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arXiv:2602.22312

Robustness-Runtime Tradeoff for Quantum State Transfer

Twesh Upadhyaya, Yifan Hong, T. C. Mooney, Alexey V. Gorshkov

quant-phphysics.atom-phSubmitted Feb 25, 2026• Announced Feb 27, 2026• 0 citations
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Abstract

Quantum state transfer is the primitive of transporting an unknown state on one site of a lattice to another. Using power-law interactions, recent state transfer protocols achieve speedup by utilizing the intermediate ancilla sites. However, these protocols require the ancillas to be in a perfectly initialized state, which, due to noise or imperfect control, may not be the case. In this work we introduce the $\textit{robustness}$ of a state transfer protocol, which quantifies the protocol's tolerance to error in the initial ancilla state. In the Heisenberg picture, state transfer grows operators supported on the final site such that they no longer commute with all operators on the starting site. We prove that this robustness tightly bounds the Schatten $p$-norms of these commutators between initial and final-site operators. This generalizes the known cases of $p=\infty$ and $p=2$, which govern completely state-dependent and state-independent state transfer respectively, demonstrating that intermediate values of $p$ govern partially state-dependent state transfer. In conjunction with existing power-law light cones, our result gives new minimum runtimes for partially state-dependent protocols which, in certain regimes, are parametrically better than existing bounds. We introduce new robust state transfer protocols, charting the landscape between complete state-dependence and state-independence.

