On some states minimizing uncertainty relations: A new look at these relations

• URL: http://arxiv.org/abs/2411.08131v3
• Date: Tue, 11 Feb 2025 09:29:22 GMT
• Title: On some states minimizing uncertainty relations: A new look at these relations
• Authors: Krzysztof Urbanowski,
• Abstract summary: We show that there can exist a large set of states of the quantum system under considerations. These states are not eigenstates of either the observable $A$ or $B$. We additionally show that the uncertainty principle in its most general form has two faces.
• Score: 0.0
• License:
• Abstract: Analyzing Heisenberg--Robertson (HR) and Schr\"{o}dinger uncertainty relations we found, that there can exist a large set of states of the quantum system under considerations, for which the lower bound of the product of the standard deviations of a pair of non--commuting observables, $A$ and $B$, is zero. These states are not eigenstates of either the observable $A$ or $B$. The correlation function for these observables in such states is equal to zero. We have also shown that the so--called "sum uncertainty relations" also do not provide any information about lower bounds on the standard deviations calculated for these states. We additionally show that the uncertainty principle in its most general form has two faces: one is that it is a lower bound on the product of standard deviations, and the other is that the product of standard deviations is an upper bound on the modulus of the correlation function of a pair of the non--commuting observables in the state under consideration.

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)
• Measurement incompatibility is strictly stronger than disturbance [44.99833362998488]
  Heisenberg argued that measurements irreversibly alter the state of the system on which they are acting, causing an irreducible disturbance on subsequent measurements. This article shows that measurement incompatibility is indeed a sufficient condition for irreversibility of measurement disturbance. However, we exhibit a toy theory, termed the minimal classical theory (MCT), that is a counterexample for the converse implication.
  arXiv  Detail & Related papers  (2023-05-26T13:47:00Z)
• 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)
• Parameterized Multi-observable Sum Uncertainty Relations [9.571723611319348]
  We study uncertainty relations based on variance for arbitrary finite $N$ quantum observables. The lower bounds of our uncertainty inequalities are non-zero unless the measured state is a common eigenvector of all the observables.
  arXiv  Detail & Related papers  (2022-11-07T04:36:07Z)
• Concentration bounds for quantum states and limitations on the QAOA from polynomial approximations [17.209060627291315]
  We prove concentration for the following classes of quantum states: (i) output states of shallow quantum circuits, answering an open question from [DPMRF22]; (ii) injective matrix product states, answering an open question from [DPMRF22]; (iii) output states of dense Hamiltonian evolution, i.e. states of the form $eiota H(p) cdots eiota H(1) |psirangle for any $n$-qubit product state $|psirangle$, where each $H(
  arXiv  Detail & Related papers  (2022-09-06T18:00:02Z)
• Uncertainty Relations in Pre- and Post-Selected Systems [0.0]
  We derive Robertson-Heisenberg like uncertainty relation for two incompatible observables in a pre- and post-selected (PPS) system. Unlike the standard quantum system, the PPS system makes it feasible to prepare sharply a quantum state for non-commuting observables.
  arXiv  Detail & Related papers  (2022-07-15T18:15:28Z)
• Symmetric inseparability and number entanglement in charge conserving mixed states [15.57253296268595]
  We argue that even separable states may contain entanglement in fixed charge sectors, as long as the state can not be separated into charge conserving components. We demonstrate that the NE is not only a witness of symmetric inseparability, but also an entanglement monotone.
  arXiv  Detail & Related papers  (2021-10-18T15:20:07Z)
• 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)
• Attainability and lower semi-continuity of the relative entropy of entanglement, and variations on the theme [8.37609145576126]
  The relative entropy of entanglement $E_Rite is defined as the distance of a multi-part quantum entanglement from the set of separable states as measured by the quantum relative entropy. We show that this state is always achieved, i.e. any state admits a closest separable state, even in dimensions; also, $E_Rite is everywhere lower semi-negative $lambda_$quasi-probability distribution.
  arXiv  Detail & Related papers  (2021-05-17T18:03:02Z)
• 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)
• Tighter uncertainty relations based on Wigner-Yanase skew information for observables and channels [1.2375561840897742]
  Wigner-Yanase skew information, as a measure of quantum uncertainties, is used to characterize intrinsic features of the state and the observable. We investigate the sum uncertainty relations for both quantum mechanical observables and quantum channels based on skew information.
  arXiv  Detail & Related papers  (2020-02-27T02:40:23Z)

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.