相关论文: State Extended Uncertainty Relations
Certification and quantification of correlations for multipartite states of quantum systems appear to be a central task in quantum information theory. We give here a unitary quantum-mechanical perspective of both entanglement and…
Uncertainties in successive measurements of general canonically conjugate variables are examined. Such operators are approached within a limiting procedure of the Pegg-Barnett type. Dealing with unbounded observables, we should take into…
Recently, Maccone and Pati have given two stronger uncertainty relations based on the sum of variances and one of them is nontrivial when the quantum state is not an eigenstate of the sum of the observables. We derive a family of weighted…
We present the generalized state-dependent entropic uncertainty relations in multiple measurements setting, and the optimal lower bound is obtained by considering different measurement sequences. We then apply this uncertainty relation to…
The notions of error and disturbance appearing in quantum uncertainty relations are often quantified by the discrepancy of a physical quantity from its ideal value. However, these real and ideal values are not the outcomes of simultaneous…
The Heisenberg inequality \Delta X \Delta P \geq \hbar/2 can be replaced by an exact equality, for suitably chosen measures of position and momentum uncertainty, which is valid for all wavefunctions. The significance of this "exact"…
We derive and experimentally investigate a strong uncertainty relation valid for any $n$ unitary operators, which implies the standard uncertainty relation as a special case, and which can be written in terms of geometric phases. It is…
A non stationary state in the one-dimensional infinite square well formed by a combination of the ground state and the first excited one is considered. The statistical complexity and the Fisher-Shannon entropy in position and momentum are…
We address the generalized uncertainty principle in scenarios of successive measurements. Uncertainties are characterized by means of generalized entropies of both the R\'{e}nyi and Tsallis types. Here, specific features of measurements of…
Geometrical structures of quantum mechanics provide us with new insightful results about the nature of quantum theory. In this work we consider mixed quantum states represented by finite rank density operators. We review our geometrical…
The entropic uncertainty relations are a very active field of scientific inquiry. Their applications include quantum cryptography and studies of quantum phenomena such as correlations and non-locality. In this work we find…
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…
The new inequality recently found by Trifonov and called the state-extended inequality is considered in the tomographic-probability representation of quantum mechanics. The Trifonov uncertainty relations are expressed in terms of optical…
For a quantum particle with a single degree of freedom, we derive preparational sum and product uncertainty relations satisfied by $N$ linear combinations of position and momentum observables. The state-independent bounds depend on their…
We discuss an expansion of the detection probabilities of biphoton states in terms of increasing orders of the joint spectral amplitude. The expansion enables efficient time- or frequency-resolved numerical simulations involving quantum…
Measurement outcomes of a quantum state can be genuinely random (unpredictable) according to the basic laws of quantum mechanics. The Heisenberg-Robertson uncertainty relation puts constrains on the accuracy of two noncommuting observables.…
Entropic uncertainty relations $H(A)+H(B)\geqslant \gamma$ give a nonzero lower bound $\gamma$ to the sum of the Shannon entropies $H$ of the outcome probabilities of incompatible observables $A$ and $B$. They are better than the…
Uncertainty relations play a significant role in drawing a line between classical physics and quantum physics. Since the introduction by Heisenberg, these relations have been considerably explored. However, the effect of quantum…
We present observable upper bounds of squared concurrence, which are the dual inequalities of the observable lower bounds introduced in [F. Mintert and A. Buchleitner, Phys. Rev. Lett. 98, 140505 (2007)] and [L. Aolita, A. Buchleitner and…
We consider the uncertainty bound on the sum of variances of two incompatible observables in order to derive a corresponding steering inequality. Our steering criterion when applied to discrete variables yields the optimum steering range…