相关论文: Exact uncertainty relations: physical significance
A geometric approach to formulate the uncertainty principle between quantum observables acting on an $N$-dimensional Hilbert space is proposed. We consider the fidelity between a density operator associated with a quantum system and a…
The more information a measurement provides about a quantum system's position statistics, the less information a subsequent measurement can provide about the system's momentum statistics. This information trade-off is embodied in the…
Heisenberg's uncertainty principle is often cited as an example of a "purely quantum" relation with no analogue in the classical limit where $\hbar \to 0$. However, this formulation of the classical limit is problematic for many reasons,…
The Kennard-type uncertainty relation $\Delta x\Delta p >\frac{\hbar}{2}$ is formulated for a free particle with given momentum < \hat{p}>$ inside a box with periodic boundary conditions in the large box limit. Our construction of a free…
The existence of observables that are incompatible or not jointly measurable is a characteristic feature of quantum mechanics, which lies at the root of a number of nonclassical phenomena, such as uncertainty relations, wave--particle dual…
In the study of Heisenberg's error-disturbance relation, it is commonly believed that the non-unitary change of states hinders us from deducing the information encoded in original states about subsequently measured observable. However, we…
Uncertainty principle is one of the fundamental principles of quantum mechanics. In this work, we derive two uncertainty equalities, which hold for all pairs of incompatible observables. We also obtain an uncertainty relation in weak…
Recently, we have presented some simple arguments supporting the existence of certain complementarity between thermodynamic quantities of temperature and energy, an idea suggested by Bohr and Heinsenberg in the early days of Quantum…
Heisenberg's position-measurement--momentum-disturbance relation is derivable from the uncertainty relation $\sigma(q)\sigma(p) \geq \hbar/2$ only for the case when the particle is initially in a momentum eigenstate. Here I derive a new…
In this paper, we compute uncertainty relations for non-commutative space and obtain a better lower bound than the standard one obtained from Heisenberg's uncertainty relation. We also derive the reverse uncertainty relation for product and…
The indeterminacy inherent in quantum measurement is an outstanding character of quantum theory, which manifests itself typically in Heisenberg's error-disturbance uncertainty relation. In the last decade, Heisenberg's relation has been…
Exact equations are derived that relate velocity structure functions of arbitrary order with other statistics. "Exact" means that no approximations are used except that the Navier-Stokes equation and incompressibility condition are assumed…
The Koch curve is a self-similar object whose length grows unboundedly when the measuring unit by which is calculated diminishes. If this curve is considered to be the trajectory of a point corpuscle of mass m (a particle) rendering it in a…
By implicitly assuming that all possible Bell-measurements occur simultaneously, all proofs of Bell's Theorem violate Heisenberg's Uncertainty Principle. This assumption is made in the original form of Bell's inequality, in Wigner's…
Bohr and Heisenberg suggested that the thermodynamical quantities of temperature and energy are complementary in the same way as position and momentum in quantum mechanics. Roughly speaking, their idea was that a definite temperature can be…
Uncertainty relations are among the unique fingerprints of quantum physics, being direct expression of non-commutativity and complementarity. Entropic uncertainty relations arise in quantum information theory as the most natural expression…
Aiming towards a geometric description of quantum theory, we study the coherent states-induced metric on the phase space, which provides a geometric formulation of the Heisenberg uncertainty relations (both the position-momentum and the…
A new uncertainty relation (UR) is obtained for a system of N identical pure entangled particles if we use symmetrized observables when deriving the inequality. This new expression can be written in a form where we identify a term which…
Quantum uncertainty relations impose fundamental limits on the joint knowledge that can be acquired from complementary observables: perfect knowledge of a quantum state in one basis implies maximal indetermination in all other mutually…
A universally valid uncertainty relation proposed by Ozawa is re-investigated under for the generalized equation of motion with some boundary condition. Necessary conditions for violation (lessening) of the Heisenberg-type uncertainty…