Uncertainty relations with the variance and the quantum Fisher
information based on convex decompositions of density matrices
- URL: http://arxiv.org/abs/2109.06893v5
- Date: Mon, 22 Jan 2024 11:27:00 GMT
- Title: Uncertainty relations with the variance and the quantum Fisher
information based on convex decompositions of density matrices
- Authors: G\'eza T\'oth, Florian Fr\"owis
- Abstract summary: We present several inequalities related to the Robertson-Schr"odinger uncertainty relation.
By considering a concave roof of the bound, we obtain an improvement of the Robertson-Schr"odinger uncertainty relation.
We present further uncertainty relations that provide lower bounds on the metrological usefulness of bipartite quantum states.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We present several inequalities related to the Robertson-Schr\"odinger
uncertainty relation. In all these inequalities, we consider a decomposition of
the density matrix into a mixture of states, and use the fact that the
Robertson-Schr\"odinger uncertainty relation is valid for all these components.
By considering a convex roof of the bound, we obtain an alternative derivation
of the relation in Fr\"owis et al. [Phys. Rev. A 92, 012102 (2015)], and we can
also list a number of conditions that are needed to saturate the relation. We
present a formulation of the Cram\'er-Rao bound involving the convex roof of
the variance. By considering a concave roof of the bound in the
Robertson-Schr\"odinger uncertainty relation over decompositions to mixed
states, we obtain an improvement of the Robertson-Schr\"odinger uncertainty
relation. We consider similar techniques for uncertainty relations with three
variances. Finally, we present further uncertainty relations that provide lower
bounds on the metrological usefulness of bipartite quantum states based on the
variances of the canonical position and momentum operators for two-mode
continuous variable systems. We show that the violation of well-known
entanglement conditions in these systems discussed in Duan et al., [Phys. Rev.
Lett. 84, 2722 (2000)] and Simon [Phys. Rev. Lett. 84, 2726 (2000)] implies
that the state is more useful metrologically than certain relevant subsets of
separable states. We present similar results concerning entanglement conditions
with angular momentum operators for spin systems.
Related papers
- Uncertainty relations based on state-dependent norm of commutator [0.0]
We introduce two uncertainty relations based on the state-dependent norm of commutators, utilizing generalizations of the B"ottcher-Wenzel inequality.
The first relation is mathematically proven, while the second, tighter relation is strongly supported by numerical evidence.
arXiv Detail & Related papers (2024-06-18T05:16:45Z) - State-dependent and state-independent uncertainty relations for skew information and standard deviation [0.0]
We derive uncertainty equality based on standard deviation for incompatible operators with mixed states.
We show that for pure states, the Wigner-Yanase skew information based state-independent uncertainty relations become standard deviation based state-independent uncertainty relations.
arXiv Detail & Related papers (2024-02-05T16:28:29Z) - Signatures of quantum phases in a dissipative system [13.23575512928342]
Lindbladian formalism has been all-pervasive to interpret non-equilibrium steady states of quantum many-body systems.
We study the fate of free fermionic and superconducting phases in a dissipative one-dimensional Kitaev model.
arXiv Detail & Related papers (2023-12-28T17:53:26Z) - Sequential sharing of two-qudit entanglement based on the entropic
uncertainty relation [15.907303576427644]
Entanglement and uncertainty relation are two focuses of quantum theory.
We relate entanglement sharing to the entropic uncertainty relation in a $(dtimes d)$-dimensional system via weak measurements with different pointers.
arXiv Detail & Related papers (2023-04-12T12:10:07Z) - Simulating Entanglement beyond Quantum Steering [15.808504285017948]
We quantify the resource content of such states in terms of how much shared randomness is needed to simulate their behavior.
We rigorously show that the shared randomness cost is unbounded even for some two-qubit unsteerable states.
arXiv Detail & Related papers (2023-02-17T18:52:33Z) - Strong entanglement criteria for mixed states, based on uncertainty
relations [0.0]
We show that any mixed entangled state can be characterized by our criterion.
The proposed criterion reduces to the Schrodinger-Robertson inequality for pure states.
arXiv Detail & Related papers (2022-10-29T10:00:41Z) - Einstein-Podolsky-Rosen uncertainty limits for bipartite multimode
states [0.0]
Correlations of two-party $(N, textvs,1)$-mode states are examined by using the variances of a pair of suitable EPR-like observables.
The analysis of the minimal properly normalized sums of these variances yields necessary conditions of separability and EPR unsteerability.
arXiv Detail & Related papers (2021-07-02T13:11:00Z) - Non-equilibrium stationary states of quantum non-Hermitian lattice
models [68.8204255655161]
We show how generic non-Hermitian tight-binding lattice models can be realized in an unconditional, quantum-mechanically consistent manner.
We focus on the quantum steady states of such models for both fermionic and bosonic systems.
arXiv Detail & Related papers (2021-03-02T18:56:44Z) - A Weaker Faithfulness Assumption based on Triple Interactions [89.59955143854556]
We propose a weaker assumption that we call $2$-adjacency faithfulness.
We propose a sound orientation rule for causal discovery that applies under weaker assumptions.
arXiv Detail & Related papers (2020-10-27T13:04:08Z) - Entanglement as upper bounded for the nonlocality of a general two-qubit
system [16.676050048472963]
We systematically investigate the relationship between entanglement and nonlocality of a general two-qubit system.
We find that the nonlocality of two different two-qubit states can be optimally stimulated by the same nonlocality test setting.
arXiv Detail & Related papers (2020-04-17T16:42:27Z) - Experimental Test of Tight State-Independent Preparation Uncertainty
Relations for Qubits [1.5749416770494706]
We present a neutron optical test of the tight state preparation uncertainty relations for non-independent Pauli spin states with mixed spin states.
The final results, obtained in a polarimetric experiment, reproduce the theoretical predictions evidently for arbitrary initial states variable degree polarization.
arXiv Detail & Related papers (2020-02-25T08:23:17Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.