Related papers: A spectral gap for POVMs
We consider one-dimensional chains and multi-dimensional networks of harmonic oscillators coupled to two Langevin heat reservoirs at different temperatures. Each particle interacts with its nearest neighbors by harmonic potentials and all…
We consider the statistical properties of photon detection with imperfect detectors that exhibit dark counts and less than unit efficiency, in the context of tomographic reconstruction. In this context, the detectors are used to implement…
We discuss a link between "hard" symplectic topology and an unsharpness principle for generalized quantum observables (positive operator valued measures). The link is provided by the Berezin-Toeplitz quantization.
We consider a non-compact Riemannian periodic manifold such that the corresponding Laplacian has a spectral gap. By continuously perturbing the periodic metric locally we can prove the existence of eigenvalues in a gap. A lower bound on the…
Projective (Von Neumann) Measurement of an operator (i.e. a dynamical variable) selected from a prescribed set of operators is termed unrecorded measurement (URM) when both the selected operator and the measurement outcome are unknown, i.e.…
The aim of this paper is to study the spectral gap and the logarithmic Sobolev constant for continuous spin systems. A simple but general result for estimating the spectral gap of finite dimensional systems is given by Theorem 1.1, in terms…
We study quantum measurement retrodiction using the principle of minimum change. For quantum-to-classical measurement channels, we show that all standard quantum divergences select the same retrodictive update, yielding a unique and…
We generalize Lyapunov's convexity theorem for classical (scalar-valued) measures to quantum (operator-valued) measures. In particular, we show that the range of a nonatomic quantum probability measure is a weak*-closed convex set of…
It is shown that for any irrational rotation number and any admissible gap labelling number the almost Mathieu operator (also known as Harper's operator) has a gap in its spectrum with that labelling number. This answers the strong version…
The intrinsic unsharpness of a quantum observable is studied by introducing the notion of resolution width. This quantification of accuracy is shown to be closely connected with the possibility of making approximately repeatable…
A quantum measurement can be described by a set of matrices, one for each possible outcome, which represents the positive operator-valued measure (POVM) of the sensor. Efficient protocols of POVM extraction for arbitrary sensors are…
The Heisenberg uncertainty principle imposes a fundamental restriction in quantum mechanics, stipulating that measuring one observable completely erases the information on its conjugate one, thereby preventing simultaneous measurements of…
The observables of a noisy quantum system can be estimated by appropriately filtering the records of their continuous measurement. Such filtering is relevant for state estimation and measurement-based quantum feedback control. It is…
We address the use of optical parametric oscillator (OPO) to counteract phase-noise in quantum optical communication channels, and demonstrate reduction of phase diffusion for coherent signals travelling through a suitably tuned OPO. In…
Quantum instruments describe outcome probability as well as state change induced by measurement of a quantum system. Incompatibility of two instruments, i. e. the impossibility to realize them simultaneously on a given quantum system,…
It is the purpose of the present contribution to demonstrate that the generalization of the concept of a quantum mechanical observable from the Hermitian operator of standard quantum mechanics to a positive operator-valued measure is not a…
A generic qubit unitary operator affected by depolarizing noise is duplicated and inserted in a quantum switch process realizing a superposition of causal orders. The characterization of the resulting switched quantum channel is worked out…
While the standard approach to quantum systems studies length preserving linear transformations of wave functions, the Markov picture focuses on trace preserving operators on the space of Hermitian (self-adjoint) matrices. The Markov…
Motivated by quantum resource theories, we introduce a notion of incompatibility for quantum measurements relative to a reference basis. The notion arises by considering states diagonal in that basis and investigating whether probability…
The ability to characterise and discern quantum channels is a crucial aspect of noisy quantum technologies. In this work, we explore the problem of distinguishing quantum channels when limited to sub-exponential resources, framed as von…