Related papers: Quantum Channel Conditioning and Measurement Model…
Let $K$ be a convex subset of the state space of a finite dimensional $C^*$-algebra. We study the properties of channels on $K$, which are defined as affine maps from $K$ into the state space of another algebra, extending to completely…
We demonstrate that the task of determining an unknown quantum state can be accomplished efficiently by making a sequential measurement of two observables $\hat{A}$ and $\hat{B}$, provided that the two observables are chosen in such a way…
We consider a nontrivial class of infinite dimensional quantum channels characterized by finiteness of the Holevo capacity. Some general properties of channels of this class are described. In particular, a special sufficient condition of…
In the Contextuality-by-Default theory random variables representing measurement outcomes are labeled contextually, i.e., not only by what they measure but also under what conditions (in what contexts) the measurements are made, including…
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 $\langle\phi|\psi\rangle$…
We work out a classification scheme for quantum modeling in Hilbert space of any kind of composite entity violating Bell's inequalities and exhibiting entanglement. Our theoretical framework includes situations with entangled states and…
Postselected quantum metrological scheme is especially advantageous when the final measurements are either very noisy or expensive in practical experiments. In this work, we put forward a general theory on the compression channels in…
Quantum channels, also called quantum operations, are linear, trace preserving and completely positive transformations in the space of quantum states. Such operations describe discrete time evolution of an open quantum system interacting…
The action of qubit channels on projective measurements on a qubit state is used to establish an equivalence between channels and properties of generalized measurements characterized by bias and sharpness parameters. This can be interpreted…
In the absence of a satisfactory interpretation of quantum theory, physical law lacks physical basis. This paper reviews the orthodox, or Dirac-von Neumann interpretation, and makes explicit that Hilbert space describes propositions about…
The problem of an optimal mapping between Hilbert spaces $IN$ and $OUT$, based on a series of density matrix mapping measurements $\rho^{(l)} \to \varrho^{(l)}$, $l=1\dots M$, is formulated as an optimization problem maximizing the total…
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…
We look into the task of differentiating between any two quantum channels and reconstructing them from the obtained measurement statistics with possibly limited information about the experimental set-up. We employ the communication matrix…
This expository article gives an overview of the theory of hypothesis testing of quantum states in finite dimensional Hilbert spaces. Optimal measurement strategy for testing binary quantum hypotheses, which result in minimum error…
We study quantum channels with respect to their image, i.e., the image of the set of density operators under the action of the channel. We first characterize the set of quantum channels having polytopic images and show that additivity of…
Observables and instruments have played significant roles in recent studies on the foundations of quantum mechanics. Sequential products of effects and conditioned observables have also been introduced. After an introduction in Section~1,…
We introduce a holographic framework for analyzing the steady states of repeated quantum channels with strong symmetries. Using channel-state duality, we show that the steady state of a $d$-dimensional quantum channel is holographically…
We introduce three metrics on the set of quantum probability measures over a compact Hausdorff space and characterize them in terms of the completely bounded norm of the corresponding unital completely positive maps. We extend the existing…
The problem of identifying measurement scenarios capable of revealing state-independent contextuality in a given Hilbert space dimension is considered. We begin by showing that for any given dimension $d$ and any measurement scenario…
We investigate the advantage of coherent superposition of two different coded channels in quantum metrology. In a continuous variable system, we show that the Heisenberg limit $1/N$ can be beaten by the coherent superposition without the…