Storage-Lifetime Limits of Encrypted Quantum Cloning: Bare Idle vs. XY4 Dynamical Decoupling on a 156-Qubit IBM Heron Processor

EC-STORAGE-001 — Storage-Lifetime Limits of Encrypted Quantum Cloning: Bare Idle vs. XY4 Dynamical Decoupling on a 156-Qubit IBM Heron Processor Date of experiment: 2026-07-10 (UTC) · Backend: ibm_kingston (IBM Heron r3, 156 qubits) · Job ID: d987hal2su3c739iu6qg Record version: v1.0 · DOI: 10.5281/zenodo.21299091 Plain-language summary A famous rule of quantum physics — the no-cloning theorem — says you cannot photocopy an unknown quantum state. In January 2026, Yamaguchi and Kempf published a lawful workaround, best pictured as gift vouchers rather than photocopies: from one quantum state you can create several sealed, encrypted copies, where any one of them — but only one, ever — can be redeemed for the original using a shared one-time key. Redeeming a voucher voids all the others. No law is broken, because at no moment do two readable originals exist; each sealed copy, on its own, is provably blank. Copies of what, exactly? A quantum state that nobody knows — that is the whole point. If you knew the state you could simply write it down and remake it; no cloning needed. The voucher scheme works even for a state that was never written down anywhere. To test that honestly, this experiment (like the original one) used the strictest possible payload: not a known message, but entanglement. We took two qubits that were quantum-linked, kept one as a reference, and turned the other into encrypted vouchers. The test of success is then unfakeable: after redeeming a voucher, is the qubit that comes out still quantum-linked to the reference we kept? That link cannot be counterfeited by any classical means, so if it survives, the voucher genuinely carried the quantum original. Our fidelity numbers measure exactly the strength of that surviving link, and the "0.5 witness" threshold in our results is the line below which no genuine quantum link can be certified any more. Their follow-up experiment on IBM hardware showed these vouchers can be created and redeemed reliably even on today's noisy machines, and proposed quantum cloud storage as a headline application: park encrypted copies of quantum data now, redeem one later. That proposal raises the question the original experiments did not measure: vouchers sitting in a drawer — how fast do they expire? Quantum states spoil. The information in the sealed copies lives in an invisible web of correlations linking the copies to their key qubits, and hardware noise steadily tears that web. Its shelf life under real noise is the number that matters for storage — and it was unknown. This experiment measured it, on ibm_kingston — the same machine used in the original demonstration. We created the vouchers, let them sit for a controlled waiting time, then redeemed one and checked whether the quantum link to our reference had survived. We did this two ways: leaving the qubits alone during storage ("bare"), and protecting them with a standard pulse technique called XY4 dynamical decoupling — a technique the original authors tested on their (storage-free) circuits and found unhelpful. Findings, in plain terms: Bare shelf life is about 9 microseconds. After ~9 µs of unprotected storage on this hardware, the redeemed copy no longer passes the entanglement test — the voucher has effectively expired. By 45–60 µs the stored quantum information is essentially gone. Notably, the web of correlations decays faster than any of the individual qubits involved, because tearing any strand damages the whole — a real trade-off of spreading information out for protection. Standard protective pulses double it. With XY4 applied during storage, the window extends to ~19 µs, and the fitted decay time doubles (8.8 → 17.3 µs). Dynamical decoupling does help encrypted clones — in the storage regime, which is precisely the regime the original study did not probe. A co-located "weather station" tracked the noise. Three nearby qubits ran a small stabilizer-frame sensor (a QuantaCore runtime primitive) inside every circuit, reporting two things at once: how fast quantum coherence was decaying that session, and a slow, steady drift in the qubits' phase reference (~2° per microsecond). Storage decisions on shared quantum hardware will need exactly this kind of live telemetry. The practical reading: on present-day superconducting hardware, "quantum cloud storage" of encrypted clones is a microseconds-scale proposition, not a park-it-overnight one — but the window is measurable, extensible with known techniques, and monitorable in real time. All three of those properties are prerequisites for engineering around it. And to be clear about what this does not mean: the no-cloning theorem was never in danger — not from the original work, and not from ours. The theorem forbids two readable copies from ever coexisting, and this protocol respects that at every instant. What was discovered in 2026 is how much copying-like structure quantum mechanics lawfully permits; what we measured is how long that structure survives in the real world. Background and motivation Kempf and Yamaguchi proved that encrypted clones of an unknown qubit can be created unitarily, with single-use decryption (PRL, Jan 2026; arXiv:2501.02757). The