Secure key distribution based on Popescu-Rohrlich box fraction of dimensionally restricted nonlocality

We study a problem of interconvertibility of two supraquantum resources: one is the so-called Popescu-Rohrlich (PR) box, which violates Clauser-Horne-Shimony-Holt inequality up to the maximal algebraic bound, and the second is the so-called random access code (RAC). The latter is a functionality that enables Bob (receiver) to choose one of two bits of Alice. It is known that a PR box supplemented with one bit of communication can be used to simulate a RAC. We ask the converse question: to what extent can a RAC can simulate a PR box? To this end, we introduce a "racbox": a box such that when it is supplemented with one bit of communication it offers a RAC. As said, a PR box can simulate a racbox. The question we raise is whether any racbox can simulate a PR box. We show that a nonsignaling racbox, indeed, can simulate a PR box; hence, these two resources are equivalent. We also provide an example of a signaling racbox that cannot simulate a PR box. We give a resource inequality between racboxes and PR boxes and show that it is saturated.

In the well-studied Bell experiment consisting of two parties, two measurement settings per party, and two possible outcomes per setting, it is known that if the experiment obeys no-signaling constraints, then the set of admissible experimental probability distributions is fully characterized as the convex hull of 24 distributions: eight Popescu–Rohrlich (PR) boxes and 16 local deterministic distributions. Furthermore, it turns out that in the case, any nonlocal nonsignaling distribution can always be uniquely expressed as a convex combination of exactly one PR box and (up to) eight local deterministic distributions. In this representation each PR box will always occur only with a fixed set of eight local deterministic distributions with which it is affiliated. In this paper, we derive multiple practical applications of this result: we demonstrate an analytical proof that the minimum detection efficiency for which nonlocality can be observed is even for theories constrained only by the no-signaling principle, and we develop new algorithms that speed the calculation of important statistical functions of Bell test data. Finally, we enumerate the vertices of the no-signaling polytope for the ‘chained Bell’ scenario and find that similar decomposition results are possible in this general case. Here, our results allow us to prove the optimality of a bound, derived in Barrett et al (2006 Phys. Rev. Lett. 97 170409), on the proportion of local theories in a local/nonlocal mixture that can be inferred from the experimental violation of a chained Bell inequality.

In a no-signaling world, the outputs of a nonlocal box cannot be completely predetermined, a feature that is exploited in many quantum information protocols exploiting non-locality, such as device-independent randomness generation and quantum key distribution. This relation between non-locality and randomness can be formally quantified through the min-entropy, a measure of the unpredictability of the outputs that holds conditioned on the knowledge of any adversary that is limited only by the no-signaling principle. This quantity can easily be computed for the noisy Popescu-Rohrlich (PR) box, the paradigmatic example of non-locality. In this paper, we consider the min-entropy associated to several copies of noisy PR boxes. In the case where n noisy PR-boxes are implemented using n non-communicating pairs of devices, it is known that each PR-box behaves as an independent biased coin: the min-entropy per PR-box is constant with the number of copies. We show that this doesn't hold in more general scenarios where several noisy PR-boxes are implemented from a single pair of devices, either used sequentially n times or producing n outcome bits in a single run. In this case, the min-entropy per PR-box is smaller than the min-entropy of a single PR-box, and it decreases as the number of copies increases.

It is known that there exist non-local correlations that respect no-signaling criterion, but violate Bell-type inequalities more than quantum-mechanical correlations. Such super quantum correlations were introduced as the Popescu-Rohrlich (PR) box. We consider such non-local boxes with two/three inputs and two/three outputs. We show that these super quantum correlations can lead to signaling when at least one of the input bit has access to a word line along a closed time-like curve.

The study of no-signaling polytopes is addressed under an alternative approach, focusing on the skeleton graph of the polytopes rather than on the Bell inequalities solely. The paper starts with the study of the Bell scenario where one of the parties (Bob) has three output options (2223 scenario). We found that in this polytope the Popescu-Rohrlich (PR) vertices are interconnected, making up two networks around the polytope of local correlations, which is a new feature in relation to the 2222 polytope. We also found that in this scenario each CHSH inequality is violated by five PR vertices: the PR vertex associated to that inequality and its four adjacent PR vertices. Later, we study the facet structure of the corresponding polytope of local correlations. What we obtain is a one-to-one correspondence between some two-dimensional faces of the no-signaling polytope defined by specific loops in the adjacency networks of PR vertices, the lifting Bell functions, and the nontrivial facets of the local polytope. Finally, by studying the skeleton graphs of the polytopes for the general $222{v}_{B}$ scenarios, where ${v}_{B}$ is the number of possible Bob's outcomes, a striking high degeneracy is unveiled. We show that the set of local vertices exhibits a much higher degeneracy than the PR vertices, which in turn are more degenerate than a regular vertex.

