Estimation of multivariate traces of states given partial classical information

Abstract

Bargmann invariants of order $n$, defined as multivariate traces of quantum states $\text{Tr}[{\rho }_1{\rho }_2\dots {\rho }_n]$, are useful in applications ranging from quantum metrology to certification of nonclassicality. A standard quantum circuit used to estimate Bargmann invariants is the cycle test. In this work, we propose generalizations of the cycle test applicable to a situation where $n$ systems are given and unknown, and classical information on $m$ systems ($m\le n)$ is available, allowing estimation of invariants of order $n+m$. Our main result is a generalization of results on 4th order invariants appearing in double weak values from Chiribella et al. [Phys. Rev. Research 6, 043043 (2024)]. The use of classical information on some of the states enables circuits on fewer qubits and with fewer gates, decreasing the experimental requirements for their estimation, and enabling multiple applications we briefly review.

10 pages, 8 figures. Comments are welcome!

References in corpus (73)

• Quantum Computing in the NISQ era and beyond
• Quantum fingerprinting
• Colloquium: Understanding Quantum Weak Values: Basics and Applications
• Quantum computations without definite causal structure
• Measuring the scrambling of quantum information
• Computational advantage from quantum-controlled ordering of gates
• Perfect discrimination of no-signalling channels via quantum superposition of causal structures
• The SWAP test and the Hong-Ou-Mandel effect are equivalent
• Group-Invariant Quantum Machine Learning
• The power of random measurements: measuring Tr(ρ^n) on single copies of ρ
• Entanglement Spectrum, Critical Exponents and Order Parameters in Quantum Spin Chains
• Quantum Metrology with Indefinite Causal Order
• The quasiprobability behind the out-of-time-ordered correlator
• Exponential Error Suppression for Near-Term Quantum Devices
• Quantum Refrigeration with Indefinite Causal Order
• Indefinite causal order enables perfect quantum communication with zero capacity channels
• Scalable measures of magic resource for quantum computers
• Partial indistinguishability theory for multi-photon experiments in multiport devices
• Sequential weak measurement
• Out-of-Time-Ordered-Correlator Quasiprobabilities Robustly Witness Scrambling
• A generalized Pancharatnam geometric phase formula for three level systems
• Emergent irreversibility and entanglement spectrum statistics
• Entanglement spectroscopy on a quantum computer
• Kirkwood-Dirac quasiprobability approach to the statistics of incompatible observables
• Measuring Polynomial Invariants of Multi-Party Quantum States
• Quantum circuits for measuring weak values, Kirkwood--Dirac quasiprobability distributions, and state spectra
• Measuring nonstabilizerness via multifractal flatness
• Quantum circuits with classical versus quantum control of causal order
• Work extraction from coherently activated maps via quantum switch
• Optimal Strategies of Quantum Metrology with a Strict Hierarchy
• Properties and Applications of the Kirkwood-Dirac Distribution
• Determination of weak values of quantum operators using only strong measurements
• Bargmann Invariants and Geometric Phases - a Generalised Connection
• Quasiprobabilities in quantum thermodynamics and many-body systems
• Witnessing genuine multi-photon indistinguishability
• Quantum Virtual Cooling
• Experimental Aspects of Indefinite Causal Order in Quantum Mechanics
• Unitary-invariant witnesses of quantum imaginarity
• Interfering distinguishable photons
• A simple proof that anomalous weak values require coherence
• Bargmann invariants and off-diagonal geometric phases for multi-level quantum systems -- a unitary group approach
• Quantifying n-photon indistinguishability with a cyclic integrated interferometer
• Strong unitary and overlap uncertainty relations: theory and experiment
• Beyond Shannon Limits: Quantum Communications through Quantum Paths
• Multivariate trace estimation in constant quantum depth
• Exchange Gate on the Qudit Space and Fock Space
• Experimental certification of contextuality, coherence and dimension in a programmable universal photonic processor
• Determining eigenvalues of a density matrix with minimal information in a single experimental setting
• Collective phases of identical particles interfering on linear multiports
• Experimental quantification of genuine four-photon indistinguishability
• Probing finite coarse-grained virtual Feynman histories with sequential weak values
• Quantum and classical bounds for two-state overlaps
• Structural Features of Sequential Weak Measurements
• Beyond the Berry Phase: Extrinsic Geometry of Quantum States
• Distinguishability and mixedness in quantum interference
• A universal scheme for robust self-testing in the prepare-and-measure scenario
• Coherence and contextuality in a Mach-Zehnder interferometer
• Measuring incompatibility and clustering quantum observables with a quantum switch
• Inequalities witnessing coherence, nonlocality, and contextuality
• Demonstration of universal time-reversal for quantum processes
• Kirkwood-Dirac representations beyond quantum states (and their relation to noncontextuality)
• Witnesses of coherence and dimension from multiphoton indistinguishability tests
• Experimentally demonstrating indefinite causal order algorithms to solve the generalized Deutsch's problem
• Dimension-independent weak value estimation via controlled SWAP operations
• Semi-device independent characterization of multiphoton indistinguishability
• Efficient distributed inner product estimation via Pauli sampling
• Activation of thermal states by coherently controlled thermalization processes
• In the shadow of the Hadamard test: Using the garbage state for good and further modifications
• Indefinite causal key distribution
• Efficient quantum algorithms for testing symmetries of open quantum systems
• Certifying nonstabilizerness in quantum processors
• Generalising multipartite concentratable entanglement for practical applications: mixed, qudit, and optical states
• Resource-efficient algorithm for estimating the trace of quantum state powers