experimental companion (arXiv:2602.10695) demonstrated the protocol on IBM Heron processors at up to 154 qubits, established that it composes in parallel, series, and interleaved configurations, and proposed redundant quantum storage as an application. Incidental observations in that paper — a ~3 µs measurement-induced idle visibly degrading CHSH values, and a fidelity drop attributed to increased time-to-decryption — indicated strong idle sensitivity, but no systematic storage-delay scan was performed, and their error-mitigation comparison (dynamical decoupling, Pauli twirling) was carried out on gate-depth-dominated circuits, where they reported no significant improvement. This experiment fills that specific gap: a pre-registered storage-delay scan of the n = 2 encrypted-cloning protocol, bare versus XY4-protected, on the same backend model and physical device as the original main experiments. Experiment design Protocol: n = 2 encrypted cloning exactly as published (arXiv:2602.10695, Eqs. 1–4): payload qubit A entangled with reference Ã; signal–noise Bell pairs (S₁,N₁), (S₂,N₂); encryption unitary applied to (A, S₁, S₂); storage delay τ; decryption of clone S₁ using key qubits {N₁, N₂}; entanglement fidelity F_e(Ã, S₁) estimated with the parity-oscillation measurement (POM) scheme of the original paper (3 measurement settings, local rotations only). Storage window: τ ∈ {0, 5, 10, 20, 30, 45, 60} µs, inserted between encoding and decryption on all six protocol qubits. Arms: bare (plain delay) and dd (XY4 sequence, symmetric placement, applied simultaneously to the six protocol qubits). Runtime-level dynamical decoupling and twirling were explicitly disabled so the two arms are defined solely by the circuits. Batch discipline: all 42 circuits (7 delays × 2 arms × 3 POM settings) interleaved in a single job (2048 shots per circuit) to hold session conditions fixed across the comparison. Estimated QPU execution time: ≈ 23 s. Qubit selection: protocol qubits were chosen by a noise-aware preflight pass over the same-day calibration snapshot (T₂-weighted for a storage-dominated experiment, with two-qubit-gate and readout error terms), rather than automated transpiler placement. Selected protocol qubits: Ã=104, A=105, S₁=106, S₂=117, N₁=107, N₂=125 (T₂ range 178–368 µs against a chip median of 128 µs that day). The full calibration snapshot is included in this deposit. Sensor: a three-qubit stabilizer-frame witness (QuantaCore C2 midpoint-refresh primitive) executed inside every circuit on a co-located triplet placed ≥ 2 couplings from the protocol set. It reports a rotation-invariant plane fidelity F = √(⟨ZYZ⟩² + ⟨ZXZ⟩²) and the in-plane frame angle. Preparation and refresh internals are proprietary and not enabling-disclosed here; the sensor's outputs are fully included in the data files. Validation gates (all passed before submission): (1) gate-level encode/decode circuits verified numerically against the published unitaries, including exact payload recovery (F = 1.000000) and per-clone maximal mixedness; (2) all 42 circuits, with delays, DD pulses, and mid-circuit sensor resets included, reproduced ideal F_e = 1 in noiseless simulation; (3) exact batch transpiled and costed before submission. One job, no reruns. Results arm τ (µs) F_e ±σ witness (>0.5) sensor F_plane bare 0 0.847 0.009 ✓ 0.837 bare 5 0.633 0.010 ✓ 0.796 bare 10 0.466 0.010 ✗ 0.754 bare 20 0.275 0.010 ✗ 0.670 bare 30 0.212 0.010 ✗ 0.571 bare 45 0.192 0.010 ✗ 0.431 bare 60 0.235 0.010 ✗ 0.326 dd 0 0.854 0.009 ✓ 0.851 dd 5 0.700 0.010 ✓ 0.782 dd 10 0.638 0.010 ✓ 0.794 dd 20 0.478 0.011 ✗ 0.698 dd 30 0.347 0.011 ✗ 0.580 dd 45 0.230 0.011 ✗ 0.478 dd 60 0.196 0.010 ✗ 0.304 Decay constants. Fitting F_e(τ) = 0.25 + a·e^(−τ/T) (0.25 = fully-mixed floor): bare: T = 8.81 ± 0.30 µs (a = 0.613 ± 0.009) XY4: T = 17.27 ± 0.54 µs (a = 0.617 ± 0.008) extension factor: 1.96 ± 0.09 Witness crossings (interpolated): F_e falls below the 0.5 entanglement witness at ≈ 9.0 µs (bare) and ≈ 18.6 µs (XY4). Consistency checks. The two τ = 0 arms are identical circuits and agree (0.847 vs 0.854, Δ = 0.007 ± 0.013). τ = 0 fidelities sit at the upper end of the original paper's cross-session range (F_e = 0.833 ± 0.027) despite a below-median calibration day, consistent with the preflight qubit selection doing useful work; a controlled comparison against automated placement was not performed and is not claimed. Decomposition (secondary finding). The POM estimator separates a population term P from a phase term χ. In the bare arm both collapse together toward the mixed-state values. In the XY4 arm, P is strongly preserved (0.71 at 30 µs, 0.58 at 60 µs) while χ crosses zero near 30 µs and becomes significantly negative (−0.18 ± 0.02 at 45–60 µs). A negative χ indicates coherent phase evolution rather than pure decoherence. This is consistent with residual two-qubit ZZ interactions, which simultaneous same-phase pulses on coupled qubits do not refocus — a known limitation of simultaneous XY4 — though ZZ was not independently measured here and this interpretation is a hypothesis. Two implications, stated at the evidence ceiling: (i) the DD-arm F_e at late τ likely understates the recoverable correlation, since coherent phase is in principle trackable or correctable; (ii) staggered