Uncertainty relations from state polynomial optimization
- URL: http://arxiv.org/abs/2310.00612v2
- Date: Mon, 8 Jul 2024 07:39:05 GMT
- Title: Uncertainty relations from state polynomial optimization
- Authors: Moisés Bermejo Morán, Felix Huber,
- Abstract summary: We find a complete semidefinite programming hierarchy that converges to tight uncertainty relations.
Our hierarchy applies to a wide range of scenarios including tensor-products of Pauli, Heisenberg-Weyl, and fermionic operators.
- Score: 3.069335774032178
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Uncertainty relations are a fundamental feature of quantum mechanics. How can these relations be found systematically? Here we make use of the state polynomial optimization framework from Klep et al. [arXiv:2301.12513] to bound the sum of squared expectation values of operators, that are subject to prescribed commutation relations. This yields a complete semidefinite programming hierarchy that converges to tight uncertainty relations. Our hierarchy applies to a wide range of scenarios including tensor-products of Pauli, Heisenberg-Weyl, and fermionic operators, as well as higher order moments.
Related papers
- Tensor cumulants for statistical inference on invariant distributions [49.80012009682584]
We show that PCA becomes computationally hard at a critical value of the signal's magnitude.
We define a new set of objects, which provide an explicit, near-orthogonal basis for invariants of a given degree.
It also lets us analyze a new problem of distinguishing between different ensembles.
arXiv Detail & Related papers (2024-04-29T14:33:24Z) - Explicit error bounds for entanglement transformations between sparse
multipartite states [0.0]
A nontrivial family of such functional exponents has recently been constructed.
We derive a new regularised formula for these functionals in terms of a subadditive upper bound.
Our results provide explicit bounds on the success probability of transformations by local operations and classical communication.
arXiv Detail & Related papers (2023-09-20T16:06:48Z) - State polynomials: positivity, optimization and nonlinear Bell
inequalities [3.9692590090301683]
This paper introduces states in noncommuting variables and formal states of their products.
It shows that states, positive over all and matricial states, are sums of squares with denominators.
It is also established that avinetengle Kritivsatz fails to hold in the state setting.
arXiv Detail & Related papers (2023-01-29T18:52:21Z) - Improved Quantum Algorithms for Fidelity Estimation [77.34726150561087]
We develop new and efficient quantum algorithms for fidelity estimation with provable performance guarantees.
Our algorithms use advanced quantum linear algebra techniques, such as the quantum singular value transformation.
We prove that fidelity estimation to any non-trivial constant additive accuracy is hard in general.
arXiv Detail & Related papers (2022-03-30T02:02:16Z) - A Quantum Optimal Control Problem with State Constrained Preserving
Coherence [68.8204255655161]
We consider a three-level $Lambda$-type atom subjected to Markovian decoherence characterized by non-unital decoherence channels.
We formulate the quantum optimal control problem with state constraints where the decoherence level remains within a pre-defined bound.
arXiv Detail & Related papers (2022-03-24T21:31:34Z) - High Fidelity Quantum State Transfer by Pontryagin Maximum Principle [68.8204255655161]
We address the problem of maximizing the fidelity in a quantum state transformation process satisfying the Liouville-von Neumann equation.
By introducing fidelity as the performance index, we aim at maximizing the similarity of the final state density operator with the one of the desired target state.
arXiv Detail & Related papers (2022-03-07T13:27:26Z) - R\'enyi divergence inequalities via interpolation, with applications to
generalised entropic uncertainty relations [91.3755431537592]
We investigate quantum R'enyi entropic quantities, specifically those derived from'sandwiched' divergence.
We present R'enyi mutual information decomposition rules, a new approach to the R'enyi conditional entropy tripartite chain rules and a more general bipartite comparison.
arXiv Detail & Related papers (2021-06-19T04:06:23Z) - QuantumCumulants.jl: A Julia framework for generalized mean-field
equations in open quantum systems [0.0]
We present an open-source framework that fully automizes equations of motion of operators up to a desired order.
After reviewing the theory we present the framework and showcase its usefulness in a few example problems.
arXiv Detail & Related papers (2021-05-04T08:53:02Z) - Fermionic duality: General symmetry of open systems with strong
dissipation and memory [0.0]
We present a nontrivial fermionic duality relation between the evolution of states (Schr"odinger) and of observables (Heisenberg)
We show how this highly nonintuitive relation can be understood and exploited in analytical calculations within all canonical approaches to quantum dynamics.
arXiv Detail & Related papers (2021-04-22T17:37:42Z) - Relevant OTOC operators: footprints of the classical dynamics [68.8204255655161]
The OTOC-RE theorem relates the OTOCs summed over a complete base of operators to the second Renyi entropy.
We show that the sum over a small set of relevant operators, is enough in order to obtain a very good approximation for the entropy.
In turn, this provides with an alternative natural indicator of complexity, i.e. the scaling of the number of relevant operators with time.
arXiv Detail & Related papers (2020-07-31T19:23:26Z)
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.