Researchers at the Indian Institute of Technology Hyderabad have developed a new protocol to certify entangled basis measurements using a semi-device-independent approach in a prepare-measure scenario. The work details a method for verifying entanglement without requiring full control over the quantum device, potentially easing the path toward practical verification of quantum systems.

This protocol focuses on a tri-partite system where two senders can each transmit $2^{m}$ inputs to a single receiver, and the researchers demonstrate that nonlinear witnesses within a classical causal model exceed classical bounds. The results show this approach can certify both the entangled basis measurement and the states prepared by the two senders.

Semi-Device-Independent Certification of Multi-Qubit Entangled Measurements

A new certification protocol allows verification of entangled basis measurements with relaxed requirements for quantum device control, a departure from traditional methods demanding complete control. This approach, detailed in recent work, uses a semi-device-independent (SDI) framework within a prepare-measure (PM) scenario to assess multi-qubit entanglement. The researchers adopted a classical causal-model framework to demonstrate the nonclassicality of quantum measurements, introducing nonlinear witnesses to analyze the system.

These witnesses, applied within the classical model, revealed that the optimal quantum value exceeds established classical bounds, a key indicator of genuine entanglement. The study details a self-testing protocol for a 16-outcome entangled basis measurement, where projectors are maximally entangled across every 1|3 bipartition, meaning the entanglement is evenly distributed across the qubits.

Calculations show that = 32, a value that self-tests the measurement projector to be maximally entangled across every 1|3 bipartition. Further analysis extends to the case of m = 3, establishing a weaker self-testing result for an eight-outcome entangled basis measurement that ensures maximal entanglement across at least one bipartition. The protocol centers on a joint measurement with 2^m outcomes, denoted by 𝐛 = where b_i ∈ 0, 1 for all i = 1, 2,., m, performed by the receiver.

This setup allows for certification of measurements with an increasing number of outcomes as the number of qubits increases, demonstrating the potential for scaling quantum communication protocols. “Entangled basis measurements play a pivotal role in quantum information theory,” the paper states, “in particular in fundamental protocols such as entanglement swapping, dense coding and quantum teleportation.

Classical Causal Models for PM Scenario Certification

A new certification protocol uses classical causal models to demonstrate nonclassicality in quantum measurements, exceeding established classical limits. The research team’s framework adopts a classical causal model to assess the nonclassical nature of measurements performed by the receiver. This model considers two senders, independently preparing quantum states based on their inputs, and transmitting them to the receiver, who then performs a joint measurement.

The receiver’s measurement outcome, defined by $2^{m}$ possibilities, is then analyzed within the classical model, allowing for certification of the entangled basis measurement without full knowledge of the internal workings of the quantum devices used by the senders. The ability to certify quantum states and measurements with reduced control over the underlying hardware is a critical step toward practical quantum information processing.

Bell’s Theorem and Device-Independent Self-Testing

The ability to certify entangled basis measurements and prepared states without fully characterizing a quantum device represents an advancement in quantum information processing, and a new protocol achieves this through a semi-device-independent (SDI) approach. This work moves beyond traditional methods by focusing on a prepare-measure (PM) scenario involving two senders and a single receiver, allowing for certification even with limited control over the underlying hardware.

The researchers introduce nonlinear witnesses in classical causal models and demonstrate that the optimal quantum value exceeds the classical bounds. Expanding the system’s capabilities, the researchers further demonstrate self-testing of an eight-outcome entangled measurement, building upon previously introduced witnesses with key modifications. The receiver now performs a measurement yielding eight outcomes, denoted by $b_{1} b_{2} b_{3}$ , where each $b_{i}$ can be either 0 or 1.

This certification is a validation of the specific basis measurement and the quality of the prepared states, offering a higher level of assurance for quantum information processing tasks. The work provides a new tool for verifying quantum resources, potentially easing the path toward practical quantum technologies.

