Related papers: Lie algebraic invariants in quantum linear optics
A quantum state contains the maximal amount of information available for a given quantum system. In this paper we use weak-value expressions to reconstruct quantum states of continuous-variable systems in the quantum optical domain. The…
In this paper we give a geometrical framework for the design of observers on finite-dimensional Lie groups for systems which possess some specific symmetries. The design and the error (between true and estimated state) equation are explicit…
This paper considers the design of nonlinear observers for invariant systems posed on finite-dimensional connected Lie groups with measurements generated by a transitive group action on an associated homogeneous space. We consider the case…
The aim of this note is to present a unified approach to the results given in \cite{bb99} and \cite{bs04} which also covers examples of models not presented in these two papers (e.g. $d$-dimensional Minkowski space-time for $d\geq 3$).…
This paper presents three non-linear observers on three examples of engineering interest: a chemical reactor, a non-holonomic car, and an inertial navigation system. For each example, the design is based on physical symmetries. This…
We report the first experimental demonstration of conditional preparation of a non classical state of light in the continuous variable regime. Starting from a non degenerate OPO which generates above threshold quantum intensity correlated…
Quantum number-path entanglement is a resource for super-sensitive quantum metrology and in particular provides for sub-shotnoise or even Heisenberg-limited sensitivity. However, such number-path entanglement has thought to have been…
We develop a framework for learning properties of quantum states beyond the assumption of independent and identically distributed (i.i.d.) input states. We prove that, given any learning problem (under reasonable assumptions), an algorithm…
With a Bayesian approach, the linear optics correction algorithm for storage rings is revisited. Starting from the Bayes' theorem, a complete linear optics model is simplified as "likelihood functions" and "prior probability distributions".…
The evolution of quantum light through linear optical devices can be described by the scattering matrix $S$ of the system. For linear optical systems with $m$ possible modes, the evolution of $n$ input photons is given by a unitary matrix…
Let $\ket{\0}$ and $\ket{\1}$ be two states that are promised to come from known subsets of orthogonal subspaces, but are otherwise unknown. Our paper probes the question of what can be achieved with respect to the basis…
A simple procedure to obtain complete, closed expressions for Lie algebra invariants is presented. The invariants are ultimately polynomials in the group parameters. The construction of finite group elements require the use of projectors,…
We previously established that in principle, it is possible to quantum compute using passive linear optics with photo-detectors (quant-ph/0006088). Here we describe techniques based on error detection and correction that greatly improve the…
We consider the 2-generated free metabelian associative and Lie algebras over the complex field and the invariants of the dihedral groups of finite order acting on these algebras. In the associative case we find a finite set of generators…
We investigate which pure states of $n$ photons in $d$ modes can be transformed into each other via linear optics, without post-selection. In other words, we study the local unitary (LU) equivalence classes of symmetric many-qudit states.…
We present a method for implementing an optical neural network using only linear optical resources, namely field displacement and interferometry applied to coherent states of light. The nonlinearity required for learning in a neural network…
Lie algebraic techniques are powerful and widely-used tools for studying dynamics and metrology in quantum optics. When the Hamiltonian generates a Lie algebra with finite dimension, the unitary evolution can be expressed as a finite…
The ability to perform high-precision optical measurements is paramount to science and engineering. Laser interferometry enables interaction-free sensing with a precision ultimately limited by shot noise. Quantum optical sensors can surpass…
Precision metrology and quantum measurement often demand matter be prepared in well defined quantum states for both internal and external degrees of freedom. Laser-cooled neutral atoms localized in a deeply confining optical potential…
We propose a scheme to prepare a maximally entangled state for two Lambda-type atoms trapped in separate optical cavities coupled through an optical fiber based on the combined effect of the unitary dynamics and the dissipative process. Our…