Bell inequality violations correspond to behavior of entangled quantum systems that cannot be simulated classically. We give two new two-player games with are stronger, fully explicit, and arguably simpler than earlier work.The first game is based on the Hidden Matching problem communication complexity, introduced by Bar-Yossef, Jayram, Kerenidis. This can won probability 1 a strategy using maximally state local dimension n (e.g., log EPR-pairs), while we show winning any classical differs...

Tensor networks, widely used for providing efficient representations of low-energy states local quantum many-body systems, have been recently proposed as machine learning architectures which could present advantages with respect to traditional ones. In this work we show that tensor-network especially prospective properties privacy-preserving learning, is important in tasks such the processing medical records. First, describe a new privacy vulnerability feedforward neural illustrating it...

We introduce two generalizations of Kochen-Specker (KS) sets: projective KS sets and generalized sets. then use to characterize all graphs for which the chromatic number is strictly larger than quantum number. Here, defined via a nonlocal game based on graph coloring. further show that from any with separation between these quantities, one can construct classical channel entanglement assistance increases one-shot zero-error capacity. As an example, we exhibit new family channels exponential increase.

The quantum chromatic number of a graph $G$ is sandwiched between its and clique number, which are well known NP-hard quantities. We restrict our attention to the rank-1 $\chi_q^{(1)}(G)$, upper bounds but defined under stronger constraints. study relation with $\chi(G)$ minimum dimension orthogonal representations $\xi(G)$. It that $\xi(G) \leq \chi_q^{(1)}(G) \chi(G)$. answer three open questions about these relations: we give necessary sufficient condition have = \chi_q^{(1)}(G)$, exhibit...

Matrix product states and projected entangled pair (PEPS) are powerful analytical numerical tools to assess quantum many-body systems in one higher dimensions, respectively. While matrix comprehensively understood, PEPS fundamental questions, relevant analytically as well numerically, remain open, such how encode symmetries full generality, or stabilize methods using canonical forms. Here, we show that these key problems, a number of related algorithmically undecidable, is, they cannot be...

Entangled quantum systems can exhibit correlations that cannot be simulated classically. For historical reasons such are called “Bell inequality violations.” We give two new two-player games with Bell violations stronger, fully explicit, and arguably simpler than earlier work. The first game is based on the Hidden Matching problem of communication complexity, introduced by Bar-Yossef, Jayram, Kerenidis. This won probability 1 a strategy using maximally entangled state local dimension $n$...

We study the use of quantum entanglement in zero-error source-channel coding problem. Here, Alice and Bob are connected by a noisy classical one-way channel, given correlated inputs from random source. Their goal is for to learn Alice's input while using channel as little possible. In regime, optimal rates source codes graph parameters known Witsenhausen rate Shannon capacity, respectively. The Lov\'asz theta number, parameter defined semidefinite program, gives best efficiently-computable...

This paper presents, via an explicit example with a real-world dataset, hands-on introduction to the field of quantum machine learning (QML). We focus on case single qubit, using data re-uploading techniques. After discussion relevant background in computing and we provide thorough explanation models that consider, implement different proposed formulations toy datasets qiskit SDK. find that, as classical neural networks, number layers is determining factor final accuracy models. Moreover,...

Is the world quantum? An active research line in quantum foundations is devoted to exploring what constraints can rule out postquantum theories that are consistent with experimentally observed results. We explore this question context of epistemics, and ask whether agreement between observers serve as a physical principle must hold for any theory world. Aumann's seminal Agreement Theorem states two (of classical systems) cannot agree disagree. propose an extension theorem no-signaling...

The main goal of this master's thesis is to introduce Quantum Natural Language Processing (QNLP) in a way understandable by both the NLP engineer and quantum computing practitioner. QNLP recent application that aims at representing sentences' meaning as vectors encoded into computers. To achieve this, distributional words extended compositional sentences (DisCoCat model) : words' meanings are composed through syntactic structure sentence. This done using an algorithm based on tensor...

Tensor networks, widely used for providing efficient representations of low-energy states local quantum many-body systems, have been recently proposed as machine learning architectures which could present advantages with respect to traditional ones. In this work we show that tensor network especially prospective properties privacy-preserving learning, is important in tasks such the processing medical records. First, describe a new privacy vulnerability feedforward neural illustrating it...

We study the effects of quantum entanglement on performance two classical zero-error communication tasks among multiple parties. Both are generalizations two-party channel-coding problem, where a sender and receiver want to perfectly communicate messages through one-way noisy channel. If parties allowed share entanglement, there several positive results that show existence channels for which they can strictly more than what could do with resources. In first task, one wants common message...

We describe a construction that maps any connected graph G on three or more vertices into larger graph, H(G), whose independence number is strictly smaller than its Lovász which equal to fractional packing number. The of H(G) represent all possible events consistent with the stabilizer group state associated G, and exclusive are adjacent. Mathematically, corresponds orbit under local complementation. Physically, translates graph-theoretic terms connection between Bell inequality maximally...

We construct a non-locality game that can be won with certainty by quantum strategy using log n shared EPR-pairs, while any classical has winning probability at most 1/2+O(log n/sqrt{n}). This improves upon recent result of Junge et al. in number ways.

The Agreement Theorem Aumann (1976 Ann. Stat. 4 , 1236–1239. ( doi:10.1214/aos/1176343654 )) states that if two Bayesian agents start with a common prior, then they cannot have knowledge hold different posterior probabilities of some underlying event interest. In short, the ‘agree to disagree’. This result applies in classical domain where probability theory applies. But non-classical domains, such as quantum world, does not apply. Inspired principally by their use mechanics, we employ...