Related papers: The Solution to the Frame Quantum Detection Proble…
We consider the problem of designing an optimal quantum detector to minimize the probability of a detection error when distinguishing between a collection of quantum states, represented by a set of density operators. We show that the design…
The quantum separability problem consists in deciding whether a bipartite density matrix is entangled or separable. In this work, we propose a machine learning pipeline for finding approximate solutions for this NP-hard problem in…
In this paper, we consider an open quantum system undergoing imperfect and indirect measurement. For quantum non-demolition (QND) measurement, we show that the system evolves on an appropriately chosen manifold and we express the exact…
The quantum state of a light beam can be represented as an infinite dimensional density matrix or equivalently as a density on the plane called the Wigner function. We describe quantum tomography as an inverse statistical problem in which…
Ever since entanglement was identified as a computational and cryptographic resource, effort has been made to find an efficient way to tell whether a given density matrix represents an unentangled, or separable, state. Essentially, this is…
This work concerns some issues about the interplay of standard and geometric (Hamiltonian) approaches to finite-dimensional quantum mechanics, formulated in the projective space. Our analysis relies upon the notion and the properties of…
We solve the general problem of determining, through imaging, the three-dimensional positions of $N$ weak incoherent point-like emitters in an arbitrary spatial configuration. We show that a structured measurement strategy in which a linear…
A complex frame is a collection of vectors that span $\mathbb{C}^M$ and define measurements, called intensity measurements, on vectors in $\mathbb{C}^M$. In purely mathematical terms, the problem of phase retrieval is to recover a complex…
In the study of quantum limits to parameter estimation, the high dimensionality of the density operator and that of the unknown parameters have long been two of the most difficult challenges. Here we propose a theory of quantum…
Finite frame quantization is a discrete version of the coherent state quantization. In the case of a quantum system with finite-dimensional Hilbert space, the finite frame quantization allows us to associate a linear operator to each…
We derive the form of the quantum filter equation describing the continuous observation of the phase of a quantum system in an arm of an interferometer via non-demolition measurements when the statistics of an input field used for the…
Accurately establishing the state of large-scale quantum systems is an important tool in quantum information science; however, the large number of unknown parameters hinders the rapid characterisation of such states, and reconstruction…
The quantum measurement problem is formulated in the form of an insolubility theorem that states the impossibility of obtaining, for all available object preparations, a mixture of states of the compound object and apparatus system that…
The estimation of the density matrix of a $k$-level quantum system is studied when the parametrization is given by the real and imaginary part of the entries and they are estimated by independent measurements. It is established that the…
We present a numerical method for solving the separability problem of Gaussian quantum states in continuous-variable quantum systems. We show that the separability problem can be cast as an equivalent problem of determining the feasibility…
Ever since entanglement was identified as a computational and cryptographic resource, researchers have sought efficient ways to tell whether a given density matrix represents an unentangled, or separable, state. This paper gives the first…
We solve the problem of best approximation by Parseval frames to an arbitrary frame in a subspace of an infinite dimensional Hilbert space. We explicitly describe all the solutions and we give a criterion for uniqueness. This best…
The recognition of entanglement states is a notoriously difficult problem when no prior information is available. Here, we propose an efficient quantum adversarial bipartite entanglement detection scheme to address this issue. Our proposal…
We investigate the problem of estimating simultaneously multiple parameters encoded in the shape of the modes on which the light is expanded. For this, we generalize the mode-encoded parameter estimation theory as introduced in Ref.[1] to a…
Quantum computers have the potential to solve certain problems faster than classical computers by exploiting quantum mechanical effects such as superposition. However, building high-quality quantum software is challenging due to the…