相关论文: Intrinsic unsharpness and approximate repeatabilit…
The topic of measurement in relativistic quantum field theory is addressed in this article. Some of the long standing problems of this subject are highlighted, including the incompatibility of an instantaneous ``collapse of the…
A basic problem in machine learning is to find a mapping $f$ from a low dimensional latent space $\mathcal{Y}$ to a high dimensional observation space $\mathcal{X}$. Modern tools such as deep neural networks are capable to represent general…
When one takes into account gravitation, the measurement of space and time cannot be carried out with infinite accuracy. When quantum mechanics is reformulated taking into account this lack of accuracy, the resolution of the measurement…
In this work, we investigate the incompatibility of random quantum measurements. Most previous work has focused on characterizing the maximal amount of white noise that any fixed number of incompatible measurements with a fixed number of…
The quantum mechanical measurement problem does not arise in the quantum real number approach to quantum measurements of the first kind. The attributes of individual microscopic systems in the experimental ensemble always have qr-number…
The experimental evaluation of many quantum mechanical quantities requires the estimation of several directly measurable observables, such as local observables. Due to the necessity to repeat experiments on individual quantum systems in…
Incompatibility of certain measurements -- impossibility of obtaining deterministic outcomes simultaneously -- is a well known property of quantum mechanics. This feature can be utilized in many contexts, ranging from Bell inequalities to…
Inverse problems play a key role in modern image/signal processing methods. However, since they are generally ill-conditioned or ill-posed due to lack of observations, their solutions may have significant intrinsic uncertainty. Analysing…
There are four reasons why our present knowledge and understanding of quantum mechanics could be regarded as incomplete. Firstly, the principle of linear superposition has not been experimentally tested for position eigenstates of objects…
Exact conditions on the clock parameters corresponding to the minimal uncertainty in distance measurement are derived in uniform manner for any number of space time dimensions. The result espouses the holography principle no matter what the…
We propose a classification of measurement apparatuses based on their reliability and accessibility. Our notion of reliability parameterises the possibility of getting unexpected wrong results when using the apparatus in a given time…
High-dimensional datasets typically cluster around lower-dimensional manifolds but are also often marred by severe noise, obscuring the intrinsic geometry essential for downstream learning tasks. We present a quantum algorithm for…
The fundamental principles of complementarity and uncertainty are shown to be related to the possibility of joint unsharp measurements of pairs of noncommuting quantum observables. A new joint measurement scheme for complementary…
Even though measurement results obtained in the real world are generally both noisy and continuous, quantum measurement theory tends to emphasize the ideal limit of perfect precision and quantized measurement results. In this article, a…
The use of real clocks and measuring rods in quantum mechanics implies a natural loss of unitarity in the description of the theory. We briefly review this point and then discuss the implications it has for the measurement problem in…
Several quantities of interest in quantum information, including entanglement and purity, are nonlinear functions of the density matrix and cannot, even in principle, correspond to proper quantum observables. Any method aimed to determine…
Quantum coherence is one of the most basic characteristics of quantum mechanics. Here we give some methods to detect and measure quantum coherence. Firstly, we propose a coherence criterion without full quantum state tomography based on…
To investigate the possibility that intrinsic gravitational decoherence can be theoretically demonstrated within canonical quantum gravity, we develop a model of a self-gravitating interferometer. We search for evidence in the resulting…
The fact that there are quantum observables without a simultaneous measurement is one of the fundamental characteristics of quantum mechanics. In this work we expand the concept of joint measurability to all kinds of possible measurement…
The more information a measurement provides about a quantum system's position statistics, the less information a subsequent measurement can provide about the system's momentum statistics. This information trade-off is embodied in the…