Certification of entangled quantum states and quantum measurements in Hilbert spaces of arbitrary dimension

• URL: http://arxiv.org/abs/2302.01325v1
• Date: Thu, 2 Feb 2023 18:54:51 GMT
• Title: Certification of entangled quantum states and quantum measurements in Hilbert spaces of arbitrary dimension
• Authors: Shubhayan Sarkar
• Abstract summary: Device-independent (DI) certification of composite quantum systems has attracted considerable attention lately. In this thesis, we construct schemes to device-independently certify quantum states and quantum measurements in Hilbert spaces of arbitrary dimension.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The emergence of quantum theory at the beginning of 20$-th$ century has changed our view of the microscopic world and has led to applications such as quantum teleportation, quantum random number generation and quantum computation to name a few, that could never have been realised using classical systems. One such application that has attracted considerable attention lately is device-independent (DI) certification of composite quantum systems. The basic idea behind it is to treat a given device as a black box that given some input generates an output, and then to verify whether it works as expected by only studying the statistics generated by this device. The novelty of these certification schemes lies in the fact that one can almost completely characterise the device (up to certain equivalences) under minimal physically well-motivated assumptions such as that the device is described using quantum theory. The resource required in most of these certification schemes is quantum non-locality. In this thesis, we construct schemes to device-independently certify quantum states and quantum measurements in Hilbert spaces of arbitrary dimension along with the optimal amount randomness that one can extract from any quantum system of arbitrary dimension.

Related papers

• The curse of random quantum data [62.24825255497622]
  We quantify the performances of quantum machine learning in the landscape of quantum data. We find that the training efficiency and generalization capabilities in quantum machine learning will be exponentially suppressed with the increase in qubits. Our findings apply to both the quantum kernel method and the large-width limit of quantum neural networks.
  arXiv  Detail & Related papers  (2024-08-19T12:18:07Z)
• Quantum Equilibrium Propagation for efficient training of quantum systems based on Onsager reciprocity [0.0]
  Equilibrium propagation (EP) is a procedure that has been introduced and applied to classical energy-based models which relax to an equilibrium. Here, we show a direct connection between EP and Onsager reciprocity and exploit this to derive a quantum version of EP. This can be used to optimize loss functions that depend on the expectation values of observables of an arbitrary quantum system.
  arXiv  Detail & Related papers  (2024-06-10T17:22:09Z)
• Quantum data learning for quantum simulations in high-energy physics [55.41644538483948]
  We explore the applicability of quantum-data learning to practical problems in high-energy physics. We make use of ansatz based on quantum convolutional neural networks and numerically show that it is capable of recognizing quantum phases of ground states. The observation of non-trivial learning properties demonstrated in these benchmarks will motivate further exploration of the quantum-data learning architecture in high-energy physics.
  arXiv  Detail & Related papers  (2023-06-29T18:00:01Z)
• Simple Tests of Quantumness Also Certify Qubits [69.96668065491183]
  A test of quantumness is a protocol that allows a classical verifier to certify (only) that a prover is not classical. We show that tests of quantumness that follow a certain template, which captures recent proposals such as (Kalai et al., 2022) can in fact do much more. Namely, the same protocols can be used for certifying a qubit, a building-block that stands at the heart of applications such as certifiable randomness and classical delegation of quantum computation.
  arXiv  Detail & Related papers  (2023-03-02T14:18:17Z)
• A prototype of quantum von Neumann architecture [0.0]
  We propose a model of universal quantum computer system, the quantum version of the von Neumann architecture. It uses ebits as elements of the quantum memory unit, and qubits as elements of the quantum control unit and processing unit. Our primary study demonstrates the manifold power of quantum information and paves the way for the creation of quantum computer systems.
  arXiv  Detail & Related papers  (2021-12-17T06:33:31Z)
• Efficient criteria of quantumness for a large system of qubits [58.720142291102135]
  We discuss the dimensionless combinations of basic parameters of large, partially quantum coherent systems. Based on analytical and numerical calculations, we suggest one such number for a system of qubits undergoing adiabatic evolution.
  arXiv  Detail & Related papers  (2021-08-30T23:50:05Z)
• Test of Quantumness with Small-Depth Quantum Circuits [1.90365714903665]
  Recently, we have shown how to construct a test of quantumness based on the learning with errors (LWE) assumption. This test has lead to several cryptographic applications. In this paper, we show that this test of quantumness, and essentially all the above applications, can actually be implemented by a very weak class of quantum circuits.
  arXiv  Detail & Related papers  (2021-05-12T08:16:20Z)
• Towards understanding the power of quantum kernels in the NISQ era [79.8341515283403]
  We show that the advantage of quantum kernels is vanished for large size datasets, few number of measurements, and large system noise. Our work provides theoretical guidance of exploring advanced quantum kernels to attain quantum advantages on NISQ devices.
  arXiv  Detail & Related papers  (2021-03-31T02:41:36Z)
• Imaginary Time Propagation on a Quantum Chip [50.591267188664666]
  Evolution in imaginary time is a prominent technique for finding the ground state of quantum many-body systems. We propose an algorithm to implement imaginary time propagation on a quantum computer.
  arXiv  Detail & Related papers  (2021-02-24T12:48:00Z)
• Maximal entropy approach for quantum state tomography [3.6344381605841187]
  Current quantum computing devices are noisy intermediate-scale quantum $($NISQ$)$ devices. Quantum tomography tries to reconstruct a quantum system's density matrix by a complete set of observables. We propose an alternative approach to quantum tomography, based on the maximal information entropy, that can predict the values of unknown observables.
  arXiv  Detail & Related papers  (2020-09-02T04:39:45Z)
• Quantum supremacy in driven quantum many-body systems [0.0]
  We show that quantum supremacy can be obtained in generic periodically-driven quantum many-body systems. Our proposal opens the way for a large class of quantum platforms to demonstrate and benchmark quantum supremacy.
  arXiv  Detail & Related papers  (2020-02-27T07:20:15Z)

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.