Comments
16 pages, 5 figures

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Quantum state transfer is the primitive of transporting an unknown state on one site of a lattice to another. Using power-law interactions, recent state transfer protocols achieve speedup by utilizing the intermediate ancilla sites. However, these protocols require the ancillas to be in a perfectly initialized state, which, due to noise or imperfect control, may not be the case. In this work we introduce the robustness\textit{robustness}robustness of a state transfer protocol, which quantifies the protocol's tolerance to error in the initial ancilla state. In the Heisenberg picture, state transfer grows operators supported on the final site such that they no longer commute with all operators on the starting site. We prove that this robustness tightly bounds the Schatten ppp-norms of these commutators between initial and final-site operators. This generalizes the known cases of p=∞p=\inftyp=∞ and p=2p=2p=2, which govern completely state-dependent and state-independent state transfer respectively, demonstrating that intermediate values of ppp govern partially state-dependent state transfer. In conjunction with existing power-law light cones, our result gives new minimum runtimes for partially state-dependent protocols which, in certain regimes, are parametrically better than existing bounds. We introduce new robust state transfer protocols, charting the landscape between complete state-dependence and state-independence.
Quantum state transfer on qubit lattices is a crucial step in a panoply of quantum information processing tasks. Understanding its fundamental limits in the presence of practical imperfections remains a pressing open question. In particular, it is unclear how thermal noise in the intermediate ancilla sites impedes transfer. In this work, we derive tight lower bounds on the necessary growth of commutator norms to achieve approximate state transfer. Specializing to 1D power-law systems with thermal ancilla states, we demonstrate that state transfer runtimes depend sensitively on the scaling of temperature with system size, improving logarithmic bounds to algebraic ones. Our work extends previous results on exact state transfer to the qualitatively different and more practically relevant regime of approximate state transfer.
We derive a universal performance limit for coherent quantum control in the presence of modeled and unmodeled uncertainties. For any target unitary WWW that is implementable in the absence of error, we prove that the worst-case (and hence the average) gate fidelity obeys the lower bound $F \ge \Flb\bigl(\tf \Omeff\bigr)$, where $\tf$ is the gate duration and $\Omeff$ is a single frequency-like measure that aggregates \emph{all} bounded uncertainty sources, e.g., coherent control imperfections, unknown couplings, and residual environment interactions, without assuming an initially factorizable system-bath state or a completely positive map. The bound is obtained by combining an interaction-picture averaging method with a Bellman-Gronwall inequality and holds for any finite-norm Hamiltonian decomposition. Hence it applies equally to qubits, multi-level qudits, and ancilla-assisted operations. Because $\Flb$ depends only on the dimensionless product $\tf\Omeff$, it yields a device-independent metric that certifies whether a given hardware platform can, in principle, reach a specified fault-tolerance threshold, and also sets a quantitative target for robust-control synthesis and system identification.
Using a global optimization algorithm we obtain spin chains with site-dependent exchange coefficients which allow almost perfect quantum state transfer between the extremes of the chains without any further time-dependent external control. We consider chains with isotropic and anisotropic Heisenberg Hamiltonian with up to 100 spins. The method allow us to choose the arrival of the transferred state by changing the range available to the exchange coupling strengths. We consider short transferred times, in particular shorter than those achievable with known time-dependent control schemes. The chains obtained with the optimization method show some remarkable and interesting traits as, for instance, the scaling of the magnitude of the exchange couplings needed to achieve near perfect state transfer with the length of the chain and the arrival time. This scaling makes it possible to decide if the chain with site-dependent coefficients can be implemented in an actual system according to the range of interactions allowed in it. We compare the robustness of the transmission protocol against static disorder on the exchange coefficients using different figures of merit, which allow us to conclude that the isotropic Heisenberg chain is the best option when compared with anisotropic chains. This comparison is relevant since the method allow us to start with chains that all achieve near perfect quantum state transfer, regime that was not available previously in these chains without time-dependent external control.
Entanglement, measurement, and classical communication together enable teleportation of quantum states between distant parties, in principle, with perfect fidelity. To what extent do correlations and entanglement of a many-body wave function transfer under teleportation protocols? We address this question for the case of an imperfectly teleported quantum critical wave function, focusing on the ground state of a critical Ising chain. We demonstrate that imperfections, e.g., in the entangling gate adopted for a given protocol, effectively manifest as weak measurements acting on the otherwise pristinely teleported critical state. Armed with this perspective, we leverage and further develop the theory of measurement-altered quantum criticality to quantify the resilience of critical-state teleportation. We identify classes of teleportation protocols for which imperfection (i) preserves both the universal long-range entanglement and correlations of the original quantum critical state, (ii) weakly modifies these quantities away from their universal values, and (iii) obliterates long-range entanglement altogether while preserving power-law correlations, albeit with a new set of exponents. We also show that mixed states describing the average over a series of sequential imperfect teleportation events retain pristine power-law correlations due to a “built-in” decoding algorithm, though their entanglement structure measured by the negativity depends on errors similarly to individual protocol runs. These results may allow one to design teleportation protocols that optimize against errors—highlighting a potential practical application of measurement-altered criticality. Published by the American Physical Society 2024
Quantum state engineering plays a vital role in various applications in the field of quantum information. Different strategies, including drive-and-dissipation, adiabatic cooling, and measurement-based steering, have been proposed for state generation and manipulation, each with its upsides and downsides. Here, we address a class of measurement-based state engineering protocols where a sequence of generalized measurements is employed to steer a quantum system toward a desired (pure or mixed) target state. Previously studied measurement-based protocols relied on idealized procedures and avoided exploration of the effects of various errors stemming from imperfections of experimental realizations and external noise. We employ the quantum trajectory formalism to provide a detailed analysis of the robustness of these steering protocols against multiple classes of errors. We study a set of realistic errors that can be classified as dynamic or static, depending on whether they remain unchanged while running the protocol. More specifically, we investigate the impact of the erroneous choice of detector-system coupling, erroneous re-initialization of the detector state following a measurement step, fluctuating steering directions, and environmentally induced errors in the detector-system interaction. We show that the protocol remains fully robust against the erroneous choice of detector-system coupling parameters and presents reasonable robustness against other types of errors. Our analysis employs various quantifiers such as fidelity, trace distance, and linear entropy to characterize the protocol's robustness and provide analytical results for these quantifiers against various errors. We introduce averaging hierarchies of stochastic equations describing individual quantum trajectories associated with detector readouts. Subsequently, we demonstrate the commutation between the classical expectation value and the time-ordering operator of the exponential of a Hamiltonian with multiplicative white noise, as well as the commutation of the expectation value and the partial trace with respect to detector outcomes. Our ideas are implemented and demonstrated for a specific class of steering platforms, addressing a single qubit. Published by the American Physical Society 2024
Abstract Designing a good transfer channel for arbitrary quantum states in spin chains implies optimising a cost function, usually the averaged fidelity of transmission. The fidelity of transmission measures how much the transferred state resembles the state prepared at the beginning of the transfer protocol. When averaged over all the possible initial states, the figure of merit quantifies the quality of the protocol. There are proposals for optimising a given Hamiltonian to accomplish a particular task. The transfer of quantum states is one of them. In particular, we consider the design of Heisenberg spin chains using a genetic algorithm. This very efficient algorithm allows us to study different properties of Hamiltonians with good to excellent transfer ability. Using an evolutionary population method results in exchange coefficient strengths that change abruptly from site to site, which could hinder implementing an actual physical system with such exchange coefficients. By modifying the cost function, we obtain Hamiltonians with exchange coefficients varying smoothly along the chain length without compromising their transfer ability concerning the rough ones. Besides, both kinds of chain Hamiltonians show similar robustness against static disorder. By studying the statistical properties of the eigenvalues of Hamiltonians with varying transfer abilities, we determine the ensemble of random matrices to which the spectra belong.