Bipartite entanglement detection by local generalized measurements
- URL: http://arxiv.org/abs/2305.14226v1
- Date: Tue, 23 May 2023 16:40:48 GMT
- Title: Bipartite entanglement detection by local generalized measurements
- Authors: Maximilian Schumacher, Gernot Alber
- Abstract summary: Entanglement detection by local measurements, which can possibly be performed by far distant observers, are of particular interest for applications in quantum key distribution and quantum communication.
In this paper sufficient conditions for arbitrary dimensional bipartite entanglement detection based on correlation matrices and joint probability of distributions are investigated.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Entanglement detection by local measurements, which can possibly be performed
by far distant observers, are of particular interest for applications in
quantum key distribution and quantum communication. In this paper sufficient
conditions for arbitrary dimensional bipartite entanglement detection based on
correlation matrices and joint probability distributions of such local
measurements are investigated. In particular, their dependence on the nature of
the local measurements is explored for typical bipartite quantum states and for
measurements involving local orthonormal hermitian operators bases (LOOs) or
generalized measurements based on informationally complete positive operator
valued measures of the recently introduced $(N,M)$-type ($(N,M)$-POVMs)
\cite{NMPOVM}. It is shown that symmetry properties of $(N,M)$-POVMs imply that
sufficient conditions for bipartite entanglement detection exhibit peculiar
scaling properties relating different equally efficient local entanglement
detection scenarios. For correlation-matrix based bipartite local entanglement
detection, for example, this has the consequence that LOOs and all
informationally complete $(N,M)$-POVMs are equally powerful. With the help of a
hit-and-run Monte-Carlo algorithm the effectiveness of local entanglement
detection of typical bipartite quantum states is explored numerically. For this
purpose Euclidean volume ratios between locally detectable entangled states and
all bipartite quantum states are determined.
Related papers
- Classification of joint quantum measurements based on entanglement cost of localization [42.72938925647165]
We propose a systematic classification of joint measurements based on entanglement cost.
We show how to numerically explore higher levels and construct generalizations to higher dimensions and multipartite settings.
arXiv Detail & Related papers (2024-08-01T18:00:01Z) - Entanglement cost of discriminating quantum states under locality
constraints [7.0937306686264625]
We show that a pure state can be optimally discriminated against any other state with the assistance of a single Bell state.
This study advances our understanding of the pivotal role played by entanglement in quantum state discrimination, serving as a crucial element in unlocking quantum data hiding against locally constrained measurements.
arXiv Detail & Related papers (2024-02-28T16:16:50Z) - 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) - Local Purity Distillation in Quantum Systems: Exploring the Complementarity Between Purity and Entanglement [41.94295877935867]
We introduce and develop the framework of Gibbs-preserving local operations and classical communication.
We focus on systems with fully degenerate local Hamiltonians, where local cooling aligns with the extraction of local purity.
Our findings open doors to various practical applications, including techniques for entanglement detection and estimation.
arXiv Detail & Related papers (2023-11-20T14:58:31Z) - Many-body entropies and entanglement from polynomially-many local measurements [0.26388783516590225]
We show that efficient estimation strategies exist under the assumption that all the spatial correlation lengths are finite.
We argue that our method could be practically useful to detect bipartite mixed-state entanglement for large numbers of qubits available in today's quantum platforms.
arXiv Detail & Related papers (2023-11-14T12:13:15Z) - Enhanced Entanglement in the Measurement-Altered Quantum Ising Chain [46.99825956909532]
Local quantum measurements do not simply disentangle degrees of freedom, but may actually strengthen the entanglement in the system.
This paper explores how a finite density of local measurement modifies a given state's entanglement structure.
arXiv Detail & Related papers (2023-10-04T09:51:00Z) - Quantum State Tomography for Matrix Product Density Operators [28.799576051288888]
Reconstruction of quantum states from experimental measurements is crucial for the verification and benchmarking of quantum devices.
Many physical quantum states, such as states generated by noisy, intermediate-scale quantum computers, are usually structured.
We establish theoretical guarantees for the stable recovery of MPOs using tools from compressive sensing and the theory of empirical processes.
arXiv Detail & Related papers (2023-06-15T18:23:55Z) - Typical bipartite steerability and generalized local quantum
measurements [0.0]
Recently proposed correlation-matrix based sufficient conditions for bipartite steerability from Alice to Bob are applied.
It is shown that this sufficient condition exhibits a peculiar scaling property.
Results are compared with a recently proposed method which reduces the determination of bipartite steerability from Alice's qubit to Bob's arbitrary dimensional quantum system.
arXiv Detail & Related papers (2023-05-29T09:48:12Z) - Resource-efficient high-dimensional entanglement detection via symmetric
projections [0.0]
We introduce two families of criteria for detecting and quantifying the entanglement of a bipartite quantum state of arbitrary local dimension.
Both criteria give a qualitative result in terms of the state's entanglement dimension and a quantitative result in terms of its fidelity with the maximally entangled state.
arXiv Detail & Related papers (2023-04-09T16:38:36Z) - Upper Bounds on the Distillable Randomness of Bipartite Quantum States [15.208790082352351]
distillable randomness of a bipartite quantum state is an information-theoretic quantity.
We prove measures of classical correlations and prove a number of their properties.
We then further bound these measures from above by some that are efficiently computable by means of semi-definite programming.
arXiv Detail & Related papers (2022-12-18T12:06:25Z) - Efficient Bipartite Entanglement Detection Scheme with a Quantum
Adversarial Solver [89.80359585967642]
Proposal reformulates the bipartite entanglement detection as a two-player zero-sum game completed by parameterized quantum circuits.
We experimentally implement our protocol on a linear optical network and exhibit its effectiveness to accomplish the bipartite entanglement detection for 5-qubit quantum pure states and 2-qubit quantum mixed states.
arXiv Detail & Related papers (2022-03-15T09:46:45Z)
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.