相关论文: Quantum States Allowing Minimum Uncertainty Produc…

The uncertainty relation for angle and angular momentum has a lower bound which depends on the form of the state. Surprisingly, this lower bound can be very large. We derive the states which have the lowest possible uncertainty product for…

In the present paper we construct a properly defined quantum state expressed in terms of elliptic Jacobi theta functions for the self-adjoint observables angular position $\theta$ and the corresponding angular momentum operator $L =…

The equality in the uncertainty principle for linear momentum and position is obtained for states which also minimize the uncertainty product. However, in the uncertainty relation for angular momentum and angular position both sides of the…

In our previous work we have found a lower bound for the multipartite uncertainty product of the position and momentum observables over all separable states. In this work we are trying to minimize this uncertainty product over a broader…

Uncertainty relations between a bounded coordinate operator and a conjugate momentum operator frequently appear in quantum mechanics. We prove that physically reasonable minimum-uncertainty solutions to such relations have quantized…

Which quantum states minimise the unavoidable uncertainty arising from the non-commutativity of two observables? The immediate answer to such a question is: it depends. Due to the plethora of uncertainty measures there are many answers.…

Necessary and sufficient condition for the existence of a minimum uncertainty state for an arbitrary pair of observables is given.

We discuss the uncertainty relation for the azimuthal angle $\phi$ and the $z$-component of the angular momentum $L_z$. To this end we derive the uncertainty relation for an arbitrary pair of observables and discuss the conditions for its…

The uncertainty relations for angle and angular momentum are revisited. We use the exponential of the angle instead of the angle itself and adopt dispersion as a natural measure of resolution. We find states that minimize the uncertainty…

This paper presents the uncertainty related to position and momentum localization of a quantum state in terms of entropic uncertainty relations. We slightly improve the inequality given in [Phys. Rev. A 74, 052101 (2006)] and introduce a…

The uncertainty of a quantum state is given by the composition of two components. The first is called the quantum component and is given by the probability distribution of an observable relative to the state. The second is the classical…

The uncertainty relations for the position and momentum of a quantum particle on a circle are identified minimized by the corresponding coherent states. The sqeezed states in the case of the circular motion are introduced and discussed in…

We rederive uncertainty relations for the angular position and momentum of a particle on a circle by employing the exponential of the angle instead of the angle itself, which leads to circular variance as a natural measure of resolution.…

Squeezing experiments which are capable of creating a minimum uncertainty state during the nonlinear process, for example optical parametric amplification, are commonly used to produce light far below the quantum noise limit. This report…

We provide a simple proof for the necessity of conditions for discriminating with minimum error between a known set of quantum states.

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…

We express the condition for a phase space Gaussian to be the Wigner distribution of a mixed quantum state in terms of the symplectic capacity of the associated Wigner ellipsoid. Our results are motivated by Hardy's formulation of the…

For linear combinations of quantum product averages in an arbitrary bipartite state, we derive new quantum Bell-form and CHSH-form inequalities with the right-hand sides expressed in terms of a bipartite state. This allows us to specify in…

The uncertainty associated with probing the quantum state is expressed as the effective abundance (measure) of possibilities for its collapse. New kinds of uncertainty limits entailed by quantum description of the physical system arise in…

The relativistic angular momentum is introduced as an extension of the non-relativistic analysis of allowed states in the phase space for a quantum particle. The paper shows the conceptual basis of the approach. An interesting feature of…