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Register a new userProgramming Telepathy: Implementing Quantum Non-Locality Games
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Quantum pseudo-telepathy is an intriguing phenomenon which results from the application of quantum information theory to communication complexity. To demonstrate this phenomenon researchers in the field of quantum communication complexity devised a number of quantum non-locality games. The setting of these games is as follows: the players are separated so that no communication between them is possible and are given a certain computational task. When the players have access to a quantum resource called entanglement, they can accomplish the task: something that is impossible in a classical setting. To an observer who is unfamiliar with the laws of quantum mechanics it seems that the players employ some sort of telepathy; that is, they somehow exchange information without sharing a communication channel. This paper provides a formal framework for specifying, implementing, and analysing quantum non-locality games.
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This paper describes a quantum programming environment, named $Q|SIrangle$. It is a platform embedded in the .Net language that supports quantum programming using a quantum extension of the $mathbf{while}$-language. The framework of the platform includes a compiler of the quantum $mathbf{while}$-language and a suite of tools for simulating quantum computation, optimizing quantum circuits, and analyzing and verifying quantum programs. Throughout the paper, using $Q|SIrangle$ to simulate quantum behaviors on classical platforms with a combination of components is demonstrated. The scalable framework allows the user to program customized functions on the platform. The compiler works as the core of $Q|SIrangle$ bridging the gap from quantum hardware to quantum software. The built-in decomposition algorithms enable the universal quantum computation on the present quantum hardware.
With the potential of quantum algorithms to solve intractable classical problems, quantum computing is rapidly evolving and more algorithms are being developed and optimized. Expressing these quantum algorithms using a high-level language and making them executable on a quantum processor while abstracting away hardware details is a challenging task. Firstly, a quantum programming language should provide an intuitive programming interface to describe those algorithms. Then a compiler has to transform the program into a quantum circuit, optimize it and map it to the target quantum processor respecting the hardware constraints such as the supported quantum operations, the qubit connectivity, and the control electronics limitations. In this paper, we propose a quantum programming framework named OpenQL, which includes a high-level quantum programming language and its associated quantum compiler. We present the programming interface of OpenQL, we describe the different layers of the compiler and how we can provide portability over different qubit technologies. Our experiments show that OpenQL allows the execution of the same high-level algorithm on two different qubit technologies, namely superconducting qubits and Si-Spin qubits. Besides the executable code, OpenQL also produces an intermediate quantum assembly code (cQASM), which is technology-independent and can be simulated using the QX simulator.
We implemented the protocol of entanglement assisted orientation in the space proposed by Brukner et al (quant-ph/0603167). We used min-max principle to evaluate the optimal entangled state and the optimal direction of polarization measurements which violate the classical bound.
Non-contextuality (NC) and Bell inequalities can be expressed as bounds $Omega$ for positive linear combinations $S$ of probabilities of events, $S leq Omega$. Exclusive events in $S$ can be represented as adjacent vertices of a graph called the exclusivity graph of $S$. In the case that events correspond to the outcomes of quantum projective measurements, quantum probabilities are intimately related to the Grotschel-Lovasz-Schrijver theta body of the exclusivity graph. Then, one can easily compute an upper bound to the maximum quantum violation of any NC or Bell inequality by optimizing $S$ over the theta body and calculating the Lovasz number of the corresponding exclusivity graph. In some cases, this upper bound is tight and gives the exact maximum quantum violation. However, in general, this is not the case. The reason is that the exclusivity graph does not distinguish among the different ways exclusivity can occur in Bell-inequality (and similar) scenarios. An interesting question is whether there is a graph-theoretical concept which accounts for this problem. Here we show that, for any given $N$-partite Bell inequality, an edge-coloured multigraph composed of $N$ single-colour graphs can be used to encode the relationships of exclusivity between each partys parts of the events. Then, the maximum quantum violation of the Bell inequality is exactly given by a refinement of the Lovasz number that applies to these edge-coloured multigraphs. We show how to calculate upper bounds for this number using a hierarchy of semi-definite programs and calculate upper bounds for $I_3$, $I_{3322}$ and the three bipartite Bell inequalities whose exclusivity graph is a pentagon. The multigraph-theoretical approach introduced here may remove some obstacles in the program of explaining quantum correlations from first principles.
It is shown that the possibility of using Maxwell demon to cheating in quantum non-locality tests is prohibited by the Landauers erasure principle.
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