Generation of two-mode field squeezing through selective dynamics in cavity QED

We propose a scheme for the generation of a two-mode field squeezed state in cavity QED. It is based on two-channel Raman excitations of a beam of three-level atoms with random arrival times by two classical fields and two high-Q resonator modes. It is shown that by suitably choosing the intensities and detunings of fields the dynamical processes can be selective and two-mode squeezing between the cavity modes can be generated at steady state. This proposal does not need the preparation of the initial states of atoms and cavity modes, and is robust against atomic spontaneous decay.Comment: 4 pages,2 figure

Distance growth of quantum states due to initial system--environment correlations

Intriguing features of the distance between two arbitrary states of an open quantum system are identified that are induced by initial system-environment correlations. As an example, we analyze a qubit dephasingly coupled to a bosonic environment. Within tailored parameter regimes, initial correlations are shown to substantially increase a distance between two qubit states evolving to long-time limit states according to exact non-Markovian dynamics. It exemplifies the breakdown of the distance contractivity of the reduced dynamics.Comment: 4 pages, 3 figure

Optimal multiqubit operations for Josephson charge qubits

We introduce a method for finding the required control parameters for a quantum computer that yields the desired quantum algorithm without invoking elementary gates. We concentrate on the Josephson charge-qubit model, but the scenario is readily extended to other physical realizations. Our strategy is to numerically find any desired double- or triple-qubit gate. The motivation is the need to significantly accelerate quantum algorithms in order to fight decoherence.Comment: 4 pages, 5 figure

Classical Concepts in Quantum Programming

The rapid progress of computer technology has been accompanied by a corresponding evolution of software development, from hardwired components and binary machine code to high level programming languages, which allowed to master the increasing hardware complexity and fully exploit its potential. This paper investigates, how classical concepts like hardware abstraction, hierarchical programs, data types, memory management, flow of control and structured programming can be used in quantum computing. The experimental language QCL will be introduced as an example, how elements like irreversible functions, local variables and conditional branching, which have no direct quantum counterparts, can be implemented, and how non-classical features like the reversibility of unitary transformation or the non-observability of quantum states can be accounted for within the framework of a procedural programming language.Comment: 11 pages, 4 figures, software available from http://tph.tuwien.ac.at/~oemer/qcl.html, submitted for QS2002 proceeding

Ground-state geometric quantum computing in superconducting systems

We present a theoretical proposal for the implementation of geometric quantum computing based on a Hamiltonian which has a doubly degenerate ground state. Thus the system which is steered adiabatically, remains in the ground-state. The proposed physical implementation relies on a superconducting circuit composed of three SQUIDs and two superconducting islands with the charge states encoding the logical states. We obtain a universal set of single-qubit gates and implement a non-trivial two-qubit gate exploiting the mutual inductance between two neighboring circuits, allowing us to realize a fully geometric ground-state quantum computing. The introduced paradigm for the implementation of geometric quantum computing is expected to be robust against environmental effects.Comment: 9 pages, 5 figures. Final version with notation and typos correcte

Option Pricing in Multivariate Stochastic Volatility Models of OU Type

We present a multivariate stochastic volatility model with leverage, which is flexible enough to recapture the individual dynamics as well as the interdependencies between several assets while still being highly analytically tractable. First we derive the characteristic function and give conditions that ensure its analyticity and absolute integrability in some open complex strip around zero. Therefore we can use Fourier methods to compute the prices of multi-asset options efficiently. To show the applicability of our results, we propose a concrete specification, the OU-Wishart model, where the dynamics of each individual asset coincide with the popular Gamma-OU BNS model. This model can be well calibrated to market prices, which we illustrate with an example using options on the exchange rates of some major currencies. Finally, we show that covariance swaps can also be priced in closed form.Comment: 28 pages, 5 figures, to appear in SIAM Journal on Financial Mathematic

Correlations in Free Fermionic States

We study correlations in a bipartite, Fermionic, free state in terms of perturbations induced by one party on the other. In particular, we show that all so conditioned free states can be modelled by an auxiliary Fermionic system and a suitable completely positive map.Comment: 17 pages, no figure

Locking classical information

It is known that the maximum classical mutual information that can be achieved between measurements on a pair of quantum systems can drastically underestimate the quantum mutual information between those systems. In this article, we quantify this distinction between classical and quantum information by demonstrating that after removing a logarithmic-sized quantum system from one half of a pair of perfectly correlated bitstrings, even the most sensitive pair of measurements might only yield outcomes essentially independent of each other. This effect is a form of information locking but the definition we use is strictly stronger than those used previously. Moreover, we find that this property is generic, in the sense that it occurs when removing a random subsystem. As such, the effect might be relevant to statistical mechanics or black hole physics. Previous work on information locking had always assumed a uniform message. In this article, we assume only a min-entropy bound on the message and also explore the effect of entanglement. We find that classical information is strongly locked almost until it can be completely decoded. As a cryptographic application of these results, we exhibit a quantum key distribution protocol that is "secure" if the eavesdropper's information about the secret key is measured using the accessible information but in which leakage of even a logarithmic number of key bits compromises the secrecy of all the others.Comment: 32 pages, 2 figure

Analysis of a convenient information bound for general quantum channels

Open questions from Sarovar and Milburn (2006 J.Phys. A: Math. Gen. 39 8487) are answered. Sarovar and Milburn derived a convenient upper bound for the Fisher information of a one-parameter quantum channel. They showed that for quasi-classical models their bound is achievable and they gave a necessary and sufficient condition for positive operator-valued measures (POVMs) attaining this bound. They asked (i) whether their bound is attainable more generally, (ii) whether explicit expressions for optimal POVMs can be derived from the attainability condition. We show that the symmetric logarithmic derivative (SLD) quantum information is less than or equal to the SM bound, i.e.\ $H(\theta) \leq C_{\Upsilon}(\theta)$ and we find conditions for equality. As the Fisher information is less than or equal to the SLD quantum information, i.e. $F_M(\theta) \leq H(\theta)$, we can deduce when equality holds in $F_M(\theta) \leq C_{\Upsilon}(\theta)$. Equality does not hold for all channels. As a consequence, the attainability condition cannot be used to test for optimal POVMs for all channels. These results are extended to multi-parameter channels.Comment: 16 pages. Published version. Some of the lemmas have been corrected. New resuts have been added. Proofs are more rigorou

A very brief introduction to quantum computing and quantum information theory for mathematicians

This is a very brief introduction to quantum computing and quantum information theory, primarily aimed at geometers. Beyond basic definitions and examples, I emphasize aspects of interest to geometers, especially connections with asymptotic representation theory. Proofs of most statements can be found in standard references