We introduce information erasure and quantum imprint as two properties that classify quantum instruments. Information erasure is the property that an appropriate postselection can render the distribution of earlier measurement outcomes independent of the initial quantum state while retaining all outcome branches. Quantum imprint is the complementary property that no admissible postselection can eliminate this state dependence. We show that this classification has a nontrivial structure and that the natural intuition that measurements providing more information about the initial quantum state should be less likely to exhibit information erasure does not hold in general. We further show that, under a sufficiently reliable postselection, information erasure enables first-order separation of state-preparation and measurement (SPAM) errors. Specifically, the first-order contribution of state-preparation error vanishes from the posterior distribution, whereas visible first-order contributions of measurement error remain. This result recasts SPAM error separation from the problem of simultaneously characterizing state preparation and measurement into the problem of realizing a reliable postselection.
We introduce information erasure and quantum imprint as two properties that classify quantum instruments. Information erasure is the property that an appropriate postselection can render the distribution of earlier measurement outcomes independent of the initial quantum state while retaining all outcome branches. Quantum imprint is the complementary property that no admissible postselection can eliminate this state dependence. We show that this classification has a nontrivial structure and that the natural intuition that measurements providing more information about the initial quantum state should be less likely to exhibit information erasure does not hold in general. We further show that, under a sufficiently reliable postselection, information erasure enables first-order separation of state-preparation and measurement (SPAM) errors. Specifically, the first-order contribution of state-preparation error vanishes from the posterior distribution, whereas visible first-order contributions of measurement error remain. This result recasts SPAM error separation from the problem of simultaneously characterizing state preparation and measurement into the problem of realizing a reliable postselection.
Correctly characterizing state preparation and measurement (SPAM) processes is a necessary step towards building reliable quantum processing units (QPUs). In this work, we discuss the subtleties behind separately measuring SPAM errors. We propose a protocol that can separately estimate SPAM errors, in the case where quantum gates are ideal. In the case where the quantum gates are imperfect, we derive bounds on the estimated SPAM error rates, based on gate error measures, which can be estimated independently of SPAM processes. Our method shows that the gauge ambiguity in characterizing SPAM operations can be resolved by assuming that there exists one qubit whose initial state is uncorrelated with other qubits in a QPU. We test the protocol on a publicly available five-qubit QPU and demonstrate its validity by comparing our results with simulations.
A projective measurement cannot decrease the von Neumann entropy if the outcome is ignored. However, under certain sound assumptions and using the quantum violation of Leggett-Garg inequalities, we have previously demonstrated that this property is not inherited by a classical simulation of such a measurement process. In the simulation, a measurement erases prior information by partially resetting the system, suggesting that the quantum-state update following a measurement cannot be entirely epistemic. The erasure of information has been proved by assuming that the maximally mixed quantum state corresponds to maximal ignorance of the classical state. A more intricate proof employed the weaker hypothesis that the entropy is finite at some stage of the simulation. In this paper, we focus on the quantum-foundational implications of this theorem. We first provide a simple proof by directly using the second hypothesis. Second, we identify information erasure as the mechanism breaking the time symmetry in ontological theories. This symmetry break has been previously proved by Pusey and Leifer. Third, we show that information erasure and, thus, symmetry break can be avoided by employing a branching a la many-worlds theory. The information flow and the time asymmetry are transferred to the measurement devices and the subsequent comparison of results, which inherently involve time-asymmetric processes. Thus, causality and the absence of information erasure suggest that measurements have multiple actual outcomes. Similarly, Deutsch and Hayden argued that Bell's theorem leads to the same conclusion if locality is given for granted. We conclude by showing that the problem of the clumsiness loophole in an experimental Leggett-Garg test of macrorealism is mitigated by the information-erasure theorem.
When quantum states are used to send classical information, the receiver performs a measurement on the signal states. The amount of information extracted is often not optimal due to the receiver's measurement scheme and experimental apparatus. For quantum nondemolition measurements, there is potentially some residual information in the postmeasurement state, while part of the information has been extracted and the rest is destroyed. Here, we propose a framework to characterize a quantum measurement by how much information it extracts and destroys, and how much information it leaves in the residual postmeasurement state. The concept is illustrated for several receivers discriminating coherent states.
Abstract In many platforms, errors from state-preparation and measurement (SPAM) dominate over single-qubit gate errors. To inform further hardware improvements and the development of more effective SPAM mitigation strategies, it is necessary to separately characterize the error contributions from SP and measurement (M). Here, we show how to construct a protocol that can efficiently and separately characterize the SP and M error parameters by using only high-fidelity single-qubit gates and repeated single-qubit measurements without reset. The measurements are assumed to be non-destructive and M errors are taken to be (spatially and temporally) uncorrelated and classical. Notably, the circuit depth of the protocol is independent of system size, and the target parameters may be characterized to a precision that is only limited by the number of experimental repetitions. We employ our protocol for the parallel characterization of SPAM errors on multiple qubits in the IBM quantum platform devices, where we find SP infidelities up to 6.57% and readout assignment errors up to 19.1%. Using numerical simulations, we also demonstrate how measurement-error mitigation that does not properly account for SP errors generally leads to a biased estimate of measured observable expectation values.
Describing the dynamics of open systems is essential for fault-tolerant quantum computation. Under Markovian assumptions, we can characterize dissipative dynamics via the Lindbladian. Using Bell sampling, we provide an efficient, ansatz-free Lindbladian learning algorithm with polynomial-time classical postprocessing. Motivated by the prevalence of state preparation and measurement (SPAM) noise on near-term devices, we also introduce the first efficient SPAM-robust protocol capable of learning the gauge-independent components of sparse Lindbladians to arbitrary precision in the presence of constant-order SPAM error. In doing so, we provide the first rigorous characterization of the gauge degrees of freedom in noisy Lindbladian learning, precisely identifying which components remain learnable under SPAM noise.
State preparation and measurement (SPAM) errors limit the performance of many gate-based quantum computing architecures, but are partly correctable after a calibration step that requires, for an exact implementation on a register of n qubits, 2n additional characterization experiments, as well as classical post-processing. Here we introduce an approximate but efficient method for SPAM error characterization requiring the {\it classical} processing of 2n×2n real matrices, but only O(n2) measurements. The technique assumes that multi-qubit measurement errors are dominated by pair correlations, which are estimated with n(n−1)k/2 two-qubit experiments, where k is a parameter related to the accuracy. We demonstrate the technique on the IBM and Rigetti online superconducting quantum computers, allowing comparison of their SPAM errors in both magnitude and degree of correlation. We also study the correlations as a function of the register's geometric layout. We find that the pair-correlation model is fairly accurate on linear arrays of superconducting qubits. However qubits arranged in more closely spaced two-dimensional geometries exhibit significant higher-order (such as 3-qubit) SPAM error correlations.