Key distribution is a major challenge of secure communication. Computational approaches to key distribution are breached by quantum algorithms, while quantum key distribution (QKD) is an expensive, slow, and sophisticated solution. Secure key generation and distribution from unpredictable and inherent physical-layer properties of optical fiber channel is a classical, simple and cost-effective solution. However, the quasi-static nature of fiber channels dramatically limits the available key generation rate (KGR) to the order of ~kbit/s. Here we effectively accelerate the KGR by six orders of magnitude using a developed high-speed chaotic polarization scrambler (CPS) driven by digital chaos in fiber channels. An error-free KGR of 284.8 Mbit/s is experimentally demonstrated over a 24 km standard single-mode fiber (SSMF), where the generated key passes the random test suite. Moreover, we fully analyze the security mechanism and find that a strong asymmetry exists between legal and illegal users, ensuring a high-level of security against potential fiber-tapping attacks. This scheme provides a major step towards the practical implementation of the “one-time-pad” in secure data transmission over fiber networks.

This study proposes a group key service node placement method for quantum key distribution (QKD) networks based on partially trusted relays, aiming to optimize network structure, improve key distribution efficiency, reduce communication delay, and ensure transmission integrity and confidentiality. Based on graph theory, a key information model for the quantum key distribution network is established, which defines node types, functions, and connectivity. Leveraging the secure transmission protocol of quantum keys, the unconditional security of the key during transmission is ensured. Furthermore, this study proposes a QKD network architecture incorporating partially trusted relays, which combines trusted and untrusted relay technologies. An improved p-median model is introduced and solved using a greedy algorithm to ensure secure quantum key distribution and optimal deployment of group key service nodes. Experimental results demonstrate that the location of group key service nodes in quantum key distribution network ensures the minimum number of key service nodes and minimizes the path length from network demand nodes to group key service nodes. Furthermore, this method significantly improves the key distribution efficiency, success rate, security, energy consumption, resource consumption, network coverage, and blind area of quantum key distribution network.

The current state of the art in space systems would not be possible without the advances in our understanding of matter and light at the atomic level provided by quantum theory. This triumph of 20th century physics provides the foundation for most of the components employed in satellites from integrated circuits, solar cells, atomic clocks, and advanced materials. Over the past 25 years a new understanding of the relationship between quantum theory, theory and security, and computing has raised the possibility of exploiting \quantum information for computing and secure encryption key generation. The eld of quantum science exploits quantum states for processing and security applications. The power of quantum derives from the quantum nature of matter that allow algorithms with exponential speed-up when compared to the best-known classical algorithms. Quantum Key Distribution involves using quantum states, typically encoded into the phase or polarization of photons, to securely share the bits to be used to construct an encryption key. The theoretical security of quantum key distribution rests on the physical laws of quantum theory, unlike classical cryptography that relies on assumptions about the computational complexity of certain mathematical problems. In this paper we survey the state of quantum science and technology, summarizing the basic features of quantum processing and key distribution. We describe the potential for quantum computing and key distribution to support future NSS applications and missions, for both the ground and space segments. We conclude with a discussion of the current challenges with advancing quantum technology to meet these future needs.

A set of nonlocal correlations that have come to be known as a Popescu-Rohrlich (PR) box suggest themselves as a natural unit of nonlocality, much as a singlet is a natural unit of entanglement. We present two results relevant to this idea. One is that a wide class of multipartite correlations can be simulated using local operations on PR boxes only. We show this with an explicit scheme, which has the interesting feature that the number of PR boxes required is related to the computational resources necessary to represent a function defining the multipartite box. The second result is that there are quantum multipartite correlations, arising from measurements on a cluster state, that cannot be simulated with n PR boxes, for any n.

