Defense frontier analysis of quantum cryptographic systems

When a quantum cryptographic system operates in the presence of background noise, security of the key can be recovered by a procedure called key distillation. A key-distillation scheme effective against so-called individual (bitwise-independent) eavesdropping attacks involves sacrifice of some of the data through privacy amplification. We derive the amount of data sacrifice sufficient to defend against individual eavesdropping attacks in both BB84 and B92 protocols and show in what sense the communication becomes secure as a result. We also compare the secrecy capacity of various quantum cryptosystems, taking into account data sacrifice during key distillation, and conclude that the BB84 protocol may offer better performance characteristics than the B92.     

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.     

Coherent molecular resonances in quantum dot-metallic nanoparticle systems: coherent self-renormalization and structural effects

It is known that surface-plasmon resonances of metallic nanoparticles can significantly enhance the field experienced by semiconductor quantum dots. In this paper we show that, when quantum dots are in the vicinity of metallic nanoparticles and interact with coherent light sources (laser fields), coherent exciton-plasmon coupling (quantum coherence effects) can increase the amount of the plasmonic field enhancement significantly. We also study how the coherent molecular resonances generated by such a coupling process are influenced by the self-renormalization of the plasmonic fields and the structural parameters of the systems, particularly the size and shape of the metallic nanoparticle. The renormalization process happens via mutual impacts of the radiative decay rate of excitons and the coherent exciton-plasmon coupling on each other. Our results highlight the conditions where the molecular resonances become very sharp, offering optical switching processes with high extinction ratio and wide ranging device applications.     

Nonclassical features of entangled coherent states

Nonclassical features of entangled coherent states (two-mode superposition coherent states) based on two coherent states shifted in phase by π/2 are discussed. Analysis of Cauchy–Schwartz inequality, two-mode quadrature squeezing, oscillatory and sub-Poissonian photon statistics show that nonclassicality exists for these states. Furthermore, it is also observed that special states have remarkably strong nonclassical properties than the entangled coherent states based on famous even–odd coherent states.     

Numerical simulation of coherent transport in quantum wires for quantum computing

A solid-state implementation of a universal set of gates for quantum computation is proposed and analysed using a time-dependent 2D Schrödinger solver. The qubit is defined as the state of an electron propagating along a couple of quantum wires. The wires are suitably coupled through a potential barrier with variable height and/or width. It is shown how a proper design of the system allows the implementation of any one-qubit transformation. The two-qubit gate is realized through a Coulomb coupler able to entangle the quantum states of two electrons running in two wires of two different qubits. The simulated devices are GaAs—AlGaAs heterostructures that should be on the borderline of present semiconductor technology. An estimate of decoherence effects due to phonon scattering is also presented.     

Theory of the adiabatic passage in two-level quantum systems with superpositional initial states

Abstract

An analytic theory of the adiabatic passage (AP) regime of interaction of short frequency chirped laser pulses with a two-level quantum system (QS) being initially in the superpositional quantum state is presented. We show that the initial value of the non-diagonal elements of the density matrix can influence the dynamics of the population transfer during the action of the laser pulse, but do not influence essentially the final populations of the states of the QS obtained at the end of the interaction near the AP regime. A novel solution to the Bloch equations is obtained in the form of a converging power series generalizing the ordinary AP solution.     

Generalized uncertainty relations and coherent and squeezed states

Characteristic uncertainty relations and their related squeezed states are briefly reviewed and compared in accordance with the generalizations of three equivalent definitions of canonical coherent states. The standard SU(1, 1) coherent states are shown to be the unique states that minimize the Schr?dinger uncertainty relation for every pair of the three generators and the Robertson relation for the three generators. The characteristic uncertainty inequalities are naturally extended to the case of several states. It is shown that these inequalities can be written in the equivalent complementary form.     

Phase properties of coherent phase and generalized geometric states

Abstract

We examine some properties of a class of partial phase states of a single field mode. The quasiprobability distribution function and the phase properties of both the generalized geometric and even geometric states are investigated. The relation between the coherent phase states and the SU(1, 1) coherent states is sought.     

