Related papers: Overview of projective quantum measurements
A resolution of the quantum measurement problem(s) using the consistent histories interpretation yields in a rather natural way a restriction on what an observer can know about a quantum system, one that is also consistent with some results…
The paper gives a systematic review of the basic ideas of (non-relativistic) quantum mechanics including all changes that result from previous work of the authors. This shows that the new theory is self-consistent and (in certain sense)…
The purpose of this paper is to introduce techniques of obtaining optimal ways to determine a d-level quantum state or distinguish such states. It entails designing constrained elementary measurements extracted from maximal abelian subsets…
The effects of any quantum measurement can be described by a collection of measurement operators {M_m} acting on the quantum state of the measured system. However, the Hilbert space formalism tends to obscure the relationship between the…
States of a quantum mechanical system are represented by rays in a complex Hilbert space. The space of rays has, naturally, the structure of a K\"ahler manifold. This leads to a geometrical formulation of the postulates of quantum mechanics…
Biconformal spaces contain the essential elements of quantum mechanics, making the independent imposition of quantization unnecessary. Based on three postulates characterizing motion and measurement in biconformal geometry, we derive…
This note is devoted to some foundational aspects of quantum mechanics (QM) related to quantum information (QI) theory, especially quantum teleportation and ``one way quantum computing.'' We emphasize the role of the projection postulate…
We construct, for any finite dimension $n$, a new hidden measurement model for quantum mechanics based on representing quantum transition probabilities by the volume of regions in projective Hilbert space. For $n=2$ our model is equivalent…
We propose a general theoretical approach to quantum measurements based on the path (histories) summation technique. For a given dynamical variable A, the Schr\"odinger state of a system in a Hilbert space of arbitrary dimensionality is…
In quantum mechanics, physical states are represented by rays in Hilbert space $\mathscr H$, which is a vector space imbued by an inner product $\langle\,|\,\rangle$, whose physical meaning arises as the overlap $\langle\phi|\psi\rangle$…
This thesis is concerned with retrodiction and measurement in quantum optics. The latter of these two concepts is studied in particular form with a general optical multiport device, consisting of an arbitrary array of beam-splitters and…
Recently, there has been a renewed interest in the quantification of coherence or other coherence-like concepts within the framework of quantum resource theory. However, rigorously defined or not, the notion of coherence or decoherence has…
We propose a quantum interferometric protocol that leverages spin-dependent spatial displacements to enable high-precision parameter estimation beyond classical limits. By inducing a unitary coupling between a particles spin degree of…
In this work we study the unitary time-evolutions of quantum systems defined on infinite-dimensional separable time-dependent Hilbert spaces. Two possible cases are considered: a quantum system defined on a stochastic interval and another…
We present a finite set of projective measurements that, together with quantum memory and preparation of the |0> state, suffice for universal quantum computation. This extends work of Nielsen [quant-ph/0108020], who proposed a scheme in…
In this paper we introduce a projective invarinat measure on the special unitary group. It is directly related to transition probabilities. It has some interesting connection with convex geometry. Applications to approximation of quantum…
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…
We consider the problem of certification of arbitrary ensembles of pure states and projective measurements solely from the experimental statistics in the prepare-and-measure scenario assuming the upper bound on the dimension of the Hilbert…
Quantum theory does not only predict probabilities, but also relative phases for any experiment, that involves measurements of an ensemble of systems at different moments of time. We argue, that any operational formulation of quantum theory…
In quantum theory, a measurement context is defined by an orthogonal basis in a Hilbert space, where each basis vector represents a specific measurement outcome. The precise quantitative relation between two different measurement contexts…