Almost synchronous quantum correlations
- URL: http://arxiv.org/abs/2103.02468v3
- Date: Wed, 7 Jun 2023 06:16:50 GMT
- Title: Almost synchronous quantum correlations
- Authors: Thomas Vidick
- Abstract summary: The study of quantum correlation sets was initiated by Tsirelson in the 1980s and originally motivated by questions in the foundations of quantum mechanics.
Synchronous correlation sets introduced in [Paulsen et. al, JFA 2016] are a subclass of correlations that has proven particularly useful to study and arises naturally in applications.
- Score: 7.716156977428555
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The study of quantum correlation sets initiated by Tsirelson in the 1980s and
originally motivated by questions in the foundations of quantum mechanics has
more recently been tied to questions in quantum cryptography, complexity
theory, operator space theory, group theory, and more. Synchronous correlation
sets introduced in [Paulsen et. al, JFA 2016] are a subclass of correlations
that has proven particularly useful to study and arises naturally in
applications. We show that any correlation that is almost synchronous, in a
natural $\ell_1$ sense, arises from a state and measurement operators that are
well-approximated by a convex combination of projective measurements on a
maximally entangled state. This extends a result of [Paulsen et. al, JFA 2016]
which applies to exactly synchronous correlations. Crucially, the quality of
approximation is independent of the dimension of the Hilbert spaces or of the
size of the correlation. Our result allows one to reduce the analysis of many
classes of nonlocal games, including rigidity properties, to the case of
strategies using maximally entangled states which are generally easier to
manipulate.
Related papers
- Spin-bounded correlations: rotation boxes within and beyond quantum
theory [0.0]
We prove that quantum theory admits the most general rotational correlations for spins 0, 1/2, and 1.
We also prove a metrological game where beyond-quantum resources of spin 3/2 outperform all quantum resources of the same spin.
Results illuminate the question of how space constrains the structure of quantum theory.
arXiv Detail & Related papers (2023-12-14T19:00:02Z) - Taming Quantum Time Complexity [45.867051459785976]
We show how to achieve both exactness and thriftiness in the setting of time complexity.
We employ a novel approach to the design of quantum algorithms based on what we call transducers.
arXiv Detail & Related papers (2023-11-27T14:45:19Z) - Eigenstate correlations, the eigenstate thermalization hypothesis, and quantum information dynamics in chaotic many-body quantum systems [0.0]
We consider correlations between eigenstates specific to spatially extended systems and that characterise entanglement dynamics and operator spreading.
The correlations associated with scrambling of quantum information lie outside the standard framework established by the eigenstate thermalisation hypothesis (ETH)
We establish the simplest correlation function that captures these correlations and discuss features of its behaviour that are expected to be universal at long distances and low energies.
arXiv Detail & Related papers (2023-09-22T16:28:15Z) - Observing super-quantum correlations across the exceptional point in a
single, two-level trapped ion [48.7576911714538]
In two-level quantum systems - qubits - unitary dynamics theoretically limit these quantum correlations to $2qrt2$ or 1.5 respectively.
Here, using a dissipative, trapped $40$Ca$+$ ion governed by a two-level, non-Hermitian Hamiltonian, we observe correlation values up to 1.703(4) for the Leggett-Garg parameter $K_3$.
These excesses occur across the exceptional point of the parity-time symmetric Hamiltonian responsible for the qubit's non-unitary, coherent dynamics.
arXiv Detail & Related papers (2023-04-24T19:44:41Z) - Two convergent NPA-like hierarchies for the quantum bilocal scenario [2.048226951354646]
Characterising correlations that arise from locally measuring a single part of a joint quantum system is one of the main problems of quantum information theory.
We introduce a new hierarchy to prove its equivalence to the Scalar Extension and explore its relations with the known generalisations.
arXiv Detail & Related papers (2022-10-17T13:04:41Z) - Quantum correlations on the no-signaling boundary: self-testing and more [0.39146761527401425]
We prove that self-testing is possible in all nontrivial Classes beyond the known examples of Hardy-type correlations.
All correlations of $mathcalM$ in the simplest Bell scenario are attainable as convex combinations of those achievable using a Bell pair and projective measurements.
arXiv Detail & Related papers (2022-07-28T01:55:21Z) - Entropic Accord: A new measure in the quantum correlation hierarchy [0.5039813366558306]
We show a new measure of quantum correlations which we call entropic accord that fits between entanglement and discord.
We study two-qubit states which shows the relationship between the three entropic quantities.
arXiv Detail & Related papers (2022-05-13T07:16:50Z) - 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) - Experimental violations of Leggett-Garg's inequalities on a quantum
computer [77.34726150561087]
We experimentally observe the violations of Leggett-Garg-Bell's inequalities on single and multi-qubit systems.
Our analysis highlights the limits of nowadays quantum platforms, showing that the above-mentioned correlation functions deviate from theoretical prediction as the number of qubits and the depth of the circuit grow.
arXiv Detail & Related papers (2021-09-06T14:35:15Z) - Preparing random states and benchmarking with many-body quantum chaos [48.044162981804526]
We show how to predict and experimentally observe the emergence of random state ensembles naturally under time-independent Hamiltonian dynamics.
The observed random ensembles emerge from projective measurements and are intimately linked to universal correlations built up between subsystems of a larger quantum system.
Our work has implications for understanding randomness in quantum dynamics, and enables applications of this concept in a wider context.
arXiv Detail & Related papers (2021-03-05T08:32:43Z) - The principle of majorization: application to random quantum circuits [68.8204255655161]
Three classes of circuits were considered: (i) universal, (ii) classically simulatable, and (iii) neither universal nor classically simulatable.
We verified that all the families of circuits satisfy on average the principle of majorization.
Clear differences appear in the fluctuations of the Lorenz curves associated to states.
arXiv Detail & Related papers (2021-02-19T16:07:09Z)
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.