The Signal
IBM Processor Measures Entanglement Under Stochastic Resetting
Researchers compared entropy and concurrence in a quantum system subject to stochastic resetting, combining theoretical calculations with measurements on an IBM superconducting processor. The entropy measures closely followed noiseless pred
Quantum.world Team · Written with AI · fact-checked ·
“The two diagnostics respond differently because they read different components of the same reconstructed state, and a depolarizing model captures the concurrence suppression with one fitted parameter.”
Jakob Murauer, Sabine Tornow, Manas Kulkarni, Eli Barkai, Satya N. Majumdar and Monalisa Singh Roy, authors of the study
Physicists analyzed how stochastic resetting affects entanglement in a transverse-field Ising model, combining exact calculations, numerical evaluations and measurements on an IBM superconducting processor. The study examines a two-qubit system and calculates chains of up to 12 sites. On the processor, the two entropy measures closely followed noiseless predictions without fitted parameters, while concurrence—the measure of entanglement in the two-qubit stationary state—fell below theory across most of the measured range.
Reset histories and entropy
In the model, each discrete step either resets the system to a fixed pure state with probability p or applies a unitary evolution with probability 1−p. The reset-age variable is the number of unitary steps since the most recent reset. Its stationary distribution is geometric, with weight p(1−p)m for age m. The resulting stationary state is a mixture of differently evolved copies of the reset state.
The authors consider two reset states for the two-qubit system: the unentangled |00⟩ product state and the maximally entangled Bell state (|00⟩+|11⟩)/√2. The paper distinguishes two ways to calculate entropy. The trajectory-averaged entropy is calculated for each age and then averaged; the averaged-state entropy first combines the reduced states from different ages and then calculates entropy. Because entropy is nonlinear, these operations need not give the same result.
The difference, called the Jensen gap, equals the Holevo information that a subsystem retains about the time since the last reset. It bounds how much a measurement of that subsystem can reveal about reset age. The paper emphasizes that this quantity describes information about the history, not entanglement lost through averaging. The third diagnostic, concurrence, measures entanglement in the stationary two-qubit mixture.
Two-qubit measurements and chain calculations
The processor experiment used qubits 4 and 5 of IBM’s ibm_pittsburgh processor for the Bell-state reset. The researchers reconstructed states through quantum state tomography, with 104 shots per setting, and used dynamical decoupling with gate and measurement twirling. They measured at four reset probabilities—0.05, 0.35, 0.65 and 0.95—while varying the coupling ratio from 0 to 4.
Both entropy measures followed the noiseless calculations across the four reset probabilities. Concurrence was lower than the noiseless result through most of the measured range. At a resonance near coupling ratio 2.98, the ideal stationary state is a pure Bell state. For reset probability 0.05, measured concurrence there was 0.929, below the ideal value of 1.
A single-parameter model using identical single-qubit depolarizing channels captured the overall concurrence suppression at reset probability 0.05. Its fitted noise strength was 1.56 × 10−3 per step; at the resonance, it predicted concurrence of 0.916. The paper presents this as a model of the observed suppression, not a device-calibrated account of every hardware error.
For the chain calculations, the researchers evaluated the Jensen gap for subsystems including a half-chain cut. With a Bell-pair reset, the half-chain gap grew with chain length over the studied sizes, without visible saturation at smaller reset probabilities. The largest reported value was 2.55 bits at 12 sites. These are exact calculations, not measurements on a 12-qubit processor; the hardware demonstration concerns two qubits.
The study also notes that reset times are classical records. Averaging trajectory entropies using the known reset-age distribution therefore does not require postselecting complete measurement records. Resolving different ages still divides measurement statistics among separate states, increasing sampling needs. The results show that entropy and concurrence can respond differently to hardware noise, so close agreement between an entropy measurement and noiseless theory does not by itself establish that stationary-state entanglement is equally well preserved.