Abstract The problem of achieving security of device-independent (or semi-device-independent) cryptography (for quantum key distribution and randomness generation) against the most general no-signaling adversaries has remained open. It has been recognized that the realization of extremal no-signaling non-local boxes (or extremal no-signaling non-local assemblages) could provide a route toward devising such highly secure protocols. We first prove a general no-go result that in the Bell non-locality scenario, quantum theory does not allow us to realize any extremal no-signaling non-local box, even if scenarios of arbitrary sequential measurements are considered. On the other hand, we secondly prove a positive result showing that a one-sided device-independent scenario where a single party trusts their qubit system is already sufficient for quantum theory to realize a self-testing extremal non-local point within the set of no-signaling assemblages.
Abstract The problem of achieving security of device-independent (or semi-device-independent) cryptography (for quantum key distribution and randomness generation) against the most general no-signaling adversaries has remained open. It has been recognized that the realization of extremal no-signaling non-local boxes (or extremal no-signaling non-local assemblages) could provide a route toward devising such highly secure protocols. We first prove a general no-go result that in the Bell non-locality scenario, quantum theory does not allow us to realize any extremal no-signaling non-local box, even if scenarios of arbitrary sequential measurements are considered. On the other hand, we secondly prove a positive result showing that a one-sided device-independent scenario where a single party trusts their qubit system is already sufficient for quantum theory to realize a self-testing extremal non-local point within the set of no-signaling assemblages.
The study of quantum correlations is important for fundamental reasons as well as for quantum communication and information processing tasks. On the one hand, it is of tremendous interest to derive the correlations produced by measurements on separated composite quantum systems from within the set of all correlations obeying the no-signaling principle of relativity, by means of information-theoretic principles. On the other hand, an important ongoing research program concerns the formulation of device-independent cryptographic protocols based on quantum nonlocal correlations for the generation of secure keys, and the amplification and expansion of random bits against general no-signaling adversaries. In both these research programs, a fundamental question arises: Can any measurements on quantum states realize the correlations present in pure extremal no-signaling boxes? Here, we answer this question in full generality showing that no nontrivial (not local realistic) extremal boxes of general no-signaling theories can be realized in quantum theory. We then explore some important consequences of this fact.
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.
Device-independent (DI) quantum protocols use Bell inequality violations to ensure security or certify quantum properties without assumptions on the devices’ internal workings. In this work, we study the role of rank-one qubit positive operator-valued measures (POVMs) in DI scenarios. This class includes all qubit extremal POVMs, i.e., those measurements that cannot be realized as mixtures of others, as well as part of non-extremal POVMs, recently shown to be useful in sequential quantum protocols. We demonstrate that any rank-one POVM can generate correlations in bipartite scenarios that saturate a Tsirelson inequality when two parties share an arbitrary entangled two-qubit state and perform specific self-tested measurements. For extremal POVMs, such saturation enables explicit computation of guessing probability and worst-case conditional von Neumann entropy. From the Tsirelson inequality, we establish a randomness certification method that facilitates numerical simulations and we validate it through a proof-of-concept experiment with three-outcome POVMs and tilted entangled states.
By testing nonlocality, the security of entanglement-based quantum key distribution (QKD) can be enhanced to being ``device-independent.'' Here we ask whether such a strong form of security could also be established for one-way (prepare and measure) QKD. While fully device-independent security is impossible, we show that security can be guaranteed against individual attacks in a semi-device-independent scenario. In the latter, the devices used by the trusted parties are noncharacterized, but the dimensionality of the quantum systems used in the protocol is assumed to be bounded. Our security proof relies on the analogies between one-way QKD, dimension witnesses, and random-access codes.
As our foundational understanding of quantum information theory broadens, it remains to be seen whether novel foundational developments will lead to corresponding applications. Promising branches are quantum networks and quantum cryptography, which are more intertwined by the day. In particular, a fascinating phenomena is that in networks with independent sources, Bell nonlocality can take place without the need for measurement settings for the parties, i.e. in each round, each source is asked to produce the same state and each party measures the same measurement. This is in stark contrast to standard Bell nonlocality, where seed randomness is necessary to certify nonlocality and through it, randomness of the outcomes. Building on nonlocality without seed randomness in networks, we propose a device-independent quantum key distribution protocol (which can be extended to quantum conference key agreement if it involves more than 2 parties) which allows for the generation of shared secret keys without the need for input randomness. We rely on recent results on nonlocality in networks and its robustness, showing how in a ring network with N bipartite sources, one must only make standard assumptions in order to run the protocol, while no trust is required from the devices themselves. We thus give a device-independent proof of security under this network assumption in the IID setting. In summary, we propose a first-of-a-kind protocol for Device-Independent Quantum Key Distribution which is native to the network setting, and which does not demand input randomness from the parties in order to produce output randomness.
In device-independent quantum information, correlations between local measurement outcomes observed by spatially separated parties in a Bell test play a fundamental role. Even though it is long-known that the set of correlations allowed in quantum theory lies strictly between the Bell-local set and the no-signaling set, many questions concerning the geometry of the quantum set remain unanswered. Here, we revisit the problem of when the boundary of the quantum set coincides with the no-signaling set in the simplest Bell scenario. In particular, for each Class of these common boundaries containing k zero probabilities, we provide a (5−k) -parameter family of quantum strategies realizing these (extremal) correlations. We further prove that self-testing is possible in all nontrivial Classes beyond the known examples of Hardy-type correlations, and provide numerical evidence supporting the robustness of these self-testing results. Candidates of one-parameter families of self-testing correlations from some of these Classes are identified. As a byproduct of our investigation, if the qubit strategies leading to an extremal nonlocal correlation are local-unitarily equivalent, a self-testing statement provably follows. Interestingly, all these self-testing correlations found on the no-signaling boundary are provably non-exposed. An analogous characterization for the set M of quantum correlations arising from finite-dimensional maximally entangled states is also provided. En route to establishing this last result, we show that all correlations of M in the simplest Bell scenario are attainable as convex combinations of those achievable using a Bell pair and projective measurements. In turn, we obtain the maximal Clauser-Horne-Shimony-Holt Bell inequality violation by any maximally entangled two-qudit state and a no-go theorem regarding the self-testing of such states.