Related papers: Quantum Kaleidoscopes and Bell's theorem
We introduce a new notion of a sufficient subalgebra for quantum states: a subalgebra is 2- sufficient for a pair of states $\{\rho_0,\rho_1\}$ if it contains all Bayes optimal tests of $\rho_0$ against $\rho_1$. In classical statistics,…
In contrast to the wide-spread opinion that any separable quantum state satisfies every classical probabilistic constraint, we present a simple example where a separable quantum state does not satisfy the original Bell inequality although…
In quantum physics the term `contextual' can be used in more than one way. One usage, here called `Bell contextual' since the idea goes back to Bell, is that if $A$, $B$ and $C$ are three quantum observables, with $A$ compatible (i.e.,…
It is well known that correlations predicted by quantum mechanics cannot be explained by any classical (local-realistic) theory. The relative strength of quantum and classical correlations is usually studied in the context of Bell…
In the 20th century, quantum mechanics connected the particle and wave concepts of light and thereby made mechanisms accessible that had never been imagined before. Processes such as stimulated emission and quantum entanglement have…
A system of quantum reasoning for a closed system is developed by treating non-relativistic quantum mechanics as a stochastic theory. The sample space corresponds to a decomposition, as a sum of orthogonal projectors, of the identity…
Bell nonlocality and Kochen-Specker contextuality are two remarkable nonclassical features of quantum theory, related to strong correlations between outcomes of measurements performed on quantum systems. Both phenomena can be witnessed by…
For a two-particle two-state system, sets of compatible propositions exist for which quantum mechanics and noncontextual hidden-variable theories make conflicting predictions for every individual system whatever its quantum state. This…
In 1960, the mathematician Ernst Specker described a simple example of nonclassical correlations which he dramatized using a parable about a seer who sets an impossible prediction task to his daughter's suitors. We revisit this example…
The characterization of a quantum system can be complicated by non-ideal measurement processes. In many systems, the underlying physical measurement is only sensitive to a single fixed state, complementary outcomes are inferred by…
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…
A recently proposed test of quantumness [R. Alicki and N. Van Ryn, J. Phys. A: Math. Theor. 41 062001 (2008)] is put into a broader mathematical and physical perspective. The notion of quantumness witness is introduced, in analogy to…
Given a finite set of linearly independent quantum states, an observer who examines a single quantum system may sometimes identify its state with certainty. However, unless these quantum states are orthogonal, there is a finite probability…
Getting the mathematical rules for quantised black holes correctly is far from straightforward. Many earlier treatises got it not quite correctly. The general relativistic transformation linking the distant observer (who only detects…
Under the principle that quantum mechanical observables are invariant under relevant symmetry transformations, we explore how the usual, non-invariant quantities may capture measurement statistics. Using a relativisation mapping, viewed as…
A standard approach in the foundations of quantum mechanics studies local realism and hidden variables models exclusively in terms of violations of Bell-like inequalities. Thus quantum nonlocality is tied to the celebrated no-go theorems,…
Entanglement of quantum states is absolutely essential for modern quantum sciences and technologies. It is natural to extend the notion of entanglement to quantum observables dual to quantum states. For quantum states, various separability…
Two quantum Macro-states and their Macroscopic Quantum Superpositions (MQS) localized in two far apart, space - like separated sites can be non-locally correlated by any entangled couple of single-particles having interacted in the past.…
The Church-Turing thesis is one of the pillars of computer science; it postulates that every classical system has equivalent computability power to the so-called Turing machine. While this thesis is crucial for our understanding of…
Measurements in quantum theory can fail to be jointly measurable. Like entanglement, this incompatibility of measurements is necessary but not sufficient for violating Bell inequalities. The (in)compatibility relations among a set of…