Communication complexity quantifies how difficult it is for two distant computers to evaluate a functionf(X,Y), where the stringsXandYare distributed to the first and second computer respectively, under the constraint of exchanging as few bits as possible. Surprisingly, some nonlocal boxes, which are resources shared by the two computers, are so powerful that they allow tocollapsecommunication complexity, in the sense that any Boolean function f can be correctly estimated with the exchange of only one bit of communication. The Popescu-Rohrlich (PR) box is an example of such a collapsing resource, but a comprehensive description of the set of collapsing nonlocal boxes remains elusive.In this work, we carry out an algebraic study of the structure of wirings connecting nonlocal boxes, thus defining the notion of the "product of boxes"P⊠Q, and we show related associativity and commutativity results. This gives rise to the notion of the "orbit of a box", unveiling surprising geometrical properties about the alignment and parallelism of distilled boxes. The power of this new framework is that it allows us to prove previously-reported numerical observations concerning the best way to wire consecutive boxes, and to numerically and analytically recover recently-identified noisyPRboxes that collapse communication complexity for different types of noise models.

We present bipartite Bell-type inequalities which allow the two partners to use some nonlocal resource. Such inequalities can only be violated if the parties use a resource which is more nonlocal than the one permitted by the inequality. We introduce a family of N-input nonlocal machines, which are generalizations of the well-known PR (Popescu-Rohrlich) box. Then we construct Bell-type inequalities that cannot be violated by strategies that use one of these new machines. Finally we discuss implications for the simulation of quantum states.

Quantum correlations or entanglement is a basic ingredient for many applications of quantum information theory.One important application using quantum entanglement exploits the correlation nature of entangled photon states is quantum key distribution, which is proven unbreakable in principle and provides the highest possible security that is impossible in classical information theory. However, generating entangled photon pairs is not a simple task -- only approximately one out of a million pump photons decay into a signal and idler photon pair. This low rate of entangled photon pairs is further reduced by the overhead required in order for the rectification of the inevitable errors due to channel imperfections or caused by potential eavesdroppers. As a consequence, quantum key distribution suffers from a low bit rate, which is in the order of hundreds to thousands bits per second or below. On the other hand, the classical public key distribution does not impose a tight limit on the transmission rate. However, it is subject to the risks of eavesdroppers sitting in the middle of the insecure channel. In this paper, we propose a hybrid key distribution method which uses public key distribution method to generate a raw key, and then uses entanglement assisted communication to modify the raw key by inserting a number of quantum bits in the raw key. Building upon the foundation of the unconditional security of quantum key distribution, we use the privacy amplification to make the affection of inserted bits expand to a whole key. Our quantum entanglement assisted key distribution scheme greatly improves the efficiency of key distribution while without compromising the level of security achievable by quantum cryptography.

Most schemes of quantum key remote distribution available mainly deal with the quantum repeater based on quantum entanglement swapping. However, as the quantum repeater has many insurmountable shortcomings, this paper, relying on the existing fairly mature technique, proposes a highly efficient QKD scheme with authentication mechanism from a new perspective of scheme not based on entanglement swapping, overcoming the low efficiency of the entanglement swapping scheme. By means of the quantum authentication mechanism, this scheme is capable of preventing and detecting any active attacks from any point in the quantum network. The scheme proposed has realized authentication and key distribution in the quantum channel at the same time, providing the authentication mechanism of this type of remote key distribution network with a reference. This paper first briefly analyzes the shortcomings of the quantum repeater scheme based on entanglement swapping and introduces the idea of highly efficient quantum key negotiation by means of the pseudo random sequence. Then a key distribution with authentication protocol based on shared secret is presented followed by a description of the application of this scheme in the quantum key distribution network.

It is well known that the fair-sampling loophole in Bell test opened by the selection of the state to be measured can lead to post-quantum correlations. In this paper, we make the selection of the results after measurement, which opens the fair- sampling loophole too, and thus can lead to post-quantum correlations. This kind of result-selection loophole can be realized by pre- and post-selection processes within the “two-state vector formalism”, and a physical simulation of Popescu-Rohrlich (PR) box is designed in linear optical system. The probability distribution of the PR has a maximal CHSH value 4, i.e. it can maximally violate CHSH inequality. Because the “two-state vector formalism” violates the information causality, it opens the locality loophole too, which means that this kind of results selection within “two-state vector formalism” leads to both fair- sampling loophole and locality loophole, so we call it a comprehensive loophole in Bell test. The comprehensive loophole opened by the results selection within “two-state vector formalism” may be another possible explanation of why post-quantum correlations are incompatible with quantum mechanics and seem not to exist in nature.

The behaviors that obey the no-signaling condition are a natural set to study nonlocality: this chapter is devoted to it. First, the most famous example of a no-signaling non-quantum behavior is introduced, the so-called Popescu-Rohrlich (PR) box. Then, some “typical quantum” features are recovered in the no-signaling framework, showing that they are common to all no-signaling theories.