Related papers: Strict hierarchy between $n$-wise measurement simu…
The concept of complexity appears in virtually all areas of knowledge. Its intuitive meaning shares similarities across fields, but disagreements between its details hinders a general definition, leading to a plethora of proposed…
Quantum measurements based on mutually unbiased bases are commonly used in quantum information processing, as they are generally viewed as being maximally incompatible and complementary. Here we quantify precisely the degree of…
In this paper, we extend the standard formalism of quantum mechanics to a quantum theory for a total system including one internal measuring apparatus. The internality of the measuring apparatus implies that different decomposition of a…
Quantum coherence, incompatibility, and quantum correlations are fundamental features of quantum physics. A unified view of those features is crucial for revealing quantitatively their intrinsic connections. We define the relative quantum…
Measurements are able to fundamentally affect quantum dynamics. We here show that a continuously measured quantum many-body system can undergo a spontaneous transition from asynchronous stochastic dynamics to noise-free stable…
In contrast with classical physics, in quantum physics some sets of measurements are incompatible in the sense that they can not be performed simultaneously. Among other applications, incompatibility allows for contextuality and Bell…
Entanglement does not describe all quantum correlations and several authors have shown the need to go beyond entanglement when dealing with mixed states. Various different measures have sprung up in the literature, for a variety of reasons,…
Quantum coherence is a key resource in quantum information processing scenarios, and quantifying coherence is an important task for both quantum foundation and quantum technology. However, until now, all most of coherence measures are…
Can quantum theory be applied on all scales? While there are many arguments for the universality of quantum theory, this question remains a subject of debate. It is unknown how far the existence of macroscopic irreversibility can be derived…
The notorious `measurement problem' has been roving around quantum mechanics for nearly a century since its inception, and has given rise to a variety of `interpretations' of quantum mechanics, which are meant to evade it. We argue that no…
One of the most intriguing aspects of Quantum Mechanics is the impossibility of measuring at the same time observables corresponding to non-commuting operators. This impossibility can be partially relaxed when considering joint or…
The concept of compatibility originally emerged as a synonym for the commutativity of observables and later evolved into the notion of measurement compatibility. In any case, however, it has remained predominantly algebraic in nature, tied…
One of the most remarkable features of quantum physics is that attributes of quantum objects, such as the wave-like and particle-like behaviors of single photons, can be complementary in the sense that they are equally real but cannot be…
Joint or simultaneous measurements of non-commuting quantum observables are possible at the cost of increased unsharpness or measurement uncertainty. Many different criteria exist for defining what an "optimal" joint measurement is, with…
We introduce a hierarchical classification of theories that describe systems with fundamentally limited information content. This property is introduced in an operational way and gives rise to the existence of mutually complementary…
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…
For sharp quantum observables the following facts hold: (i) if we have a collection of sharp observables and each pair of them is jointly measurable, then they are jointly measurable all together; (ii) if two sharp observables are jointly…
Quantum coherence is a fundamental common trait of quantum phenomena, from the interference of matter waves to quantum degeneracy of identical particles. Despite its importance, estimating and measuring quantum coherence in generic, mixed…
Measurement incompatibility has proved to be an important resource for quantum information processing. In this work, we present an operational approach that leverages classical operations on the inputs (pre-processing) and outputs…
Classical and quantum measurement theories are usually held to be different because the algebra of classical measurements is commutative, however the Poisson bracket allows noncommutativity to be added naturally. After we introduce…