Related papers: Quantum Channel Conditioning and Measurement Model…
In a series of papers Tsirelson constructed from measure types of random sets and generalised random processes a new range of examples for continuous tensor product systems of Hilbert spaces introduced by Arveson for classifying…
A minimal energy quantum superposition of two maximally distinguishable, isoenergetic single mode Gaussian states is used to construct the system-environment representation of a class of linear bosonic quantum channels acting on a single…
We give a sufficient condition that an operator sum representation of a separable quantum channel in terms of product operators is the unique product representation for that channel, and then provide examples of such channels for any number…
We introduce a logic modelling some aspects of the behaviour of the measurement process, in such a way that no direct mention of quantum states is made, thus avoiding the problems associated to this rather evasive notion. We then study some…
We show that quantum measures and integrals appear naturally in any $L_2$-Hilbert space $H$. We begin by defining a decoherence operator $D(A,B)$ and it's associated $q$-measure operator $\mu (A)=D(A,A)$ on $H$. We show that these operators…
This paper provides a systematic study of the operational idea that a quantum ``state'' is only defined up to what can be distinguished by a chosen family of observables. Concretely, any von Neumann algebra of observables $\mathscr{M}$…
A measurement on a section K of the set of states of a finite dimensional C*-algebra is defined as an affine map from K to a probability simplex. Special cases of such sections are used in description of quantum networks, in particular…
In a recent work, arXiv:2503.05884, we proposed a unified notion of nonclassicality that applies to arbitrary processes in quantum theory, including individual quantum states, measurements, channels, set of these, etc. This notion is…
Quantum instruments are mathematical devices introduced to describe the conditional state change during a quantum process. They are completely positive map valued measures on measurable spaces. We may also view them as non-commutative…
We demonstrate that quantum instruments can provide a unified operational foundation for quantum theory. Since these instruments directly correspond to laboratory devices, this foundation provides an alternate, more experimentally grounded,…
We study one-mode Gaussian quantum channels in continuous-variable systems by performing a black-box characterization using complete positivity and trace preserving conditions, and report the existence of two subsets that do not have a…
Joint Gaussian measurements of two quantum systems can be used for quantum communication between remote parties, as in teleportation or entanglement swapping protocols. Many types of physical error sources throughout a protocol can be…
We consider a general symplectic transformation (also known as linear canonical transformation) of quantum-mechanical observables in a quantized version of a finite-dimensional system with configuration space isomorphic to $ \mathbb{R}^{q}…
Quantum measurement is a physical process. What physical resources and constraints does quantum mechanics require for measurement to produce the classical world we observe? Treating measurement as a fully unitary quantum process, our goal…
A simple criterion for local equality between the constrained Holevo capacity and the quantum mutual information of a quantum channel is obtained. It implies that the set of all states for which this equality holds is determined by the…
It is shown that quantum mechanics is noncontextual if quantum properties are represented by subspaces of the quantum Hilbert space (as proposed by von Neumann) rather than by hidden variables. In particular, a measurement using an…
We investigate the quantum capacity of noisy quantum channels which can be represented by coupling a system to an effectively small environment. A capacity formula is derived for all cases where both system and environment are…
We investigate the measurement incompatibility of continuous-variable systems with infinite-dimensional Hilbert spaces under the influence of pure losses, a fundamental noise source in quantum optics, and a significant challenge for…
We present strategies how to reconstruct (estimate) properties of a quantum channel described by the map E based on incomplete measurements. In a particular case of a qubit channel a complete reconstruction of the map E can be performed via…
We will give a new model for measurements of a quantum system such that the measuring apparatuses are described by a unital separable non-type I nuclear simple C$^*$-algebra equipped with certain unital endomorphisms and pure states. An…