Related papers: Direct Measurement of Density Matrices via Dense Dual Bases

Direct Measurement of Density Matrices via Dense Dual Bases

URL: http://arxiv.org/abs/2409.03435v2
Date: Wed, 27 Nov 2024 03:26:39 GMT
Title: Direct Measurement of Density Matrices via Dense Dual Bases
Authors: Yu Wang, Hanru Jiang, Yongxiang Liu, Keren Li,
Abstract summary: We introduce Dense Dual Bases (DDB), a novel set of (2d) observables designed to enable the complete characterization of any (d)-dimensional quantum state. First, they enable direct measurement of density matrix elements without auxiliary systems, allowing any element to be extracted using only three selected observables. Second, QST for unknown rank-(r) density matrices--excluding only a negligible subset--can be achieved with (O(rlog d)) observables, significantly improving measurement efficiency.
Score: 8.502021723268465
License:
Abstract: Efficient understanding of a quantum system fundamentally relies on the selection of observables. Pauli observables and mutually unbiased bases (MUBs) are widely used in practice and are often regarded as theoretically optimal for quantum state tomography (QST). However, Pauli observables require a large number of measurements for full-state tomography and do not permit direct measurement of density matrix elements with a constant number of observables. For MUBs, the existence of complete sets of $d+1$ bases in all dimensions remains unresolved, highlighting the need for alternative observables. In this work, we introduce Dense Dual Bases (DDB), a novel set of $2d$ observables specifically designed to enable the complete characterization of any $d$-dimensional quantum state. These observables offer two key advantages. First, they enable direct measurement of density matrix elements without auxiliary systems, allowing any element to be extracted using only three selected observables. Second, QST for unknown rank-$r$ density matrices--excluding only a negligible subset--can be achieved with $O(r \log d)$ observables, significantly improving measurement efficiency. As for circuit implementation, each observable is iteratively generated and can be efficiently decomposed into $O(n^4)$ elementary gates for an $n$-qubit system. These advances establish DDB as a practical and scalable alternative to traditional methods, offering promising opportunities to advance the efficiency and scalability of quantum system characterization.

Related papers

Precision bounds for multiple currents in open quantum systems [37.69303106863453]
We derivation quantum TURs and KURs for multiple observables in open quantum systems undergoing Markovian dynamics. Our bounds are tighter than previously derived quantum TURs and KURs for single observables. We also find an intriguing quantum signature of correlations captured by the off-diagonal element of the Fisher information matrix.
arXiv Detail & Related papers (2024-11-13T23:38:24Z)
Optimal quantum state tomography with local informationally complete measurements [25.33379738135298]
We study whether a general MPS/MPDO state can be recovered with bounded errors using only a number of state copies in the number of qubits. We provide a positive answer for a variety of common many-body quantum states, including typical short-range entangled states, random MPS/MPDO states, and thermal states of one-dimensional Hamiltonians.
arXiv Detail & Related papers (2024-08-13T17:58:02Z)
Applicability of Measurement-based Quantum Computation towards Physically-driven Variational Quantum Eigensolver [17.975555487972166]
Variational quantum algorithms are considered one of the most promising methods for obtaining near-term quantum advantages. The roadblock to developing quantum algorithms with the measurement-based quantum computation scheme is resource cost. We propose an efficient measurement-based quantum algorithm for quantum many-body system simulation tasks, called measurement-based Hamiltonian variational ansatz (MBHVA)
arXiv Detail & Related papers (2023-07-19T08:07:53Z)
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)
Efficient learning of ground & thermal states within phases of matter [1.1470070927586014]
We consider two related tasks: (a) estimating a parameterisation of a given Gibbs state and expectation values of Lipschitz observables on this state; and (b) learning the expectation values of local observables within a thermal or quantum phase of matter.
arXiv Detail & Related papers (2023-01-30T14:39:51Z)
Directly Characterizing the Coherence of Quantum Detectors by Sequential Measurement [17.71404984480176]
Many specific properties can be determined by a part of matrix entries of the measurement operators. We propose a general framework to directly obtain individual matrix entries of the measurement operators. We experimentally implement this scheme to monitor the coherent evolution of a general quantum measurement.
arXiv Detail & Related papers (2021-11-19T17:09:48Z)
Reachable sets for two-level open quantum systems driven by coherent and incoherent controls [77.34726150561087]
We study controllability in the set of all density matrices for a two-level open quantum system driven by coherent and incoherent controls. For two coherent controls, the system is shown to be completely controllable in the set of all density matrices.
arXiv Detail & Related papers (2021-09-09T16:14:23Z)
Determination of All Unknown Pure Quantum States with Two Observables [3.19428095493284]
Efficiently extracting information from pure quantum states using minimal observables on the main system is a longstanding and fundamental issue in quantum information theory. We show that two orthogonal bases are capable of effectively filtering up to $2d-1$ finite candidates by disregarding a measure-zero set. We also show that almost all pure qudits can be uniquely determined by adaptively incorporating a POVM in the middle, followed by measuring the complementary observable.
arXiv Detail & Related papers (2021-08-12T13:46:14Z)
Hamiltonian-Driven Shadow Tomography of Quantum States [0.0]
We study the scenario in which the unitary channel can be shallow and is generated by a quantum chaotic Hamiltonian via time evolution. We find that it can be more efficient than the unitary-2-design-based shadow tomography in a sequence of intermediate time windows. In particular, the efficiency of predicting diagonal observables is improved by a factor of $D$ without sacrificing the efficiency of predicting off-diagonal observables.
arXiv Detail & Related papers (2021-02-19T19:30:18Z)
Direct measurement of density-matrix elements using a phase-shifting technique Tianfeng [0.0]
A direct measurement protocol allows reconstructing specific elements of the density matrix of a quantum state without using quantum state tomography. Here, we present a direct measurement scheme based on phase-shifting operations which do not need ancillary pointers. Our method can be used in quantum information applications where only partial information about the quantum state needs to be extracted.
arXiv Detail & Related papers (2021-01-14T11:37:06Z)
Cartan sub-algebra approach to efficient measurements of quantum observables [0.0]
We provide a unified Lie algebra for developing efficient measurement schemes for quantum observables. The framework is based on two elements: 1) embedding the observable operator in a Lie algebra and 2) transforming Lie algebra elements into those of a Cartan sub-algebra.
arXiv Detail & Related papers (2020-07-02T16:32:48Z)

This list is automatically generated from the titles and abstracts of the papers in this site.