A new general quantum state verification protocol by the classical shadow method

• URL: http://arxiv.org/abs/2410.15870v3
• Date: Tue, 22 Apr 2025 12:50:02 GMT
• Title: A new general quantum state verification protocol by the classical shadow method
• Authors: Xiaodi Li,
• Abstract summary: We propose a new verification protocol that integrates key ideas from both the conventional framework and the shadow overlap protocol.<n>Our approach enhances the capabilities of the shadow overlap protocol while addressing some of its limitations.
• Score: 8.509045288392391
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Verifying whether a quantum device produces a specific state is a fundamental task in many applications of modern quantum technologies. In the conventional framework of quantum state verification, designing an optimal or efficient protocol for each type of state often requires intricate customization. Recently, Hsin-Yuan Huang et al. introduced a novel approach called the shadow overlap protocol in arXiv:2404.07281v1, which leverages classical shadows to efficiently verify multiple types of states simultaneously. In this paper, we propose a new verification protocol that integrates key ideas from both the conventional framework and the shadow overlap protocol. To achieve this, we first reformulate the shadow overlap protocol using the language of hypothesis testing, which also underpins the conventional framework, and then analyze the similarities and differences between them. Our approach enhances the capabilities of the shadow overlap protocol while addressing some of its limitations, leading to improved sample complexity and a more natural treatment of states with specific structures. Finally, we demonstrate the effectiveness of our protocol by applying it to GHZ states and stabilizer states.

Related papers

• Protocols and Trade-Offs of Quantum State Purification [4.732131350249]
  We introduce a general state purification framework designed to achieve the highest fidelity with a specified probability. For i.i.d. quantum states under depolarizing noise, our framework can replicate the purification protocol proposed by Barenco and al. We prove the protocols' optimality for two copies of noisy states with any dimension and confirm its optimality for higher numbers of copies and dimensions.
  arXiv  Detail & Related papers  (2024-04-01T14:34:45Z)
• Efficient Local Classical Shadow Tomography with Number Conservation [0.0]
  Shadow tomography aims to build a classical description of a quantum state from a sequence of simple random measurements. We propose and analyze a new local shadow protocol adapted to systems with fundamental number conservation laws, such as ultracold atoms.
  arXiv  Detail & Related papers  (2023-11-15T19:00:01Z)
• Entanglement Purification of Hypergraph States [0.0]
  Entanglement purification describes a primitive in quantum information processing, where several copies of noisy quantum states are distilled into few copies of nearly-pure states of high quality. We present optimized protocols for the purification of hypergraph states, which form a family of multi-qubit states that are relevant from several perspectives.
  arXiv  Detail & Related papers  (2023-01-26T19:00:01Z)
• Quantifying protocol efficiency: a thermodynamic figure of merit for classical and quantum state-transfer protocols [0.0]
  We focus on classical and quantum protocols transferring a state across a double-well potential. The classical protocols are achieved by deforming the potential, while the quantum ones are assisted by a counter-diabatic driving. We show that quantum protocols perform more quickly and accurately.
  arXiv  Detail & Related papers  (2022-12-20T09:19:51Z)
• Conference key agreement in a quantum network [67.410870290301]
  Quantum conference key agreement (QCKA) allows multiple users to establish a secure key from a shared multi-partite entangled state. In a quantum network, this protocol can be efficiently implemented using a single copy of a N-qubit Greenberger-Horne-Zeilinger (GHZ) state to distil a secure N-user conference key bit.
  arXiv  Detail & Related papers  (2022-07-04T18:00:07Z)
• A multiplexed synthesizer for non-Gaussian photonic quantum state generation [0.0]
  We propose an innovative approach that drastically simplifies the preparation of non-Gaussian states. We show that our protocol can be used to generate high-quality and high-amplitude Schr"odinger cat states.
  arXiv  Detail & Related papers  (2022-06-29T21:11:27Z)
• Commitment capacity of classical-quantum channels [70.51146080031752]
  We define various notions of commitment capacity for classical-quantum channels. We prove matching upper and lower bound on it in terms of the conditional entropy.
  arXiv  Detail & Related papers  (2022-01-17T10:41:50Z)
• Dynamical learning of a photonics quantum-state engineering process [48.7576911714538]
  Experimentally engineering high-dimensional quantum states is a crucial task for several quantum information protocols. We implement an automated adaptive optimization protocol to engineer photonic Orbital Angular Momentum (OAM) states. This approach represents a powerful tool for automated optimizations of noisy experimental tasks for quantum information protocols and technologies.
  arXiv  Detail & Related papers  (2022-01-14T19:24:31Z)
• Interactive Protocols for Classically-Verifiable Quantum Advantage [46.093185827838035]
  "Interactions" between a prover and a verifier can bridge the gap between verifiability and implementation. We demonstrate the first implementation of an interactive quantum advantage protocol, using an ion trap quantum computer.
  arXiv  Detail & Related papers  (2021-12-09T19:00:00Z)
• Reinforcement learning-enhanced protocols for coherent population-transfer in three-level quantum systems [50.591267188664666]
  We deploy a combination of reinforcement learning-based approaches and more traditional optimization techniques to identify optimal protocols for population transfer. Our approach is able to explore the space of possible control protocols to reveal the existence of efficient protocols. The new protocols that we identify are robust against both energy losses and dephasing.
  arXiv  Detail & Related papers  (2021-09-02T14:17:30Z)
• Experimental multi-state quantum discrimination through a Quantum network [63.1241529629348]
  We have experimentally implemented two discrimination schemes in a minimum-error scenario based on a receiver featured by a network structure and a dynamical processing of information. The first protocol achieves binary optimal discrimination, while the second one provides a novel approach to multi-state quantum discrimination, relying on the dynamical features of the network-like receiver.
  arXiv  Detail & Related papers  (2021-07-21T09:26:48Z)
• On Information-Theoretic Classical Verification of Quantum Computers [0.38073142980733]
  We show that any protocol from this family is bound to require an extremely powerful prover. We hint at possible ways one might try to realize a protocol where the prover can be weaker, namely a quantum computer.
  arXiv  Detail & Related papers  (2021-05-12T20:10:35Z)
• Classical Shadows With Noise [0.0]
  We study the effects of noise on the classical shadows protocol. We derive an analytical upper bound for the sample complexity in terms of a shadow seminorm for both local and global noise. Our results can be used to prove rigorous sample complexity upper bounds in the cases of depolarizing noise and amplitude damping.
  arXiv  Detail & Related papers  (2020-11-23T17:43:42Z)
• 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)
• Fast and robust quantum state tomography from few basis measurements [65.36803384844723]
  We present an online tomography algorithm designed to optimize all the aforementioned resources at the cost of a worse dependence on accuracy. The protocol is the first to give provably optimal performance in terms of rank and dimension for state copies, measurement settings and memory. Further improvements are possible by executing the algorithm on a quantum computer, giving a quantum speedup for quantum state tomography.
  arXiv  Detail & Related papers  (2020-09-17T11:28:41Z)

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.