Related papers: Weakly sufficient quantum statistics
We give a sufficient condition for the quantum adiabatic approximation, which is quantitative and can be used to estimate error caused by this approximation. We also discuss when the traditional condition is sufficient.
We examine the quantitative condition which has been widely used as a criterion for the adiabatic approximation but was recently found insufficient. Our results indicate that the usual quantitative condition is sufficient for a special…
A so called 'weak value' of an observable in quantum mechanics (QM) may be obtained in a weak measurement + post-selection procedure on the QM system under study. Applied to number operators, it has been invoked in revisiting some QM…
We consider methods for obtaining local lower bounds on characteristics of quantum (correspondingly, classical) systems, i.e. lower bounds valid in the trace norm $\epsilon$-neighborhood of a given state (correspondingly, probability…
The average result of a weak measurement of some observable $A$ can, under post-selection of the measured quantum system, exceed the largest eigenvalue of $A$. The nature of weak measurements, as well as the presence of post-selection and…
Although there is no consensus regarding the "reality" of the past of a quantum particle, in situations where there is only one trajectory with nonvanishing quantum wave of the particle between its emission and detection points, it seems…
The problem of how to obtain quasi-classical states for quantum groups is examined. A measure of quantum indeterminacy is proposed, which involves expectation values of some natural quantum group operators. It is shown that within any…
The real part of the weak value is identified as the conditional Bayes probability through the quantum analog of the Bayes relation. We present an explicit protocol to get the the weak values in a simple Mach-Zehnder interferometer model…
Quantum mechanics presents peculiar properties that, on the one hand, have been the subject of several theoretical and experimental studies about its very foundations and, on the other hand, provide tools for developing new technologies,…
We use multi-time correlation functions of quantum systems to construct random variables with statistical properties that reflect the degree of complexity of the underlying quantum dynamics.
Originally, quantum probability theory was developed to analyze statistical phenomena in quantum systems, where classical probability theory does not apply, because the lattice of measurable sets is not necessarily distributive. On the…
A central problem in quantum information is to determine the minimal physical resources that are required for quantum computational speedup and, in particular, for fault-tolerant quantum computation. We establish a remarkable connection…
The goal of quantum benchmarking is to certify that imperfect quantum communication devices (e.g., quantum channels, quantum memories, quantum key distribution systems) can still be used for meaningful quantum communication. However, the…
We formulate incomplete classical statistics for situations where the knowledge about the probability distribution outside a local region is limited. The information needed to compute expectation values of local observables can be collected…
Every quantum state can be represented as a probability distribution over the outcomes of an informationally complete measurement. But not all probability distributions correspond to quantum states. Quantum state space may thus be thought…
It is known that weak l-sequential supercyclicity implies weak quasistability, and it is still unknown weather weak l-sequential supercyclicity implies weak stability, much less whether weak supercyclicity implies weak stability (although…
Heisenberg-limited and weak measurements are the two intriguing notions, used in recent times for enhancing the sensitivity of measurements in quantum metrology. Using a quantum cat state, endowed with sub-Planck structure, we connect these…
This article is an introduction to quant-ph/0302092. We propose to quantify how "quantum" a set of quantum states is. The quantumness of a set is the worst-case difficulty of transmitting the states through a classical communication…
We study the possibility to describe pure quantum states and evens with classical probability distributions and conditional probabilities and show that the distributions and/or conditional probabilities have to assume negative values,…
Quantum statistics originate from the physics of state preparation. It is therefore wrong to think of quantum states as fundamental. In fact, quantum states are merely summaries of dynamical processes that randomize the properties of the…