arXiv subjects

D. D'Alessandro

Publications and source records attributed to D. D'Alessandro.

7 recordsLinked to original sources

arXiv2006

Quantum measurement of a mesoscopic spin ensemble

We describe a method for precise estimation of the polarization of a mesoscopic spin ensemble by using its coupling to a single two-level system. Our approach requires a minimal number of measurements on the two-level system for a given measurement precision. We consider the application of this method to the case of nuclear spin ensemble defined by a single electron-charged quantum dot: we show that decreasing the electron spin dephasing due to nuclei and increasing the fidelity of nuclear-spin-based quantum memory could be within the reach of present day experiments.

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arXiv2005

Incoherent control and entanglement for two-dimensional coupled systems

We investigate accessibility and controllability of a quantum system S coupled to a quantum probe P, both described by two-dimensional Hilbert spaces, under the hypothesis that the external control affects only P. In this context accessibility and controllability properties describe to what extent it is possible to drive the state of the system S by acting on P and using the interaction between the two systems. We give necessary and sufficient conditions for these properties and we discuss the relation with the entangling capability of the interaction between S and P. In particular, we show that controllability can be expressed in terms of the SWAP operator, acting on the composite system, and its square root.

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arXiv2005

Further results on the observability of quantum systems under general measurement

In this paper, we present a collection of results on the observability of quantum mechanical systems, in the case the output is the result of a discrete nonselective measurement. By defining an effective observable we extend previous results, on the Lie algebraic characterization of observable systems, to general measurements. Further results include the characterization of a `best probe' (i.e. a minimally disturbing probe) in indirect measurement and a study of the relation between disturbance and observability in this case. We also discuss how the observability properties of a quantum system relate to the problem of state reconstruction. Extensions of the formalism to the case of selective measurements are also given.

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arXiv2002

Notions of controllability for quantum mechanical systems

In this paper, we define four different notions of controllability of physical interest for multilevel quantum mechanical systems. These notions involve the possibility of driving the evolution operator as well as the state of the system. We establish the connections among these different notions as well as methods to verify controllability. The paper also contains results on the relation between the controllability in arbitrary small time of a system varying on a compact transformation Lie group and the corresponding system on the associated homogeneous space. As an application, we prove that, for the system of two interacting spin 1/2 particles, not every state transfer can be obtained in arbitrary small time.

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arXiv2001

Uniform Finite Generation of Compact Lie Groups and universal quantum gates

Consider a compact connected Lie group $G$ and the corresponding Lie algebra $\cal L$. Let $\{X_1,...,X_m\}$ be a set of generators for the Lie algebra $\cal L$. We prove that $G$ is uniformly finitely generated by $\{X_1,...,X_m\}$. This means that every element $K \in G$ can be expressed as $K=e^{Xt_1}e^{Xt_2} \cdot \cdot \cdot e^{Xt_l}$, where the indeterminates $X$ are in the set $\{X_1,...,X_m \}$, $t_i \in \RR$, $i=1,...,l$, and the number $l$ is uniformly bounded. This extends a previous result by F. Lowenthal in that we do not require the connected one dimensional Lie subgroups corresponding to the $X_i$, $i=1,...,m$, to be compact. We discuss the consequence of this result to the question of universality of quantum gates in quantum computing.

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arXiv2001

The Lie algebra Structure and Nonlinear Controllability of Spin Systems

In this paper, we study the controllability properties and the Lie algebra structure of networks of particles with spin immersed in an electro-magnetic field. We relate the Lie algebra structure to the properties of a graph whose nodes represent the particles and an edge connects two nodes if and only if the interaction between the two corresponding particles is active. For networks with different gyromagnetic ratios, we provide a necessary and sufficient condition of controllability in terms of the properties of the above mentioned graph and describe the Lie algebra structure in every case. For these systems all the controllability notions, including the possibility of driving the evolution operator and/or the state, are equivalent. For general networks (with possibly equal gyromagnetic ratios), we give a sufficient condition of controllability. A general form of interaction among the particles is assumed which includes both Ising and Heisenberg models as special cases. Assuming Heisenberg interaction we provide an analysis of low dimensional cases (number of particles less then or equal to three) which include necessary and sufficient controllability conditions as well as a study of their Lie algebra structure. This also, provides an example of quantum mechanical systems where controllability of the state is verified while controllability of the evolution operator is not.

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arXiv2001

Control of one and two homonuclear spins

We consider the problem of steering control for the systems of one spin 1/2 particle and two interacting homonuclear spin 1/2 particles in an electro-magnetic field. The describing models are bilinear systems whose state varies on the Lie group of special unitary matrices of dimensions two and four, respectively. By performing decompositions of Lie groups, taking into account the describing equations at hand, we derive control laws to steer the state of the system to any desired final configuration. Explicit formulas are given for the parameters involved in the control algorithms. Moreover, the proposed algorithms allow for arbitrary bounds on the magnitude of the controls and for some flexibility in the specification of the final time which must be greater than a given value but otherwise arbitrary.

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