Observation of the full hierarchy of temporal quantum correlations in a superconducting qubit ✦
Temporal quantum correlations form a logical hierarchy: non-macrorealism, temporal steering, and temporal nonseparability. By manipulating the dynamics of a superconducting qubit, the full hierarchy of these correlations was experimentally recorded for the first time. The complex behavior, including sudden death and revival of temporal steering, is shown to uniquely characterize qubit quality in realistic quantum circuits. These results can be used to uncover the causal fabric of quantum networks, analyze non-Markovianity in open systems, and pinpoint security limits for quantum key distribution. As a demonstration, the non-Markovianity of a single superconducting qubit on a quantum processor was exhibited.
Context
Temporal quantum correlations, first formalized as time-domain analogues of Bell's inequalities (Leggett–Garg inequalities), provide a unique tool for testing quantum nature at macroscopic scales. Just as not all entanglement violates Bell's inequality, temporal correlations form a logical hierarchy in which nonmacrorealism, temporal steerability, and temporal nonseparability are strictly ordered. Understanding this hierarchy is critically important for advancing quantum information and devices where decoherence is the main obstacle, as well as for identifying non-Markovian processes that can return information from the environment.
Methods
The experiment was conducted on a publicly accessible IBM quantum computer (ibmq_ourense), where a superconducting qubit served as the test system, and its dynamics were controlled using single- and two-qubit gates. For each type of temporal correlation, specific protocols of quantum state tomography and measurements in various bases (σx, σy, σz, and their linear combinations) were implemented. Quantum channels—amplitude damping, dephasing, and depolarization—were synthesized by decomposing them into two extremal channels with controlled probability, enabling high-fidelity simulation of different noise types (over 95%). To eliminate unwanted signaling across time, the qubit's initial state was always prepared as maximally mixed (ρ₀ = I/2).
Results
In the depolarization channel, all three temporal correlations exhibited 'sudden death'—an abrupt drop to zero at different values of the dimensionless decoherence parameter γt. For instance, nonmacrorealism (quantity Bmax) vanished at γt ≈ 0.3, while temporal steerability (TSR) and nonseparability (f-function) persisted longer, disappearing later and at different thresholds. This confirmed the strict hierarchy: any system exhibiting nonmacrorealism necessarily possesses temporal steerability and nonseparability, but not vice versa. During free qubit evolution (outside controlled channels), a revival of temporal steerability was observed—a hallmark of non-Markovian decoherence, reminiscent of information backflow from the environment and well described by an interaction model with an idle qubit.
Implications
The results provide a new perspective on how quantum systems lose their 'temporal' properties under noise. The discovered hierarchy can serve as a benchmark test for evaluating qubit quality and decoherence depth, surpassing standard T1 and T2 metrics. Moreover, it opens the way to detecting and quantifying non-Markovianity—environment memory effects that can be both detrimental and beneficial in quantum communication tasks.
Future development
In the near term, similar measurements are planned to be extended to multi-qubit systems, enabling exploration of temporal hierarchies in quantum networks and causal structures akin to recent works on quantum advantage in causal inference. Adaptation of the proposed measures for continuous monitoring of quantum processors and refining security bounds for quantum key distribution is also anticipated.
Impact
The work will influence several adjacent fields: benchmarking quantum computers (especially in noisy intermediate-scale quantum, NISQ regimes), development of quantum cryptography protocols with trusted and untrusted devices, as well as fundamental research on open quantum systems and the physics of non-Markovian processes.
Next steps
Next steps include implementing the hierarchy on various physical platforms, including superconducting and photonic qubits, and studying the impact of non-Markovian noise on other measures of quantum correlations, such as discord or quantum memory.
Key open problems
Observing the hierarchy directly addresses unresolved questions about the boundary between quantum and classical worlds, particularly the problem of macrorealism and the scale at which superposition can persist. It also sheds light on the reversibility of quantum evolution and the nature of the arrow of time in open systems through analysis of non-Markovian returns.
🎯 The 'sudden death' of entanglement, discovered in 2007, found a mirror reflection in temporal correlations: just as two particles abruptly cease to be entangled, a qubit in time can suddenly lose its quantum connections, and then, with environmental memory, regain them.
Key numbers
- gate operation time: ∼0.1 µs
- threshold of sudden death of nonmacrorealism (γt): ≈0.3
- quantum channel fidelity: >0.95
- typical revival time of TSR in free evolution: ∼15–20 µs
- number of qubits used (target + control): 2