Device-independent quantum memory certification in two-point measurement experiments

TL;DR

This work presents a device-independent method to certify quantum memories using two-point measurement TPM experiments that compare temporal correlations against classical causal models. By employing instrumental variables, Pearl-type inequalities, and ACDE-based cross-talk diagnostics, the approach isolates genuine quantum effects from experimental imperfections. The authors demonstrate a proof-of-principle TPM certification on a trapped-ion processor, achieving a DI memory fidelity bound F_{ m Memory} ≥ 0.92 with Γ_{ m Pr(AB|X)} = 0.642 ± 0.052, while showing how memory degradation leads to classicality over time. The results establish temporal correlations and causal modelling as practical benchmarks for quantum technologies and open avenues to certify other quantum primitives, with potential extensions to photonic and optomechanical memories and beyond.

Abstract

Quantum memories are key components of emerging quantum technologies. They are designed to store quantum states and retrieve them on demand without losing features such as superposition and entanglement. Verifying that a memory preserves these features is indispensable for applications such as quantum computation, cryptography and networks, yet no general and assumption-free method has been available. Here, we present a device-independent approach for certifying black-box quantum memories, requiring no trust in any part of the experimental setup. We do so by probing quantum systems at two points in time and then confronting the observed temporal correlations against classical causal models through violations of causal inequalities. We perform a proof-of-principle experiment in a trapped-ion quantum processor, where we certify 35 ms of a qubit memory. Our method establishes temporal correlations and causal modelling as practical and powerful tool for benchmarking key ingredients of quantum technologies, such as quantum gates or implementations of algorithms.

Figures (9)

• Figure 1: Quantum memory certification. A quantum memory is expected to reliably store quantum states, yet real devices are imperfect. Noise can induce decoherence and dissipation, effectively classicalising the memory so that only classical information is transmitted. If that happens, the process is reduced to one in which the system is measured and a state is prepared based on the measurement outcome. In other words, the device no longer functions as a genuine quantum memory and must be ruled out.
• Figure 2: Two-point measurement experiments.A. To test a quantum memory (QM), we consider the scenario where quantum systems are measured at two consecutive points in time. B. The observed statistics are then compared against a classical causal model in which outcomes are part of a time series. These models are represented by Bayesian networks, where the nodes correspond to the variables which are connected by arrows if causal influence is possible. Interventions make causal influences explicit and empirically accessible. Classical-quantum gaps in temporal correlations certify the quantum memory.
• Figure 3: Experiment and results. Panel A. shows the implemented sequence step by step. The ions are confined in a macroscopic linear Paul trap, and we consider two experiments ($\#1$ and $\#2$). Panels B. and C. display the experimental results, rescaled such that positive values indicate a violation of classicality. In B., we observe the classicalisation of a quantum memory with increasing waiting time, where the dark-blue line denotes the expected behaviour from dephasing and fidelity, with the blue shaded region indicating one-$\sigma$ shot-noise uncertainty. In C., quantumness is shown versus the partial $\alpha$-swap; violations for $\pi/2 < \alpha < \pi$ certify quantum causal relations, excluding classical causal models. The blue curve represents the ideal prediction.
• Figure S1: Causal influences in TPM experiments. Bayesian networks representing classical causal models for TPM experiments. The nodes correspond to variables and arrows indicate a potential causal influence. An intervention upon $A$ allows us to access causal influences like direct causal influence $A\to B$ as well as cross-talks.
• Figure S2: Quantum common-causes and direct-causes.A. A general TPM process synthesises both common-cause and direct-cause mechanisms, encapsulated either by a pair $(\varrho, U)$ or, from an agent perspective, by a process operator $W$. B. Common-cause (CC) processes are those in which all observed correlations originate from a shared quantum state $\rho_{\bf A^\prime B}$ (should not be confused with $\varrho$ in panel A.). C. Direct-cause (DC) processes, by contrast, are those in which all observed correlations arise from the direct influence $\bf A \to B$, mediated by a quantum channel $\mathcal{N}_{\bf A\to B}$.

Theorems & Definitions (8)

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