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Schwinger's algebra of selective measurements has a natural interpretation in the formalism of groupoids. Its kinematical foundations, as well as the structure of the algebra of observables of the theory, was presented in two previous…

We consider the problem of designing a measurement to minimize the probability of a detection error when distinguishing between a collection of possibly non-orthogonal mixed quantum states. We show that if the quantum state ensemble…

NMR is emerging as a valuable testbed for the investigation of foundational questions in quantum mechanics. The present paper outlines the preparation of a class of mixed states, called pseudo-pure states, that emulate pure quantum states…

In this paper, I attempt a personal account of my understanding of the measurement problem in quantum mechanics, which has been largely in the tradition of the Copenhagen interpretation. I assume that (i) the quantum state is a…

Photons are ideal carriers for quantum information as they can have a long coherence time and can be transmitted over long distances. These properties are a consequence of their weak interactions within a nearly linear medium. To create and…

Copying information is an elementary operation in classical information processing. However, copying seems rather different in the quantum regime. Since the discovery of the universal quantum cloning machine, much has been found from the…

Classical-quantum computational complexity separations are an important motivation for the long-term development of digital quantum computers, but classical-quantum complexity equivalences are just as important in our present era of noisy…

We design the information-acquiring von Neumann architecture of a computer in a fine-grained or coarse-grained model of the registers (quickly accessible memories) in the central processing unit, where information is carried by classical…

The tomographic description of a quantum state is formulated in an abstract infinite dimensional Hilbert space framework, the space of the Hilbert-Schmidt linear operators, with trace formula as scalar product. Resolutions of the unity,…

It is proposed a possible new approach of quantum measurements (QMS), disconnected of the traditional interpretation of uncertainty relations and independent of any appeal to the strange idea of collapse (reduction) of wave functions. The…

Any observable with finite eigenvalue spectrum can be measured using a multiport apparatus realizing an appropriate unitary transformation and an array of detector instruments, where each detector operates as an indicator of one possible…

The geometry of quantum states has profound implications in quantum multiparameter estimation. While the Riemannian structure of quantum state space is well understood, the full understanding of the curvature structure of mixed quantum…

State representations summarize our knowledge about a system. When unobservable quantities are introduced the state representation is typically no longer unique. However, this non-uniqueness does not affect subsequent inferences based on…

In this paper, we study metrics of quantum states. These metrics are natural generalization of trace metric and Bures metric. We will prove that the metrics are joint convex and contractive under quantum operation. Our results can find…

Establishing a notion of the quantum state that applies consistently across space and time could be a crucial step toward formulating a relativistic quantum theory. We give an operational meaning to multipartite quantum states over…

Quantum information processing is the use of inherently quantum mechanical phenomena to perform information processing tasks that cannot be achieved using conventional classical information technologies. One famous example is quantum…

In this paper, we propose an explicit scheme to fully recover a multiple-qubit state subject to a phase damping noise. We establish the theoretical framework and the operational procedure to restore an unknown initial quantum state for an…

In quantum mechanics, the process of measurement is a subtle interplay between extraction of information and disturbance of the state of the quantum system. A quantum non-demolition (QND) measurement minimizes this disturbance by using a…

Coherent states provide an appealing method to reconstruct efficiently a pure state of a quantum mechanical spin s. A Stern-Gerlach apparatus is used to measure (4s+1) expectations of projection operators on appropriate coherent states in…

It is first shown that when the Schr\"{o}dinger equation for a wave function is written in the polar form, complete information about the system's {\em quantum-ness} is separated out in a single term $Q$, the so called `quantum potential'.…