Calculating Concentratable Entanglement in Graph States
- URL: http://arxiv.org/abs/2207.11997v1
- Date: Mon, 25 Jul 2022 09:11:28 GMT
- Title: Calculating Concentratable Entanglement in Graph States
- Abstract summary: We propose a method to calculate the purity of reduced states of graph states entirely within the stabilizer formalism.
We apply this method to find the Concentratable Entanglement of graph states, with examples including a single qubit within any graph state.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We propose a method to calculate the purity of reduced states of graph states
entirely within the stabilizer formalism, using only the stabilizer generators
for a given state. We apply this method to find the Concentratable Entanglement
of graph states, with examples including a single qubit within any graph state,
states proposed for use in quantum repeaters and states that maximise and
minimise the overall Concentratable Entanglement.
Related papers
- Gaussian fermionic embezzlement of entanglement [41.321581612257056]
We show that the embezzling property is in fact a generic property of fermionic Gaussian states.<n>We bridge finite-size systems to abstract characterizations based on the classification of von Neumann algebras.
arXiv Detail & Related papers (2025-09-19T08:26:03Z) - Tensor Train Quantum State Tomography using Compressed Sensing [2.493374942115722]
Quantum state tomography (QST) is a fundamental technique for estimating the state of a quantum system from measured data.<n>In this work, we address this challenge by parameterizing the state using a low-rank block tensor train decomposition.<n>This framework applies to a broad class of quantum states that can be well approximated by low-rank decompositions.
arXiv Detail & Related papers (2025-06-30T07:06:50Z) - Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking [45.147301546565316]
This paper considers the problem of decentralized optimization on compact submanifolds.<n>We propose an algorithm where agents update variables using quantized variables.<n>To the best of our knowledge, this is the first algorithm to achieve an $mathcalO (1/K)$ convergence rate in the presence of quantization.
arXiv Detail & Related papers (2025-06-09T01:57:25Z) - General detectability measure [53.64687146666141]
Distinguishing resource states from resource-free states is a fundamental task in quantum information.
We derived the optimal exponential decay rate of the failure probability for detecting a given $n$-tensor product state.
arXiv Detail & Related papers (2025-01-16T05:39:22Z) - Optimizing random local Hamiltonians by dissipation [44.99833362998488]
We prove that a simplified quantum Gibbs sampling algorithm achieves a $Omega(frac1k)$-fraction approximation of the optimum.
Our results suggest that finding low-energy states for sparsified (quasi)local spin and fermionic models is quantumly easy but classically nontrivial.
arXiv Detail & Related papers (2024-11-04T20:21:16Z) - Single-shot entanglement manipulation of states and channels revisited [5.23833305434825]
We study entanglement distillation and dilution of states and channels in the single-shot regime.
We show how this can be used to efficiently calculate these quantities on multiple copies of pure states.
We then turn to the one-way entanglement distillation of states and channels and provide bounds in terms of a quantity we coherent information of entanglement.
arXiv Detail & Related papers (2023-12-28T16:08:24Z) - Stabilizer Approximation [3.1798822431855975]
We propose a method to obtain the approximate groundstate for a Hamiltonian in the qubit form.
These states may serve as proper initial states for further refined computation.
arXiv Detail & Related papers (2022-09-20T09:10:28Z) - Quantum state tomography with tensor train cross approximation [84.59270977313619]
We show that full quantum state tomography can be performed for such a state with a minimal number of measurement settings.
Our method requires exponentially fewer state copies than the best known tomography method for unstructured states and local measurements.
arXiv Detail & Related papers (2022-07-13T17:56:28Z) - On the Convergence of Stochastic Extragradient for Bilinear Games with
Restarted Iteration Averaging [96.13485146617322]
We present an analysis of the ExtraGradient (SEG) method with constant step size, and present variations of the method that yield favorable convergence.
We prove that when augmented with averaging, SEG provably converges to the Nash equilibrium, and such a rate is provably accelerated by incorporating a scheduled restarting procedure.
arXiv Detail & Related papers (2021-06-30T17:51:36Z) - Quantum tomography of three-qubit generalized Werner states [0.0]
We introduce a numerical framework for quantum tomography and entanglement quantification of three-qubit generalized Werner states.
The scheme involves the single-qubit SIC-POVM, which is then generalized to perform three-qubit measurements.
As a special case, we compare the efficiency of the framework for the pure three-qubit generalized Werner state and the W state.
arXiv Detail & Related papers (2021-04-22T18:00:21Z) - Nishimori meets Bethe: a spectral method for node classification in
sparse weighted graphs [53.13327158427103]
This article unveils a new relation between the Nishimori temperature parametrizing a distribution P and the Bethe free energy on random Erdos-Renyi graphs with edge weights distributed according to P.
A numerical method is proposed to accurately estimate the Nishimori temperature from the eigenvalues of the Bethe Hessian matrix of the weighted graph.
arXiv Detail & Related papers (2021-03-05T09:45:56Z) - Entanglement purification by counting and locating errors with
entangling measurements [62.997667081978825]
We consider entanglement purification protocols for multiple copies of qubit states.
We use high-dimensional auxiliary entangled systems to learn about number and positions of errors in the noisy ensemble.
arXiv Detail & Related papers (2020-11-13T19:02:33Z) - Local optimization on pure Gaussian state manifolds [63.76263875368856]
We exploit insights into the geometry of bosonic and fermionic Gaussian states to develop an efficient local optimization algorithm.
The method is based on notions of descent gradient attuned to the local geometry.
We use the presented methods to collect numerical and analytical evidence for the conjecture that Gaussian purifications are sufficient to compute the entanglement of purification of arbitrary mixed Gaussian states.
arXiv Detail & Related papers (2020-09-24T18:00:36Z) - Dissipative engineering of Gaussian entangled states in harmonic
lattices with a single-site squeezed reservoir [0.0]
We study the dissipative preparation of many-body entangled Gaussian states in bosonic lattice models.
We show that in this way it is possible to prepare, in the steady state, the wide class of pure states.
This includes non-trivial multipartite entangled states such as cluster states suitable for measurement-based quantum computation.
arXiv Detail & Related papers (2020-08-06T09:36:06Z) - 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) - An algorithm for tailoring a quadratic lattice with a local squeezed
reservoir to stabilize generic chiral states with non-local entanglement [0.0]
We show a new approach to the generation of custom entangled many-body states through reservoir engineering.
We outline an algorithm where, beginning with a desired set of squeezing correlations, one uses the symmetry to constrain the Hamiltonian.
We demonstrate how to use this process to stabilize two unique pure states with non-local correlations that could be useful for quantum information applications.
arXiv Detail & Related papers (2020-02-12T20:30:08Z)
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.