Abstract One of the striking properties of quantum mechanics is the occurrence of the Bell-type non-locality. They are a fundamental feature of the theory that allows two parties that share an entangled quantum system to observe correlations stronger than possible in classical physics. In addition to their theoretical significance, non-local correlations have practical applications, such as device-independent randomness generation, providing private unpredictable numbers even when they are obtained using devices delivered by an untrusted vendor. Thus, determining the quantity of certifiable randomness that can be produced using a specific set of non-local correlations is of significant interest. In this paper, we present an experimental realization of recent Bell-type operators designed to provide private random numbers that are secure against adversaries with quantum resources. We use semi-definite programming to provide lower bounds on the generated randomness in terms of both min-entropy and von Neumann entropy in a device-independent scenario. We compare experimental setups providing Bell violations close to the Tsirelson’s bound with lower rates of events, with setups having slightly worse levels of violation but higher event rates. Our results demonstrate the first experiment that certifies close to two bits of randomness from binary measurements of two parties. Apart from single-round certification, we provide an analysis of finite-key protocol for quantum randomness expansion using the Entropy Accumulation theorem and show its advantages compared to existing solutions.
Abstract One of the striking properties of quantum mechanics is the occurrence of the Bell-type non-locality. They are a fundamental feature of the theory that allows two parties that share an entangled quantum system to observe correlations stronger than possible in classical physics. In addition to their theoretical significance, non-local correlations have practical applications, such as device-independent randomness generation, providing private unpredictable numbers even when they are obtained using devices delivered by an untrusted vendor. Thus, determining the quantity of certifiable randomness that can be produced using a specific set of non-local correlations is of significant interest. In this paper, we present an experimental realization of recent Bell-type operators designed to provide private random numbers that are secure against adversaries with quantum resources. We use semi-definite programming to provide lower bounds on the generated randomness in terms of both min-entropy and von Neumann entropy in a device-independent scenario. We compare experimental setups providing Bell violations close to the Tsirelson’s bound with lower rates of events, with setups having slightly worse levels of violation but higher event rates. Our results demonstrate the first experiment that certifies close to two bits of randomness from binary measurements of two parties. Apart from single-round certification, we provide an analysis of finite-key protocol for quantum randomness expansion using the Entropy Accumulation theorem and show its advantages compared to existing solutions.
One of the striking properties of quantum mechanics is the occurrence of the Bell-type non-locality. They are a fundamental feature of the theory that allows two parties that share an entangled quantum system to observe correlations stronger than possible in classical physics. In addition to their theoretical significance, non-local correlations have practical applications, such as device-independent randomness generation, providing private unpredictable numbers even when obtained using devices delivered by an untrusted vendor. Thus, determining the quantity of certifiable randomness that can be produced using a specific set of non-local correlations is of significant interest. First, we present an experimental realization of recent Bell-type operators designed to provide private random numbers that are secure against adversaries with quantum resources. We use semi-definite programming to give lower bounds on the generated randomness in terms of both min-entropy and von Neumann entropy in a device-independent scenario. Our results demonstrate the first experiment that certifies nearly two bits of randomness from binary measurements of two parties [1], [2]. Apart from single-round certification, we provide an analysis of finite-key protocol for quantum randomness expansion using the Entropy Accumulation Theorem. Second, we present an efficient and practical method for certifying quantum randomness using generalized measurements. Indeed, we have derived a method for self-testing the presence of POVMs. We present the certification of more than one bit of min-entropy from a single POVM on one of the qubits of an entangled state using a variant of the elegant Bell inequality. We also obtain more than one bit of randomness in a prepare and measure scenario of a similar structure with a POVM on a single qubit [3]. We provide numerical simulations to demonstrate the effectiveness of our randomness certification and expansion.
Two parties sharing entangled quantum systems can generate correlations that cannot be produced using only shared classical resources. These nonlocal correlations are a fundamental feature of quantum theory but also have practical applications. For instance, they can be used for device-independent random number generation, whose security is certified independently of the operations performed inside the devices. The amount of certifiable randomness that can be generated from some given nonlocal correlations is a key quantity of interest. Here, we derive tight analytic bounds on the maximum certifiable randomness as a function of the nonlocality as expressed using the Clauser-Horne-Shimony-Holt (CHSH) value. We show that for every CHSH value greater than the local value (2) and up to 3sqrt[3]/2≈2.598 there exist quantum correlations with that CHSH value that certify a maximal two bits of global randomness. Beyond this CHSH value the maximum certifiable randomness drops. We give a second family of Bell inequalities for CHSH values above 3sqrt[3]/2, and show that they certify the maximum possible randomness for the given CHSH value. Our work hence provides an achievable upper bound on the amount of randomness that can be certified for any CHSH value. We illustrate the robustness of our results, and how they could be used to improve randomness generation rates in practice, using a Werner state noise model.
