The geometry of the quantum set correlations is studied with standard tools from convex geometry. Examples counterintuitive features are found in simplest nontrivial Bell scenario, and more complex shown to persist sophisticated scenarios.

Self-testing refers to the phenomenon that certain extremal quantum correlations (almost) uniquely identify system under consideration. For instance, observing maximal violation of Clauser-Horne-Shimony-Holt (CHSH) inequality certifies two parties share a singlet. While self-testing results are known for several classes states, in many cases they only applicable if observed statistics almost perfect, which makes them unsuitable practical applications. Practically relevant bounds much less...

The goal of self-testing is to characterize an a priori unknown quantum system based solely on measurement statistics, i.e. using uncharacterized device. Here we develop methods for prepare-and-measure experiments, thus not necessarily relying entanglement and/or violation Bell inequality. We present noise-robust techniques sets states and measurements, assuming upper bound the Hilbert space dimension. discuss in detail case $2 \rightarrow 1$ random access code with qubits, which provide...

We consider the problem of certifying binary observables based on a Bell inequality violation alone, task known as self-testing measurements. introduce family commutation-based measures, which encode all distinct arrangements two projective qubit. These quantities by construction take into account usual limitations and since they are "weighted" (reduced) state, automatically deal with rank-deficient reduced density matrices. show that these measures can be estimated from observed in several...

Quantum nonlocality is developed on the basis of two most celebrated discrete structures in quantum theory.

Bit commitment is a fundamental cryptographic primitive in which Bob wishes to commit secret bit Alice. Perfectly secure between two mistrustful parties impossible through asynchronous exchange of quantum information. Perfect security however possible when Alice and split into several agents exchanging classical information at times locations suitably chosen satisfy specific relativistic constraints. Here we report on an implementation protocol using communication special relativity. Our...

We consider a game in which two separate laboratories collaborate to prepare quantum system and are then asked guess the outcome of measurement performed by third party random basis on that system. Intuitively, uncertainty principle monogamy entanglement, probability both players simultaneously succeed guessing correctly is bounded. interested question how success scales when many such games parallel. show any strategy maximizes win every individually also optimal for parallel repetition...

Mutually unbiased bases (MUBs) constitute the canonical example of incompatible quantum measurements. One standard application MUBs is task known as random access code (QRAC), in which classical information encoded a system, and later part it recovered by performing measurement. We analyze specific class QRACs, ${2}^{d}\ensuremath{\rightarrow}1$ QRAC, two dits are $d$-dimensional system. It that among rank-1 projective measurements give best performance. show (for every $d$) this cannot be...

We investigate entropic uncertainty relations for two or more binary measurements, example, spin-$\frac{1}{2}$ polarization measurements. argue that the effective anticommutators of these i.e., evaluated on state prior to measuring, are an expedient measure measurement incompatibility. Based knowledge pairwise we derive a class in terms conditional R\'enyi entropies. Our formulated measures incompatibility, which can be certified device-independent fashion. Consequently, discuss potential...

Self-testing refers to the possibility of characterizing an unknown quantum device based only on observed statistics. Here we develop methods for self-testing entangled measurements, a key element networks. Our approach is natural assumption that separated physical sources in network should be considered independent. This provides formulation problem certifying measurements. Considering setup entanglement swapping, derive robust self-test Bell-state measurement, tolerating noise levels up...

Bell inequalities are an important tool in device-independent quantum information processing because their violation can serve as a certificate of relevant properties. Probably the best known example inequality is due to Clauser, Horne, Shimony and Holt (CHSH), which defined simplest scenario involving two dichotomic measurements whose all key properties well understood. There have been many attempts generalise CHSH higher-dimensional systems, however, for most them maximal violation---the...

Bell nonlocality as a resource for device independent certification schemes has been studied extensively in recent years. The strongest form of is referred to self-testing, which given certifies the promised quantum state well measurements performed on it without any knowledge internal workings device. In spite various results self-testing protocols, remains highly nontrivial problem propose scheme qudit-qudit entangled states based violation single $d$-outcome inequality. Here we address...

Bit commitment is a fundamental cryptographic primitive in which Alice wishes to commit secret bit Bob. Perfectly secure between two mistrustful parties impossible through asynchronous exchange of quantum information. Perfect security however possible when and Bob each split into several agents exchanging classical information at times locations suitably chosen satisfy specific relativistic constraints. In this Letter we first revisit previously proposed scheme that realizes using only...

Quantum mechanics and the theory of gravity are presently not compatible. A particular question is whether causes decoherence - an unavoidable source noise. Several models for gravitational have been proposed, all which can be described quantum mechanically. In parallel, several experiments proposed to test some these models, where data obtained by such analyzed assuming mechanics. Since we may need modify account gravity, however, one validity using as a calculational tool draw conclusions...

The goal of two-party cryptography is to enable two parties, Alice and Bob, solve common tasks without the need for mutual trust. Examples such are private access a database, secure identification. Quantum communication enables security all these problems in noisy-storage model by sending more signals than adversary can store certain time frame. Here, we initiate study device-independent (DI) protocols model. Specifically, present relatively easy implement protocol cryptographic building...

Abstract In quantum mechanics performing a measurement is an invasive process which generally disturbs the system. Due to this phenomenon, there exist incompatible measurements, i.e. measurements that cannot be simultaneously performed on single copy of It then natural ask what most are. To answer question, several measures have been proposed quantify how set is, however their properties are not well-understood. work, we develop general framework encompasses all commonly used incompatibility...

We investigate how much randomness can be extracted from a generic partially entangled pure state of two qubits in device-independent setting, where Bell test is used to certify the correct functioning apparatus. For any such state, we first show that bits are always attainable both if projective measurements generate globally or nonprojective measurement locally. then prove maximum amount generated using restricted between approximately 3.58 and 3.96 bits. The upper limit rules out bound...

We investigate two-party cryptographic protocols that are secure under assumptions motivated by physics, namely special relativity and quantum mechanics.In particular, we discuss the security of bit commitment in so-called split models, i.e. models which at least one parties is not allowed to communicate during certain phases protocol.We find minimal splits necessary evade Mayers-Lo-Chau no-go argument present achieve these models.Furthermore, introduce notion local versus global command, a...

It is well known that observing nonlocal correlations allows us to draw conclusions about the quantum systems under consideration. In some cases this yields a characterisation which essentially complete, phenomenon as self-testing. Self-testing becomes particularly interesting if we can make statement robust, so it be applied real experimental setup. For simplest self-testing scenarios most robust bounds come from method based on operator inequalities. work elaborate idea and apply family of...

Quantum communication has demonstrated its usefulness for quantum cryptography far beyond key distribution. One domain is two-party cryptography, whose goal to allow two parties who may not trust each other solve joint tasks. Another interesting application position-based use the geographical location of an entity as only identifying credential. Unfortunately, security these protocols possible against all powerful adversary. However, if we impose some realistic physical constraints on...