Geometry of faithful entanglement
- URL: http://arxiv.org/abs/2008.05961v2
- Date: Mon, 15 Mar 2021 18:33:06 GMT
- Title: Geometry of faithful entanglement
- Authors: Otfried G\"uhne, Yuanyuan Mao, Xiao-Dong Yu
- Abstract summary: A typical concept in quantum state analysis is based on the idea that states in the vicinity of some pure entangled state share the same properties.
We prove a structural result on the corresponding fidelity-based entanglement witnesses, resulting in a simple condition for faithfulness of a two-party state.
- Score: 2.9475513512647455
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: A typical concept in quantum state analysis is based on the idea that states
in the vicinity of some pure entangled state share the same properties;
implying that states with a high fidelity must be entangled. States whose
entanglement can be detected in this way are also called faithful. We prove a
structural result on the corresponding fidelity-based entanglement witnesses,
resulting in a simple condition for faithfulness of a two-party state. For the
simplest case of two qubits faithfulness can directly be decided and for higher
dimensions accurate analytical criteria are given. Finally, our results show
that faithful entanglement is, in a certain sense, useful entanglement;
moreover, they establish connections to computational complexity and simplify
several results in entanglement theory.
Related papers
- Detecting unfaithful entanglement by multiple fidelities [7.320365821066744]
Certifying entanglement for unknown quantum states experimentally is a fundamental problem in quantum computing and quantum physics.
Because of being easy to implement, a most popular approach for this problem in modern quantum experiments is detecting target quantum states with fidelity-based entanglement witnesses.
Recently, it has been realized that there exist so-called unfaithful quantum states, which can be entangled, but their entanglement cannot be certified by any fidelity-based entanglement witnesses.
arXiv Detail & Related papers (2024-09-20T04:58:12Z) - An Effective Way to Determine the Separability of Quantum State [0.0]
We show that some general separability conditions are set up through constructing a measurement-induced Bloch space.
The new approach can not only reproduce many of the prevailing entanglement criteria, but also lead to even stronger results and manifest superiority for some bound entangled states.
arXiv Detail & Related papers (2024-03-12T06:17:19Z) - Almost device-independent certification of GME states with minimal
measurements [41.94295877935867]
Device-independent certification of quantum states allows the characterization of quantum states present inside a device.
A major problem in this regard is to certify quantum states using minimal resources.
We consider the multipartite quantum steering scenario with an arbitrary number of parties but only one of which is trusted in the sense that the measurements performed by the trusted party are known.
arXiv Detail & Related papers (2024-02-28T17:54:55Z) - Measurement-Device-Independent Detection of Beyond-Quantum State [53.64687146666141]
We propose a measurement-device-independent (MDI) test for beyond-quantum state detection.
We discuss the importance of tomographic completeness of the input sets to the detection.
arXiv Detail & Related papers (2023-12-11T06:40:13Z) - Faithful coherent states [13.755454713771352]
We propose the notion of faithful coherent states based on the fidelity-based coherence witness.
We can realize unitary transformations by using quantum gates and circuits.
arXiv Detail & Related papers (2022-04-27T09:47:31Z) - 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) - Non-standard entanglement structure of local unitary self-dual models as
a saturated situation of repeatability in general probabilistic theories [61.12008553173672]
We show the existence of infinite structures of quantum composite system such that it is self-dual with local unitary symmetry.
We also show the existence of a structure of quantum composite system such that non-orthogonal states in the structure are perfectly distinguishable.
arXiv Detail & Related papers (2021-11-29T23:37:58Z) - Exploring the relationship between the faithfulness and entanglement of
two qubits [2.400716652658002]
A conceptually simple and experimentally prevalent class of entanglement witnesses, known as fidelity witnesses, detect entanglement via a state's fidelity with a pure reference state.
Recent results have found that entangled states that cannot be detected by a fidelity witness, known as unfaithful states, are exceedingly common among bipartite states.
We show that even among two-qubit states, the simplest of all entangled states, unfaithful states can be created through a suitable application of decoherence and filtering to a Bell state.
arXiv Detail & Related papers (2021-02-19T19:02:27Z) - Observers of quantum systems cannot agree to disagree [55.41644538483948]
We ask whether agreement between observers can serve as a physical principle that must hold for any theory of the world.
We construct examples of (postquantum) no-signaling boxes where observers can agree to disagree.
arXiv Detail & Related papers (2021-02-17T19:00:04Z) - Gaussian Process States: A data-driven representation of quantum
many-body physics [59.7232780552418]
We present a novel, non-parametric form for compactly representing entangled many-body quantum states.
The state is found to be highly compact, systematically improvable and efficient to sample.
It is also proven to be a universal approximator' for quantum states, able to capture any entangled many-body state with increasing data set size.
arXiv Detail & Related papers (2020-02-27T15:54:44Z) - Quantifying the unextendibility of entanglement [13.718093420358827]
Entanglement is a striking feature of quantum mechanics, and it has a key property called unextendibility.
We present a framework for quantifying and investigating the unextendibility of general bipartite quantum states.
arXiv Detail & Related papers (2019-11-18T05:22:36Z)
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.