory for optimal analytical impact, the optimization program for the defender and attacker is specified. Targets can be in parallel, series, combined series-parallel, complex, k-out-of-n redundancy, independent, interdependent, and dependent. The defender and attacker determine how much to invest in defending versus attacking each of multiple targets. A target can have economic, human, and symbolic values, subjectively assessed by the defender and attacker. A contest success function determines the probability of a successful attack on each target, dependent on the investments by the defender and attacker into each target, and on characteristics of the contest. The defender minimizes the expected damage plus the defense costs. The attacker maximizes the expected damage minus the attack costs. Each agent is concerned about how his investments vary across the targets, and the impact on his utilities. Interdependent systems are analyzed where the defense and attack on one target impacts all targets. Dependent systems are analyzed applying Markov analysis and repeated games where a successful attack on one target in the first period impacts the unit costs of defense and attack, and the contest intensity, for the other target in the second period.     

Nano-optics with single quantum systems

This paper reviews the recent progress in using single quantum systems, here mainly single fluorescent molecules, as local probes for nano-optical field distributions. We start by discussing the role of the absorption cross-section for the spatial resolution attainable in such experiments and its behaviour for different environmental conditions. It is shown that the spatial distribution of field components in a high-numerical aperture laser focus can be mapped with high precision using single fluorescent molecules embedded in a thin polymer film on glass. With this proof-of-principle experiment as a starting point, the possibility of mapping strongly confined and enhanced nano-optical fields close to material structures, e.g. sharp metal tips, is discussed. The mapping of the spatial distribution of the enhanced field at an etched gold tip using a single molecule is presented as an example. Energy transfer effects and quenching are identified as possible artefacts in this context. Finally, it is demonstrated that the local quenching at a sharp metal structure nevertheless can be exploited as a novel contrast mechanism for ultrahigh-resolution optical microscopy with single-molecule sensitivity.     

Decoherence rates in large-scale quantum computers and macroscopic quantum systems

Markovian regime decoherence effects in quantum computers are studied in terms of the fidelity for the situation where the number of qubits N becomes large. A general expression giving the decoherence time scale in terms of Markovian relaxation elements and expectation values of products of system fluctuation operators is obtained, which could also be applied to study decoherence in other macroscopic systems such as Bose condensates and superconductors. A standard circuit model quantum computer involving three-state lambda system ionic qubits is considered, with qubits localized around well-separated positions via trapping potentials. The centre of mass vibrations of the qubits act as a reservoir. Coherent one and two qubit gating processes are controlled by time-dependent localized classical electromagnetic fields that address specific qubits, the two qubit gating processes being facilitated by a cavity mode ancilla, which permits state interchange between qubits. With a suitable choice of parameters, it is found that the decoherence time can be made essentially independent of N.     

Boundary slip in spin-polarized quantum systems

We describe the effects of boundary slip in spin-polarized quantum liquids and gases. The slip coefficients in boundary conditions form a 3 × 3 matrix. The off-diagonal coefficients are expressed via each other with the help of the Onsager relations. We calculate accurate lower and upper bounds of all slip coefficients for polarized degenerate Fermi liquids and for dilute gases at arbitrary temperatures. The calculations are based on the transport equation for spin-polarized systems with diffuse boundary conditions. The results for gases are especially simple in the limiting cases of low-temperature degenerate systems or in the high-temperature classical Boltzmann regime. All slip coefficients are proportional to the mean free path and increase with increasing spin polarization. As a by-product the theory describes the slip effects in binary mixtures of classical gases or Fermi liquids when the role of spin polarization is played by the concentration of the mixture.     

Electrons at the surface of quantum systems

Electrons can be trapped at the surfaces and interfaces of the condensed phases of quantum matter (in particular hydrogen and helium), where they form classical two-dimensional Coulomb systems. Apart from studying the intrinsic properties of these nearly ideal systems, like the transition from an electron gas to a Wigner solid, one can use the electrons also as a sensitive probe to investigate the surface of quantum liquids and solids. The examples presented here include the surface of solid H₂, He films, and the interface between liquid and solid He, where phenomena such as annealing, layering, and crystal growth are studied. In addition, the interaction between the electrons and long-wavelength interfacial modes leads to an electrohydrodynamic instability, which bears interesting similarities with other critical phenomena.     

Performance of photon-pair quantum key distribution systems

Abstract

We analyse the quantitative improvement in performance provided by a novel quantum key distribution (QKD) system that employs a correlated photon source (CPS) and a photon-number resolving detector (PNR). Calculations suggest that given current technology, the CPS/PNR implementation offers an improvement of several orders of magnitude in secure bit rate over previously described implementations.     

Comparing the states of many quantum systems

Abstract

We investigate how to determine whether the states of a set of quantum systems are identical or not. This paper treats both error-free comparison, and comparison where errors in the result are allowed. Error-free comparison means that we aim to obtain definite answers, which are known to be correct, as often as possible. In general, we will also have to accept inconclusive results, giving no information. To obtain a definite answer that the states of the systems are not identical is always possible, whereas in the situation considered here, a definite answer that they are identical will not be possible. The optimal universal error-free comparison strategy is a projection onto the totally symmetric and the different non-symmetric subspaces, invariant under permutations and unitary transformations. We also show how to construct optimal comparison strategies when allowing for some errors in the result, minimizing either the error probability, or the average cost of making an error. We point out that it is possible to realize universal error-free comparison strategies using only linear elements and particle detectors, albeit with less than ideal efficiency. Also minimum-error and minimum-cost strategies may sometimes be realized in this way. This is of great significance for practical applications of quantum comparison.     