SDI Protocol for Four-Outcome Entangled Measurements

The new protocol establishes a method for verifying entangled basis measurements with as few as four possible outcomes, expanding the capabilities of quantum communication systems. This certification does not require complete control over the quantum device used, a departure from many existing methods and a step toward more practical verification techniques. The protocol’s success relies on the ability to demonstrate a quantum value that surpasses any possible classical result.

Specifically, the researchers developed self-testing protocols for four-outcome measurements when each sender uses either binary or four inputs. The protocol’s utility extends to scenarios with more complex measurements, as demonstrated by their certification of a 16-outcome entangled basis measurement. The researchers explain that the receiver performs a joint measurement, denoted by 𝐛 = b₁b₂…bₘ, where each bᵢ can be either 0 or 1.

Self-Testing 16-Outcome Maximally Entangled Basis Measurements

This advancement moves beyond earlier self-testing protocols that required pre-shared entanglement between parties, a significant limitation in practical quantum network deployment. Researchers demonstrated this capability within a prepare-measure scenario, a framework where two senders transmit information to a single receiver. This methodology allows for certification of multi-qubit entangled basis measurements, with each sender capable of preparing states based on $2^{m}$ possible inputs and the receiver analyzing $2^{m}$ outcomes.

This result guarantees maximal entanglement across at least one division of the quantum system, providing a degree of confidence even when full maximal entanglement across all divisions cannot be assured. This certification extends to measurements with projectors maximally entangled across every possible division for even values of ‘m’, and at least one division for odd values, providing a versatile tool for verifying quantum resources.

Generalized Witness for 2^m-Outcome Entangled Basis Measurements

A new protocol allows certification of entangled basis measurements across an increasing number of qubits, scaling with the parameter ‘m’, without requiring complete control over the quantum devices involved. This semi-device-independent (SDI) approach moves beyond previous methods that demanded full knowledge of the underlying quantum system, offering a potentially more practical route to verifying entanglement in complex systems.

This approach differs from earlier work that focused on certifying entanglement’s presence without characterizing the specific entangled measurement being performed. The researchers specifically focused on a prepare-measure (PM) scenario, a standard configuration involving senders and a receiver, but extended it to accommodate the $2^{m}$ input capability.

While weaker than the result for even values of ‘m’, this finding still provides a valuable certification tool. “The optimal quantum bound for the witness SDI self-tests the entangled basis measurement of the receiver and the prepared states of the senders,” the researchers state, emphasizing the thoroughness of the certification process. The researchers detail that the protocol’s success relies on establishing a clear distinction between quantum and classical behavior.

By using the framework of classical causal models, they can pinpoint the point at which the quantum measurements demonstrably exceed what is possible classically. This approach not only verifies the entanglement but also provides a degree of trust in the quantum devices used, even without complete knowledge of their internal workings. The work extends scenarios beyond simple binary inputs.

Quantum Advantage in Multi-Sender Prepare-Measure Scenarios

The receiver then performs a $2^{m}$ -outcome measurement, expanding beyond scenarios limited to simple binary inputs. This approach differs from earlier self-testing protocols by focusing on a broader class of m-qubit entangled basis measurements, rather than solely verifying entanglement’s presence. The notion of self-testing was first introduced by Mayer and Yao. Since then a flurry of ingenious protocols have been developed, extending to multipartite systems and multi-outcome measurement scenario.

The protocol’s design uses the advantages of incompatible measurements performed by the receiver, a key element in achieving quantum advantage when Bob has more than one input. A diagram illustrates a scenario involving Alice and Charlie as senders, each preparing states based on their inputs, and Bob receiving and analyzing the combined result.

👉 More information
🗞 Semi-Device-Independent Certification of multi-qubit Entangled Basis Measurement
✍️ Rajat Pandey (Indian Institute of Technology Hyderabad, Kandi, Sangareddy, Telangana 502285, India); Alok Kumar Pan
🧠 ArXiv: https://arxiv.org/abs/2611.06337

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