Related papers: Mutually Unbiased Quantum Observables
The principle of relativity is extended to accommodate finite-mass observers with quantum properties by introducing two operational requirements: (i) equivalence of observers at the level of transition amplitudes, and (ii) the impossibility…
The relativistic conception of space and time is challenged by the quantum nature of physical observables. It has been known for a long time that Poincar\'e symmetry of field theory can be extended to the larger conformal symmetry. We use…
An early approach to include pointers representing measurement devices into quantum mechanics was given by von Neumann. Based on this idea, we model such pointers by qubits and couple them to a free particle, in analogy to a classical…
We present a reformulation of quantum mechanics in terms of probability measures and functions on a general classical sample space and in particular in terms of probability densities and functions on phase space. The basis of our proceeding…
It is conjectured that the question of the existence of projective planes whose order is not a power of prime is intimately linked with the problem whether there exists a set of d+1 mutually unbiased bases in a d-dimensional Hilbert space…
We investigate the problem of coexistence of position and momentum observables. We characterize those pairs of position and momentum observables which have a joint observable.
We discuss the detection of entanglement in interacting quantum spin systems. First, thermodynamic Hamiltonian-based witnesses are computed for a general class of one-dimensional spin-1/2 models. Second, we introduce optimal bipartite…
Uncertainty relations are usually stated as bounds on selected combinations of variances, but the full covariance matrix contains substantially richer information about the geometry of quantum state space and about the operational…
Mutually unbiased bases determine an optimal set of measurements to extract complete information about the quantum state of a system. However, quite often a priori information about the state exist, making some of the measurement bases…
We develop a notion of quantum observable for the general boundary formulation of quantum theory. This notion is adapted to spacetime regions rather than to hypersurfaces and naturally fits into the topological quantum field theory like…
We describe the interplay between electric-magnetic duality and higher symmetry in Maxwell theory. When the fine-structure constant is rational, the theory admits non-invertible symmetries which can be realized as composites of…
Quantum theory has the intriguing feature that is inconsistent with noncontextual hidden variable models, for which the outcome of a measurement does not depend on which other compatible measurements are being performed concurrently. While…
Uncertainty relation lies at the heart of quantum mechanics, characterizing the incompatibility of non-commuting observables in the preparation of quantum states. An important question is how to improve the lower bound of uncertainty…
Two equivalent ways of looking for mutually unbiased bases are discussed in this note. The passage from the search for d+1 mutually unbiased bases in C(d) to the search for d(d+1) vectors in C(d*d) satisfying constraint relations is…
We consider the existence of a continuous set of mutually unbiased bases for the continuous and periodic degree of freedom that describes motion on a circle (rotor degree of freedom). By a singular mapping of the circle to the line, we find…
We propose a family of lower bounds for concurrence in quantum systems using mutually unbiased measurements, which prove more effective in entanglement estimation compared to existing methods. Through analytical and numerical examples, we…
In this contribution we group the operator basis for d^2 dimensional Hilbert space in a way that enables us to relate bases of entangled states with single particle mutually unbiased state bases (MUB), each in dimensionality d. We utilize…
We consider a general symplectic transformation (also known as linear canonical transformation) of quantum-mechanical observables in a quantized version of a finite-dimensional system with configuration space isomorphic to $ \mathbb{R}^{q}…
Algebraic approach to quantum non - separability is applied to the case of two qubits. It is based on the partition of the algebra of observables into independent subalgebras and the tensor product structure of the Hilbert space is not…
We construct a single observable measurement of which mean value on four copies of an {\it unknown} two-qubit state is sufficient for unambiguous decision whether the state is separable or entangled. In other words, there exists a universal…