We investigate device-independent certification of global randomness based on Bell inequality violations in bipartite scenarios with three outcomes per party. Our goal is to determine whether multi-outcome measurements allow one to surpass the amount of randomness achievable with binary outputs in realistic scenarios. We begin by analyzing several known Bell expressions and evaluating their robustness against noise for randomness certification. We then introduce a systematic method for generating new Bell expressions within structured families and perform a large-scale numerical study. We find that a substantial number of inequalities certify significant amounts of min-entropy. In particular, we identify simple inequalities that achieve near-maximal global randomness while involving a reduced number of measurement settings, thus improving the balance between certified randomness and number of inputs. Moreover, the vast majority of nontrivial certificates exhibit robustness against realistic noise, maintaining positive certified randomness away from the ideal regime. These results demonstrate that strong device-independent randomness expansion in multi-outcome scenarios is not restricted to carefully engineered inequalities, but arises generically within suitably constructed families of Bell expressions.
One of the distinguishing features of quantum theory is that its measurement outcomes are usually unpredictable or, equivalently, random. Moreover, this randomness is certifiable with minimal assumptions in the so-called device-independent (DI) paradigm, where a device's behavior does not need to be presupposed but can be verified through the statistics it produces. In this work, we explore various forms of randomness that are certifiable in this setting, where two users can perform two binary-outcome measurements on their shared entangled state. In this case, even though the Clauser-Horne-Shimony-Holt (CHSH) Bell-inequality violation is a pre-requisite for the generation of DI certifiable randomness, the CHSH value alone does not generally give a tight bound on the certifiable randomness. Here, we determine the certifiable randomness when zero-probability constraints are incorporated into the task of DI randomness expansion for the standard local and global randomness and the so-called "blind" randomness. Asymptotically, we observe consistent improvements in the amount of DI certifiable randomness (of all kinds) as we increase the number zero constraints for a wide range of given CHSH Bell violations. However, if we further optimize over the allowed CHSH values, then benefits of these additional constraints over the standard CHSH-based protocol are only found in the case of global and blind randomness. In contrast, in the regimes of finite data, these zero constraints only give a slight improvement in the local randomness rate when compared with all existing protocols.
Device-independent randomness certification based on Bell nonlocality does not require any assumptions about the devices, thus provides adequate security. Great effort has been made to demonstrate that nonlocality is necessary for generating quantum randomness, but the minimal resource required has not been clarified. Here we prove and experimentally demonstrate that violating any two-input Bell inequality is both necessary and sufficient for certifying randomness, however, for the multiple-input cases, this sufficiency ceases to apply, leading to certain states exhibiting Bell nonlocality without the capability to certify randomness. We examine two typical classes of Bell inequalities with multiple input and multiple output, the facet inequalities and Salavrakos-Augusiak-Tura-Wittek-Acín-Pironio inequalities, in the high-dimensional photonic system, and observe that the violation of the latter one can always certify randomness which is not true for the former. The private randomness with a generation rate of 1.867±0.018 bits per photon pair is obtained in the scenario of Salavrakos-Augusiak-Tura-Wittek-Acín-Pironio inequalities with 3-input and 4-output. Our Letter unravels the internal connection between randomness and nonlocality, effectively enhancing the performance of tasks such as device-independent random number generation.
Certified randomness guaranteed to be unpredictable by adversaries is central to information security. The fundamental randomness inherent in quantum physics makes certification possible from devices that are only weakly characterized, i.e., requiring little trust in their implementation. It was recently shown that the amount of certifiable randomness can be improved using the so-called entropy accumulation theorem generalized to prepare-and-measure settings. Furthermore, this approach allows a finite-size analysis which avoids assuming that all rounds are independent and identically distributed. Here, we demonstrate this improvement in semi-device-independent randomness certification from untrusted measurements.