Bounding the detection efficiency threshold in Bell tests using multiple copies of the maximally entangled two-qubit state carried by a single pair of particles

• URL: http://arxiv.org/abs/2103.10413v2
• Date: Wed, 8 Feb 2023 14:20:54 GMT
• Title: Bounding the detection efficiency threshold in Bell tests using multiple copies of the maximally entangled two-qubit state carried by a single pair of particles
• Authors: Istv\'an M\'arton, Erika Bene, Tam\'as V\'ertesi
• Abstract summary: We investigate the critical efficiency of detectors to observe Bell nonlocality using multiple copies of the maximally entangled two-qubit state carried by a single pair of particles. We show analytically that the symmetric detection efficiency threshold decays exponentially with the number of copies of the two-qubit state.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper, we investigate the critical efficiency of detectors to observe Bell nonlocality using multiple copies of the maximally entangled two-qubit state carried by a single pair of particles, such as hyperentangled states, and the product of Pauli measurements. It is known that in a Clauser-Horne-Shimony-Holt (CHSH) Bell test the symmetric detection efficiency of $82.84\%$ can be tolerated for the two-qubit maximally entangled state. We beat this enigmatic threshold by entangling two particles with multiple degrees of freedom. The obtained upper bounds of the symmetric detection efficiency thresholds are $80.86\%$, $73.99\%$ and $69.29\%$ for two, three and four copies of the two-qubit maximally entangled state, respectively. The number of measurements and outcomes in the respective cases are 4, 8 and 16. To find the improved thresholds, we use large-scale convex optimization tools, which allows us to significantly go beyond state-of-the-art results. The proof is exact up to three copies, while for four copies it is due to reliable numerical computations. Specifically, we used linear programming to obtain the two-copy threshold and the corresponding Bell inequality, and convex optimization based on Gilbert's algorithm for three and four copies of the two-qubit state. We show analytically that the symmetric detection efficiency threshold decays exponentially with the number of copies of the two-qubit state. Our techniques can also be applied to more general Bell nonlocality scenarios with more than two parties.

Related papers

• Multiplexed qubit readout quality metric beyond assignment fidelity [0.0]
  We use detector tomography to fully characterize multi-qubit readout of superconducting transmon qubits. The impact of different readout parameters on the rate of information extraction is studied using quantum state reconstruction as a proxy. We find the most effective allocation of a fixed shot budget between detector tomography and state reconstruction in single- and two-qubit experiments.
  arXiv  Detail & Related papers  (2025-02-12T17:21:38Z)
• ParetoQ: Scaling Laws in Extremely Low-bit LLM Quantization [58.84018707089315]
  We present a unified framework for rigorous comparisons across 1-bit, 1.58-bit, 2-bit, 3-bit, and 4-bit quantization settings. We show that ternary, 2-bit, and 3-bit quantization maintains comparable performance in the size-accuracy trade-off. Considering hardware constraints, 2-bit quantization offers promising potential for memory reduction and speedup.
  arXiv  Detail & Related papers  (2025-02-04T18:59:26Z)
• Highly-entangled, highly-doped states that are efficiently cross-device verifiable [0.0]
  We introduce a class of highly entangled real quantum states that cannot be approximated by circuits with $log$-many non-Clifford gates. We prove that Bell sampling enables efficient cross-device verification (or distributed inner product estimation) for these states. We anticipate that these results could have applications in quantum cryptography and verification.
  arXiv  Detail & Related papers  (2025-01-20T19:12:34Z)
• Memory-Efficient 4-bit Preconditioned Stochastic Optimization [53.422307389223626]
  We introduce 4-bit quantization for Shampoo's preconditioners. To our knowledge, this is the first quantization approach applied to Cholesky factors of preconditioners.
  arXiv  Detail & Related papers  (2024-12-14T03:32:54Z)
• DB-LLM: Accurate Dual-Binarization for Efficient LLMs [83.70686728471547]
  Large language models (LLMs) have significantly advanced the field of natural language processing. Existing ultra-low-bit quantization always causes severe accuracy drops. We propose a novel Dual-Binarization method for LLMs, namely DB-LLM.
  arXiv  Detail & Related papers  (2024-02-19T09:04:30Z)
• Improved local models and new Bell inequalities via Frank-Wolfe algorithms [16.159626741758633]
  In Bell scenarios with two outcomes per party, we algorithmically consider the two sides of the membership problem for the local polytope. We take advantage of the recent developments in so-called Frank-Wolfe algorithms to significantly increase the convergence rate of existing methods. We present the first local models for all projective measurements with visibilities noticeably higher than the entanglement threshold.
  arXiv  Detail & Related papers  (2023-02-09T16:02:49Z)
• Device-independent randomness certification using multiple copies of entangled states [0.0]
  We show that many copies of maximally entangled two-qubit states enable for generating a greater amount of randomness than that can be certified from a single copy. We suitably invoke a family of $n$-settings Bell inequalities which is optimized for $lfloor n/2 rfloor$ copies of maximally entangled two-qubit states.
  arXiv  Detail & Related papers  (2022-12-29T15:15:15Z)
• 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)
• 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)
• Quantifying Multipartite Quantum Entanglement in a Semi-Device-Independent Manner [0.6091702876917279]
  We propose two approaches to quantify unknown multipartite quantum entanglement experimentally. We obtain useful information on the purity of target quantum state. We show that useful lower bounds for the geometric measure of entanglement can be obtained if the Bell value is larger than 3.60.
  arXiv  Detail & Related papers  (2020-08-27T11:43:29Z)
• Bayesian Bits: Unifying Quantization and Pruning [73.27732135853243]
  We introduce Bayesian Bits, a practical method for joint mixed precision quantization and pruning through gradient based optimization. We experimentally validate our proposed method on several benchmark datasets and show that we can learn pruned, mixed precision networks.
  arXiv  Detail & Related papers  (2020-05-14T16:00:34Z)

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.