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arXiv:2608.08329

Randomness Certification and Trade-offs in the Prepare-and-Broadcast Scenario

Tailan S. Sarubi, Moisés Alves, Vinícius F. Alves, Santiago Zamora, Diogo H. G. Duarte, A. de Oliveira Junior, Rafael Chaves

quant-phSubmitted Aug 8, 2026• Announced Aug 11, 2026• 0 citations
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Abstract

We investigate the prepare-and-broadcast scenario, a multipartite extension of dimension-constrained prepare-and-measure experiments in which a quantum system is distributed to multiple receivers. We derive fundamental trade-offs between prepare-and-measure witnesses, Bell nonlocality, and quantum random access code performance. We further develop a semi-device-independent randomness certification framework based on prepare-and-broadcast witnesses, showing that the maximal quantum violation certifies two bits of joint randomness, exceeding the limit achievable from the CHSH inequality while remaining robust to noise. Finally, we show that the prepare-and-broadcast scenario naturally accommodates stronger adversarial models in which the eavesdropper retains a quantum system correlated with the measurement device, providing a natural framework for semi-device-independent randomness certification against quantum side information.

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22 pages, 8 figures

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We investigate the prepare-and-broadcast scenario, a multipartite extension of dimension-constrained prepare-and-measure experiments in which a quantum system is distributed to multiple receivers. We derive fundamental trade-offs between prepare-and-measure witnesses, Bell nonlocality, and quantum random access code performance. We further develop a semi-device-independent randomness certification framework based on prepare-and-broadcast witnesses, showing that the maximal quantum violation certifies two bits of joint randomness, exceeding the limit achievable from the CHSH inequality while remaining robust to noise. Finally, we show that the prepare-and-broadcast scenario naturally accommodates stronger adversarial models in which the eavesdropper retains a quantum system correlated with the measurement device, providing a natural framework for semi-device-independent randomness certification against quantum side information.
Quantum information tasks are often analyzed under varying trust assumptions about the devices involved. The semi-device-independent (SDI) framework offers a balance between needed assumptions and experimental feasibility. In this work, we study the energy-constrained SDI scenario, where the only assumption in a prepare-and-measure setup is an upper bound on the energy of the prepared quantum states. In contrast to previous studies that restricted the preparation and measurement devices to be classically correlated, we show that allowing entanglement strictly enlarges the set of achievable correlations. We identify two operational consequences of this result. The first concerns randomness certification, where we show that allowing the adversary to employ entangled strategies may significantly reduce the amount of certifiable randomness. This includes situations where the amount of randomness drops to zero in the presence of entanglement, while it remains positive when entanglement is excluded. Second, for the task of distinguishing an arbitrary quantum channel from the identity, we show that the known dimension-independent bound on the advantage conferred by entanglement is violated under an energy constraint.
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Certifying maximal quantum randomness without assumptions about system dimension remains a pivotal challenge for secure communication and foundational studies. Here, we introduce a generalized framework to directly certify maximal randomness from observed probability distributions across systems with arbitrary user numbers, without relying on the Bell-inequality violations. By analyzing probability distributions directly, we identify a class of quantum states and projective measurements that achieve maximal randomness in bipartite and tripartite scenarios, ensuring practical feasibility. Further analysis reveals a counterintuitive trade-off governing measurement incompatibility among users: sufficient incompatibility for one user permits arbitrarily small incompatibility for others, defying conventional symmetry assumptions in the Bell test. This asymmetry provides a pathway to optimize device-independent protocols by strategically distributing quantum resources. Our results establish a versatile and experimentally accessible route to scalable randomness certification, with implications for quantum cryptography and the physics of nonlocal correlations.
A key aspect in quantum information is to understand the advantage offered by quantum systems over classical ones in communication tasks. In recent years, a fundamental approach to this problem has been developed, focusing on quantum correlations in prepare-and-measure scenarios. Inspired by the developments in Bell nonlocality and device-independent information processing, this line of research aims to characterize the possibilities and limits of quantum systems for communication, in particular to precisely capture the advantage they offer over classical systems. In addition to fundamental insights, these ideas also underpin the concept of semi-device-independent quantum information processing. Exploring trade-offs between security, performance and ease-of-implementation, this approach opens promising directions for novel quantum information processing technologies and devices. A number of protocols and proof-of-principle demonstrations have been reported in recent years, in particular for quantum randomness certification and key distribution. Here, we provide a comprehensive introduction to quantum prepare-and-measure correlations and semi-device independent applications.
The prepare-and-measure framework based on energy constraints offers a practical middle ground between fully device-dependent and device-independent quantum cryptography. The only assumption on an otherwise uncharacterized prepare-and-measure device is that the energy of the prepared states is bounded. Existing security analyses of this framework assume that the preparation and measurement devices share at most classical correlations, and under this assumption certified lower bounds on the extractable randomness have been established. Recent work has shown that an adversary who pre-distributes entanglement between the devices can mount attacks that are strictly more powerful than those available when the devices share only classical correlations, reducing the extractable randomness below the previously certified rates. This leaves open the fundamental question of whether randomness can be certified at all in this scenario. We address this open question by constructing semidefinite programming relaxations of the guessing probability by adapting the Navascués-Pironio-Acín hierarchy to the energy-constrained setting where shared entanglement between the devices is permitted. Our relaxations yield certified lower bounds on the extractable randomness without enforcing any restrictions on the dimensions of the quantum state shared between the preparation and measurement devices. We show that these certified lower bounds are strictly positive for a range of energy values, thereby answering the open question affirmatively: certified randomness generation is theoretically possible in the energy-constrained SDI framework even in the presence of a fully quantum adversary.
It has recently been shown that by broadcasting the subsystems of a bipartite quantum state, one can activate Bell nonlocality and significantly improve noise tolerance bounds for device-independent entanglement certification. In this work we strengthen these results and explore new aspects of this phenomenon. First, we prove new results related to the activation of Bell nonlocality. We construct Bell inequalities tailored to the broadcast scenario, and show how broadcasting can lead to even stronger notions of Bell nonlocality activation. In particular, we exploit these ideas to show that bipartite states admitting a local hidden-variable model for general measurements can lead to genuine tripartite nonlocal correlations. We then study device-independent entanglement certification in the broadcast scenario, and show through semidefinite programming techniques that device-independent entanglement certification is possible for the two-qubit Werner state in essentially the entire range of entanglement. Finally, we extend the concept of EPR steering to the broadcast scenario, and present novel examples of activation of the two-qubit isotropic state. Our results pave the way for broadcast-based device-independent and semi-device-independent protocols.