or crosstalk-aware decoupling sequences are the natural next arm and may extend the storage window further. Sensor telemetry. The co-located witness reported a smooth plane-fidelity decay (0.84 → 0.33 over 60 µs, strict actionability threshold F > 0.6 holding through ≈ 20–25 µs) and, independently, an approximately linear frame precession of ≈ 2.0°/µs — a coherent phase drift of the same qualitative character as the χ rotation seen in the protected protocol qubits. Within this single session these are parallel observations, not a demonstrated predictive relationship; establishing the sensor as a predictor of protocol fidelity requires multi-session data and is pre-registered as future work. Figure 1. (a) Decrypted-clone entanglement fidelity vs. storage delay, bare vs. XY4, with exponential fits, entanglement witness (0.5), and fully-mixed floor (0.25). (b) Estimator decomposition: population term P and phase term χ per arm. (c) Co-located sensor: plane fidelity decay and frame-angle precession (~2.0°/µs). Pre-registration audit Stated before data existed: "bare-arm F_e crosses the 0.5 witness in the 10–30 µs range; whether XY4 extends the crossing is the open question." Outcome: the crossing was 9.0 µs — just outside the registered band (miss, recorded here). The direction of the miss is informative: the joint state decays faster than a per-qubit 1/T₂ sum suggests, consistent with the payload residing in weight-4 stabilizer correlations whose coherences decay at the sum of constituent rates. The open question resolved affirmatively: XY4 extends the crossing by ≈ 2×. Evidence ceiling (named) Single session, single calibration epoch, single layout, one device, 2048 shots per setting. Decay constants carry fit uncertainties but no session-to-session error bars. The single-exponential model captures the gross decay scale but leaves structured late-τ residuals (up to ~6–7σ), reflecting the coherent effects described above; T values should be read as characteristic scales, not precision constants. The ZZ-crosstalk interpretation of the negative χ is a hypothesis. The sensor-as-predictor claim is explicitly not made. No error mitigation beyond the circuit-defined DD arm was applied; no readout-error correction was applied to any reported number. Data files in this deposit ec_storage_001_results_20260710T061759Z.csv / .json — all per-point results (F_e, sigma, P, chi, sensor observables) job-d987hal2su3c739iu6qg-result.json — raw result payload as returned by IBM Quantum Runtime for the single job ec_storage_001_job_d987hal2su3c739iu6qg.json — submission metadata: circuit manifest, layout, settings, circuit hashes, cost estimate kingston_cal_2026-07-09T231952Z.json — same-day calibration snapshot used for qubit selection (every selection number traces here) ec_storage_layout_report.json — ranked preflight layout report produced from that snapshot ec_storage_layout.py — the noise-aware layout-selection tool (includes the embedded algebraic self-test of the protocol circuits against the published unitaries); the proprietary sensor preparation is not contained in any deposited file ec_storage_run_public.py — public experiment driver (validate / estimate / submit / analyze) reproducing the storage-delay measurement end to end: identical circuit count, ordering, delays, arms, POM settings, estimator, and submission gates as the deposited run. The co-located proprietary witness is not included; the deposited results were produced with the full driver, whose circuits additionally carried the three witness qubits (placed ≥ 2 couplings from the protocol set). Protocol-qubit quantities (F_e, P, χ) are expected to reproduce with this script up to hardware session variation. ec_storage_001_figure1.png — Figure 1 Circuit ordering in the raw result file is deterministic and arm-major: arms in order (bare, dd), storage delays ascending (0, 5, 10, 20, 30, 45, 60 us), POM settings in order (P, M1, M2) — 42 entries total; the manifest in the submission-metadata file states the same mapping explicitly. Every quantitative claim in this record traces to these files. References K. Yamaguchi and A. Kempf, Encrypted Qubits Can Be Cloned, Phys. Rev. Lett. (2026); arXiv:2501.02757. K. Yamaguchi, L. Rullkötter, I. Shehzad, S. J. Wagner, C. Tutschku, and A. Kempf, Experimental demonstration that qubits can be cloned at will, if encrypted with a single-use decryption key, arXiv:2602.10695 (2026). (This deposit's experiment is an independent follow-up and is not affiliated with the authors.) L. Viola and S. Lloyd, Dynamical suppression of decoherence in two-state quantum systems, Phys. Rev. A 58, 2733 (1998). N. Ezzell et al., Dynamical decoupling for superconducting qubits: a performance survey, Phys. Rev. Applied 20, 064027 (2023). Qiskit contributors, Qiskit: An open-source framework for quantum computing (qiskit.org). Experiments executed via Qiskit and Qiskit IBM Runtime. Acknowledgments and disclosure Executed on IBM Quantum services (ibm_kingston). The views expressed are the author's and do not reflect the official policy or position of IBM or the IBM Quantum team. The stabilizer-frame sensor is a component of the QuantaCore™ runtime platform (Quantum-Clarity LLC); patent(s) pending. QUANTACORE™ is a trademark of Quantum-Clarity LLC. License: CC BY 4.0