Influence of friction and temperature on coherent quantum tunneling

The dynamics of a quantum particle tunneling through the barrier of an almost symmetric double-well potential is studied. The coherent quantum oscillations characteristic for isolated tunneling systems are shown to be strongly affected by the interaction with a heat bath environment. Attention is focused on the situation where the heat bath causes an Ohmic damping. This case is of potential relevance to the problem of macroscopic quantum coherence in SQUID rings. The range of parameters in which quantum coherence survives is determined and the time evolution of the occupation probabilities in the two wells is calculated.     

Generation of amplitude squeezed states of light from phase squeezed coherent states

Abstract

We propose a scheme to generate a displaced macroscopic superposition of phase squeezed coherent states by incorporating an optical parametric oscillator (OPO) and a nonlinear Kerr medium in a Mach-Zhender interferometer configuration. We show that the phase squeezed coherent state generated by the OPO evolves into a macroscopic superposition of phase squeezed coherent states on spending a specific amount of time inside a Kerr medium. The phase space displacement is achieved by the interference of the intense reference beam with the signal in the final beam splitter of the interferometer. The noise of the reference beam contaminating the signal is prevented by making this beam splitter highly reflective. We have calculated the photon number uncertainty of the outcoming beam and have shown that it is smaller than the usual amplitude squeezed coherent state's value.     

Four-mode coherent entangled state as an entanglement of two bipartite coherent entangled states

By introducing a four-mode unitary operator U = exp[?iλ(X ₁ P ₂ + X ₂ P ₃ + X ₃ P ₄ + X ₄ P ₁)], we show how a four-mode coherent entangled state can be generated by entangling a two bipartite coherent entangled state. The corresponding squeezed vacuum state U|0000? in four-mode Fock space is derived by virtue of the technique of integration within ordered production of operators, which exhibits the standard squeezing for the four-mode quadratures. A new ideal quantum mechanical representation |α, β, γ? is constructed from U|0000? in the limit of infinite squeezing, which possesses the properties of both coherent and entangled states. The entanglement involved in |α, β, γ? is explained. A scheme for generating |α, β, γ? is presented.     

Improved superresolution in coherent optical systems

Objects that temporally vary slowly can be superresolved by the use of two synchronized moving masks such as pinholes or gratings. This approach to superresolution allows one to exceed Abbe's limit of resolution. Moreover, under coherent illumination, superresolution requires a certain approximation based on the time averaging of intensity rather than of field distribution. When extensive digital postprocessing can be incorporated into the optical system, a detector array and some postprocessing algorithms can replace the grating that is responsible for information decoding. In this way, no approximation is needed and the synchronization that is necessary when two gratings are used is simplified. Furthermore, we present two novel approaches for overcoming distortions when extensive digital postprocessing cannot be incorporated into the optical system. In the first approach, one of the gratings, in the input or at the output plane, is shifted at half the velocity of the other. In the second approach, various spectral regions are transmitted through the system's aperture to facilitate postprocessing. Experimental results are provided to demonstrate the properties of the proposed methods.     

Reconstruction of quantum states of spin systems via the Jaynes principle of maximum entropy

Abstract

We apply the Jaynes principle of maximum entropy for the partial reconstruction of correlated spin states. We determine the minimum set of observables which is necessary for the complete reconstruction of the most correlated states of systems composed of spins 1/2 (e.g. the Bell and the Greenberger-Horne-Zeilinger states). We investigate to what extent an incomplete measurement can reveal non-classical features of correlated spin states.     

Scattering coherent and partially coherent space-time pulses through few-mode optical systems

We consider the spatiotemporal behavior of coherent and partially coherent, pulsed, few-mode optical systems. It is shown that there is some set of orthogonal space-time pulses at the input reference surface that maps in one-to-one correspondence with some set of orthogonal space-time pulses at the output reference surface; we call these pulses eigenfields. The spectrum of the coupling coefficients determines the amount of information that can be transmitted within a given period of time. The eigenfields are unique for a given system and can be used to propagate a field that is in any state of spatial and temporal coherence. They can also be used to account for the spatial and temporal coherence of internally generated noise and to calculate the powers, fluctuations, and correlations that would be recorded by multimode detectors. Our technique is ideal for modeling the behavior of pulsed imaging arrays and interferometers.