System approach to metrology of quantum multiparticle systems

Features of the metrology of quantum multiparticle systems in connection with general system theory and representational theory are considered. Quantitative characteristics of the periodic system of elements (PSE) are introduced and studied, including property correlation, and also system hierarchies are considered leading to its analysis and possible application of nanosystems and quantum computers. __________ Translated from Izmeritel’naya Tekhnika, No. 4. pp. 3–7, April, 2008.     

Security aspects of quantum cryptography with D-dimensional systems

Abstract

We analyse the security of quantum key distribution with three-dimensional systems, and show that this scheme is more advantageous against symmetric attacks than protocols using two-dimensional states. We generalize the resulting optimal eavesdropping transformation to cryptographic systems with arbitrary dimensions.     

Electrical transport phenomena in systems of semiconductor quantum dots

While a fairly good understanding of optical and transport properties that are associated with single quantum dots has emerged in recent years the understanding of the relation between these properties and the observed macroscopic optical and electrical properties of solid ensembles of such dots is still at a very rudimentary level. This is in particular so in regard to the transport properties where the interplay between inter-dot conduction and the connectivity of the dots network determines the macroscopic observations. Reviewing the basic concepts and issues associated with these two essential ingredients, and considering some recent experimental observations on quantum dot ensembles of CdSe and Si, an effort is made here to derive a whole-but-simple physical basis for the understanding of the transport and the optoelectronic properties of solid state ensemble of semiconductor quantum dots.     

Mesoscopic systems: classical irreversibility and quantum coherence

Mesoscopic physics is a sub-discipline of condensed-matter physics that focuses on the properties of solids in a size range intermediate between bulk matter and individual atoms. In particular, it is characteristic of a domain where a certain number of interacting objects can easily be tuned between classical and quantum regimes, thus enabling studies at the border of the two. In magnetism, such a tuning was first realized with large-spin magnetic molecules called single-molecule magnets (SMMs) with archetype Mn(12)-ac. In general, the mesoscopic scale can be relatively large (e.g. micrometre-sized superconducting circuits), but, in magnetism, it is much smaller and can reach the atomic scale with rare earth (RE) ions. In all cases, it is shown how quantum relaxation can drastically reduce classical irreversibility. Taking the example of mesoscopic spin systems, the origin of irreversibility is discussed on the basis of the Landau-Zener model. A classical counterpart of this model is described enabling, in particular, intuitive understanding of most aspects of quantum spin dynamics. The spin dynamics of mesoscopic spin systems (SMM or RE systems) becomes coherent if they are well isolated. The study of the damping of their Rabi oscillations gives access to most relevant decoherence mechanisms by different environmental baths, including the electromagnetic bath of microwave excitation. This type of decoherence, clearly seen with spin systems, is easily recovered in quantum simulations. It is also observed with other types of qubits such as a single spin in a quantum dot or a superconducting loop, despite the presence of other competitive decoherence mechanisms. As in the molecular magnet V(15), the leading decoherence terms of superconducting qubits seem to be associated with a non-Markovian channel in which short-living entanglements with distributions of two-level systems (nuclear spins, impurity spins and/or charges) leading to 1/f noise induce τ(1)-like relaxation of S(z) with dissipation to the bath of two-level systems with which they interact most. Finally, let us mention that these experiments on quantum oscillations are, most of the time, performed in the classical regime of Rabi oscillations, suggesting that decoherence mechanisms might also be treated classically.     

Capacitance theory of open quantum systems with classical contacts

We consider semiconductor devices composed of a small quantum structure as the active device region and two classical environments constituting the source- and the drain contact. The contacts are taken as free electron gases with infinite conductivity defining the chemical potentials in the contacts. The transport through the quantum structure is described in the Landauer–Büttiker formalism using electronic scattering wave functions which determine the electron density in the quantum system. In our Hartree approximation these charges and the induced charges in the contacts are the sources of the self-consistent Coulomb field. As a particular quantum structure we study a GaAs heterostructure device consisting of a two-dimensional electron gas sandwiched between a gate contact and an AlGaAs blocking barrier [see V.T. Dolgopolov et al., Phys. Low-Dim. Struct. 6 (1996) 1]. We demonstrate the quantitative agreement of our theory with the experimental results.     

Defense conversion and systems architecture: challenges to Taiwan's aircraft industry

How to establish a complex high-tech systems engineering industry is crucial for many newly industrializing countries to further their economic development beyond efficient manufacturing of relatively simple products. Because the aircraft industry is a user and driver of advanced product and process technologies, in 1990 Taiwan's government officially designated this industry as a national strategic area to receive policy support. The ultimate success of this endeavor depends on the transformation of a combat aircraft producer into a commercial champion and the sustainability of the supporting industries. However, the prospect of defense conversion is dismal. The commercial benefits of military work are minimal because military and civilian needs of design are very different and so are scale economies, scope economies, and experience curve. Moreover, neither spin-off nor dual-use strategy can apply effectively, leaving the focal company an enclave isolated from the local industry. Another insurmountable barrier is the integral architecture of the aircraft and engine systems. In this industry, most functional and design specifications and standards are imposed by the upper-tier buyers and integrators. This implies that the lower-tier firms cannot pursue their own engineering and production competence rather independently and flexibly as most other local firms in Taiwan do in the fields of highly open components and easily adjustable interfaces. This case typifies a government's futile efforts in a global industry of complex proprietary technological systems and points to the criticality of defense conversion and systems architecture in the commercial world of systems engineering.