PPT-Ph/CS 219A Quantum Computation Lecture 6. Bell Inequalities

1 Ph CS 219A Quantum Computation Lecture 6 Bell Inequalities Today we start a new topic We will explore more deeply how quantum correlations are different from classical ones Two parties in different laboratories who share quantum entanglement but are unable to communicate can perform tasks which would be impossible without the shared entanglement . 1 Introduction Quantum computation is a revolutionary idea that has fundamentally transformed our notion of feasible compu tation The most dramatic example of the power of quan tum algorithms was exhibited in Shors celebrated quan tum algorithms for Does Bell’s theorem prevent the use of causal explanations in quantum mechanics?. Part I:. Locality, Bell’s version of locality, and its discontents. The greatest mystery in science?. Locality. = “things do not go faster than . Collection of two-state quantum systems (. qubits. ). Operations which manipulate isolated . qubits. or pairs of . qubits. Initialise. . qubit. to . single state. Detect . qubit. state. Large scale device:. photons. and . without the fair-sampling assumption. Foundations of Physics 2013. LMU Munich, Germany. 30 July . 2013. Johannes Kofler. Max Planck Institute of Quantum Optics (MPQ). Garching / Munich, Germany. MAS 725. Hartmut. . Klauck. NTU. 12.3.2012. Topics . today. Superdense. . coding. Distinguishing quantum states. Bell . inequalities. Superdense Coding. Alice . has two . b. its of classical information she wants to send to Bob. Mark Williamson. m. ark.williamson@wofson.ox.ac.uk. 10.06.10. The Quantum . T. heory of Information and Computation. http://www.comlab.ox.ac.uk/activities/quantum/course/. Aims of lecture. Local hidden variable theories can be experimentally falsified.. By: Miles H. Taylor. The EPR Paradox. In 1935, physicists Albert Einstein, Boris . Podolsky. , and Nathan Rosen created a thought experiment that was supposed to show a lack of completeness in quantum mechanics, a relatively recent creation at the time. The thought experiment, later called the EPR paradox after the last names of the creators, was based upon a paradox they saw in the quantum entanglement idea of quantum mechanics regarding the fact that one cannot know observables from different sets. They began by imagining two physical systems that interact when created, so that they will be defined by a single quantum state (Blanton). In other words, one must begin by imagining two entangled particles. Even when separated, the two systems will still be described by the same wave function, no matter the distance between them, as they are still entangled. If someone measures an observable, such as the spin if the systems are photons, of one system, it “will immediately determine the measurement of the corresponding observable in the second system” (Blanton). This applies even at distances that special relativity should prohibit. Imagine that the two systems are light-years apart. According to quantum mechanics, measuring an observable in the first system forces the corresponding observable in the other system into a well-defined state immediately, despite the fact that they are not close enough to have an effect on one another. The information between the two has passed much too fast for the distance under the theory of relativity. This left two options for Einstein, . Computers in a weird universe. Patrick Rall. Ph70. May 10, 2016. Advertising. “I laughed, I cried, I fell off my chair - and I was just reading the chapter on computational complexity … How is it possible for a serious book … to be so ridiculously entertaining?”. Michael Freedman. April 23, 2009. Parsa Bonderson. Adrian Feiguin. Matthew Fisher. Michael Freedman. Matthew Hastings. Ribhu Kaul. Scott Morrison. Chetan Nayak. Simon Trebst. Kevin Walker. Zhenghan Wang. Dung Nguyen. Chicago 19. th. January. Content. Motivation . Quantum bit (qubit) vs Classical bit (bit). Quantum Computation . Quantum Communication. Conclusion. Motivation. The end of Moore’s law scaling in silicon (because of quantum effects of particle at scale smaller than 7nm).. ideas. CS 498: Spring 2017. Amit, Elena, & Sole. Next-generation computing paradigms. The . Defense Advanced Research Projects Agency (DARPA). . “... . i. n . recent years even the best computer architectures haven’t been able to keep up with demand for the kind of simulation processing power needed to handle exceedingly complex design optimization and related problems.. Solving Inequalities . Rules for . S. olving . Inequalities . The goal of an . inequality. . is to get the variable by itself . Use same rules as equations . 1 exception . If dividing or multiplying by a negative number you must switch the inequality . By: Miles H. Taylor. The EPR Paradox. In 1935, physicists Albert Einstein, Boris . Podolsky. , and Nathan Rosen created a thought experiment that was supposed to show a lack of completeness in quantum mechanics, a relatively recent creation at the time. The thought experiment, later called the EPR paradox after the last names of the creators, was based upon a paradox they saw in the quantum entanglement idea of quantum mechanics regarding the fact that one cannot know observables from different sets. They began by imagining two physical systems that interact when created, so that they will be defined by a single quantum state (Blanton). In other words, one must begin by imagining two entangled particles. Even when separated, the two systems will still be described by the same wave function, no matter the distance between them, as they are still entangled. If someone measures an observable, such as the spin if the systems are photons, of one system, it “will immediately determine the measurement of the corresponding observable in the second system” (Blanton). This applies even at distances that special relativity should prohibit. Imagine that the two systems are light-years apart. According to quantum mechanics, measuring an observable in the first system forces the corresponding observable in the other system into a well-defined state immediately, despite the fact that they are not close enough to have an effect on one another. The information between the two has passed much too fast for the distance under the theory of relativity. This left two options for Einstein, . ----a critical evaluation. Rui. Xian(Patrick. ). D. W. Leung, et al., Efficient implementation of coupled logic gates for quantum computation, Phys. Rev. A, 61, 042310(2000). CO781, July 2010. . Outline.