# Stronger uncertainty relations with improvable upper and lower bounds

@article{Zhang2017StrongerUR, title={Stronger uncertainty relations with improvable upper and lower bounds}, author={Jiandi Zhang and Yang Zhang and Chang-shui Yu}, journal={Quantum Information Processing}, year={2017}, volume={16}, pages={1-16} }

The quantum superposition principle is used to establish improved upper and lower bounds for the Maccone–Pati uncertainty inequality, which is based on a “weighted-like” sum of the variances of observables. Our bounds include free parameters that not only guarantee nontrivial bounds but also effectively control the bounds’ tightness. Significantly, these free parameters depend on neither the state nor the observables. A feature of our method is that any nontrivial bound can always be improved… Expand

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#### References

SHOWING 1-10 OF 63 REFERENCES

Weighted Uncertainty Relations

- Physics, Computer Science
- Scientific reports
- 2016

A family of weighted uncertainty relations is derived to provide an optimal lower bound for all situations and remove the restriction on the quantum state and generalization to multi-observable cases is given. Expand

Variance-based uncertainty relations

- Physics
- 2012

It is hard to overestimate the fundamental importance of uncertainty relations in quantum mechanics. In this work, I propose state-independent variance-based uncertainty relations for arbitrary… Expand

Tight State-Independent Uncertainty Relations for Qubits

- Mathematics, Physics
- 2015

The well-known Robertson–Schrodinger uncertainty relations have state-dependent lower bounds, which are trivial for certain states. We present a general approach to deriving tight state-independent… Expand

Upper bound and shareability of quantum discord based on entropic uncertainty relations

- Physics, Mathematics
- 2013

By using the quantum-memory-assisted entropic uncertainty relation (EUR), we derive a computable tight upper bound for quantum discord, which applies to an arbitrary bipartite state. Detailed… Expand

Uncertainty relation for smooth entropies.

- Mathematics, Physics
- Physical review letters
- 2011

This paper shows that security of quantum key distribution protocols implies security of smooth entropies, and shows that this security claim remains valid even if the implemented measurement devices deviate arbitrarily from the theoretical model. Expand

Stronger uncertainty relations for all incompatible observables.

- Mathematics, Medicine
- Physical review letters
- 2014

Two stronger uncertainty relations are given, relating to the sum of variances, whose lower bound is guaranteed to be nontrivial whenever the two observables are incompatible on the state of the system. Expand

Reformulating the Quantum Uncertainty Relation

- Mathematics, Physics
- Scientific reports
- 2015

This work introduces a new form of uncertainty relation which may give out complete trade-off relations for variances of observables in pure and mixed quantum systems, and may provide a geometric explanation for the reason why there are limitations on the simultaneous determination of different observable values in N-dimensional Hilbert space. Expand

Optimal entropic uncertainty relation for successive measurements in quantum information theory

- Physics
- 2003

We derive an optimal bound on the sum of entropic uncertainties of two or more observables when they are sequentially measured on the same ensemble of systems. This optimal bound is shown to be… Expand

Sum uncertainty relations for arbitrary N incompatible observables

- Mathematics, Physics
- Scientific reports
- 2015

Two uncertainty inequalities are presented in terms of the sum of variances and standard deviations, respectively, and the lower bounds of the corresponding sum uncertainty relations are explicitly derived. Expand

Entropic uncertainty relations for multiple measurements

- Physics
- 2015

We present the entropic uncertainty relations for multiple measurement settings which demonstrate the uncertainty principle of quantum mechanics. Those uncertainty relations are obtained for both… Expand