相关论文: On a certain inequality for the sum of norms and r…
We formulate uncertainty relations for arbitrary $N$ observables. Two uncertainty inequalities are presented in terms of the sum of variances and standard deviations, respectively. The lower bounds of the corresponding sum uncertainty…
Uncertainty relations are old, yet potentially rewarding to explore. By introducing a quantity called the uncertainty matrix, we provide a link between purity and observable incompatibility, and derive several stronger uncertainty relations…
Some new reverses for the generalised triangle inequality in inner product spaces and applications are given. Applications in connection to the Schwarz inequality are provided as well.
We introduce a product in all complex normed vector spaces, which generalizes the inner product of complex inner product spaces. Naturally the question occurs whether the Cauchy-Schwarz inequality is fulfilled. We provide a positive answer.…
We analyze the weak and critical points of various uncertainty relations that follow from the inequalities for the norms of vectors in the Hilbert space of states of a quantum system. There are studied uncertainty relations for sums of…
We prove a new sum uncertainty relation in quantum theory which states that the uncertainty in the sum of two or more observables is always less than or equal to the sum of the uncertainties in corresponding observables. This shows that the…
Some sharp quadratic reverses for the generalised triangle inequality in inner product spaces and applications are given.
We construct a multi-observable uncertainty equality as well as an inequality based on the sum of standard deviations in the qubit system. The obtained equality indicates that the uncertainty relation can be expressed more accurately, and…
Uniform convergence of empirical norms - empirical measures of squared functions - is a topic which has received considerable attention in the literature on empirical processes. The results are relevant as empirical norms occur due to…
Analyzing general uncertainty relations one can find that there can exist such pairs of non-commuting observables $A$ and $B$ and such vectors that the lower bound for the product of standard deviations $\Delta A$ and $\Delta B$ calculated…
Recently,D.Mondal et.al[Phys. Rev. A. 95, 052117(2017)]creatively introduce a new interesting concept of reverse uncertainty relation which indicates that one cannot only prepare quantum states with joint small uncertainty, but also with…
Refining some results of S. S. Dragomir, several new reverses of the generalized triangle inequality in inner product spaces are given. Among several results, we establish some reverses for the Schwarz inequality. In particular, it is…
Refinements of some recent reverse inequalities for the celebrated Cauchy-Bunyakovsky-Schwarz inequality in 2-inner product spaces are given. Using this framework, applications for determinantal integral inequalities are also provided.
Reverses of Schwarz, triangle and Bessel inequalities in inner product spaces that improve some earlier results are pointed out. They are applied to obtain new Gruss type inequalities in inner product spaces. Some natural applications for…
Uncertainty relations are pivotal in delineating the limits of simultaneous measurements for observables. In this paper, we derive four novel uncertainty and reverse uncertainty relations for the sum of variances of two incompatible…
Some new reverses of the Cauchy-Schwarz inequality in inner product spaces are presented in this paper.The results obtained here complement the recent work of the references.
In this paper, some reverses of the Cauchy-Bunyakovsky-Schwarz inequality in 2-inner product spaces are given. Using this framework, some applications for determinantal integral inequalities are also provided.
We consider the Sobolev norms of the pointwise product of two functions, and estimate from above and below the constants appearing in two related inequalities.
Uncertainty relations provide constraints on how well the outcomes of incompatible measurements can be predicted, and, as well as being fundamental to our understanding of quantum theory, they have practical applications such as for…
In this paper, we prove some new inequalities. To facilitate this proof, we introduce the notion of the local product on a sheet and associated space.