Estimation of correlations and non-separability in quantum channels via unitarity benchmarking

Abstract

The ability to transfer coherent quantum information between systems is a fundamental component of quantum technologies and leads to coherent correlations within the global quantum process. However correlation structures in quantum channels are less studied than those in quantum states. Motivated by recent techniques in randomized benchmarking, we develop a range of results for efficient estimation of correlations within a bipartite quantum channel. We introduce sub-unitarity measures that are invariant under local changes of basis, generalize the unitarity of a channel, and allow for the analysis of coherent information exchange within channels. Using these, we show that unitarity is monogamous, and provide a novel information-disturbance relation. We then define a notion of correlated unitarity that quantifies the correlations within a given channel. Crucially, we show that this measure is strictly bounded on the set of separable channels and therefore provides a witness of non-separability. Finally, we describe how such measures for effective noise channels can be efficiently estimated within different randomized benchmarking protocols. We find that the correlated unitarity can be estimated in a SPAM-robust manner for any separable quantum channel, and show that a benchmarking/tomography protocol with mid-circuit resets can reliably witness non-separability for sufficiently small reset errors. The tools we develop provide information beyond that obtained via simultaneous randomized benchmarking and so could find application in the analysis of cross-talk and coherent errors in quantum devices.

38 pages, 5 figures

References in corpus (17)

• QuTiP 2: A Python framework for the dynamics of open quantum systems
• t$|$ket$⟩$ : A Retargetable Compiler for NISQ Devices
• Characterization of addressability by simultaneous randomized benchmarking
• A generalized no-broadcasting theorem
• Quantum simulation of time-dependent Hamiltonians and the convenient illusion of Hilbert space
• Reducing unitary and spectator errors in cross resonance with optimized rotary echoes
• Theory of quantum system certification: a tutorial
• Randomized Benchmarking of Multi-Qubit Gates
• Random Quantum Operations
• Dynamical Entanglement
• Generating random quantum channels
• Statistical analysis of randomized benchmarking
• Quantum circuits for exact unitary $t$-designs and applications to higher-order randomized benchmarking
• Nonlocality free wirings and the distinguishability between Bell boxes
• Quantum Channel Marginal Problem
• Randomized benchmarking in the presence of time-correlated dephasing noise
• Randomized Benchmarking with Stabilizer Verification and Gate Synthesis

Cited by in corpus (3)

• Exploring Quantum Average-Case Distances: proofs, properties, and examples
• Non-unitarity maximizing unraveling of open quantum dynamics
• A simple formulation of no-cloning and no-hiding that admits efficient and robust verification