Related papers: Mutually Unbiased Quantum Observables
Quantum uncertainty relations are typically analyzed for a pair of incompatible observables, however, the concept per se naturally extends to situations of more than two observables. In this work, we obtain tripartite quantum…
In [Berta 2014 Entanglement], uncertainty relations in the presence of quantum memory was formulated for mutually unbiased bases using conditional collision entropy. In this paper, we generalize their results to the mutually unbiased…
The modern framework of state transformers, i. e., the first Kraus representation of quantum measurement, is introduced and related both to the known textbook concepts and to measurement-interaction evolution (the second Kraus…
Quantum measurements are noncontextual, with outcomes independent of which other commuting observables are measured at the same time, when consistently analyzed using principles of Hilbert space quantum mechanics rather than classical…
We deepen the theory of quasiorthogonal and approximately quasiorthogonal operator algebras through an analysis of the commutative algebra case. We give a new approach to calculate the measure of orthogonality between two such subalgebras…
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…
A set of mutually unbiased bases (MUBs) is said to be unextendible if there does not exist another basis that is unbiased with respect to the given set. Here, we prove the existence of smaller sets of MUBs in prime-squared dimensions…
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…
A prominent formulation of the uncertainty principle identifies the fundamental quantum feature that no particle may be prepared with certain outcomes for both position and momentum measurements. Often the statistical uncertainties are…
We present a new approach to the problem of mutually unbiased bases (MUBs), based on positive definite functions on the unitary group. The method provides a new proof of the fact that there are at most $d+1$ MUBs in ${\mathbb C}^d$. It may…
The structural characterization of high-dimensional mutually unbiased bases (MUBs) by classifying MUBs subsets remains a major open problem. The existing methods not only fail to conclude on the exact classification, but also are severely…
A non-associative algebra of observables cannot be represented as operators on a Hilbert space, but it may appear in certain physical situations. This article employs algebraic methods in order to derive uncertainty relations and…
We study various optimality criteria for quantum observables. Observables are represented as covariant positive operator valued measures and we consider the case when the symmetry group is compact. Phase observables are examined as an…
In the present paper, in terms of the measurability concept introduced in the previous works of the author, a quantum theory is studied. Within the framework of this concept, several examples are considered using the Schrodinger picture;…
The basic notions of quantum mechanics are formulated in terms of separable infinite dimensional Hilbert space $\mathcal{H}$. In terms of the Hilbert lattice $\mathcal{L}$ of closed linear subspaces of $\mathcal{H}$ the notions of state and…
By invoking quantum estimation theory we formulate bounds of errors in quantum measurement for arbitrary quantum states and observables in a finite-dimensional Hilbert space. We prove that the measurement errors of two observables satisfy…
We discuss some general properties of quantum gravity in De Sitter space. It has been argued that the Hilbert space is of finite dimension. This suggests a macroscopic argument that General Relativity cannot be quantized -- unless it is…
A trade-off relation on our knowledge about two noncommuting observables of a qubit system in simultaneous measurement is formulated. The obtained inequality offers a quantitative information-theoretic representation of Bohr's principle of…
We address the problem of unambiguous discrimination and identification among quantum observables. We set a general framework and investigate in details the case of qubit observables. In particular, we show that perfect discrimination with…
Various forms of optimality for quantum observables described as normalized positive operator valued measures (POVMs) are studied in this paper. We give characterizations for observables that determine the values of the measured quantity…