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Thomas Vidick - One of the best experts on this subject based on the ideXlab platform.
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three player entangled xor games are np hard to approximate
SIAM Journal on Computing, 2016Co-Authors: Thomas VidickAbstract:We show that for any $\varepsilon>0$ the problem of finding a factor $(2-\varepsilon)$ approximation to the entangled value of a three-player XOR game is NP-hard. Equivalently, the problem of approximating the largest possible quantum violation of a tripartite Bell correlation inequality to within any multiplicative constant is NP-hard. These results are the first constant-factor hardness of approximation results for entangled games or quantum violations of Bell inequalities shown under the sole assumption that P$\neq$NP. They can be thought of as an extension of H\aastad's optimal hardness of approximation results for MAX-E3-LIN2 [J. ACM, 48 (2001), pp. 798--859] to the entangled-player setting. The key Technical Component of our work is a soundness analysis of a plane-vs-point low-degree test against entangled players. This extends and simplifies the analysis of the multilinearity test by Ito and Vidick [Proceedings of the $53$rd FOCS, IEEE, Piscataway, NJ, 2012, pp. 243--252]. Our results demonstrate t...
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A parallel repetition theorem for entangled projection games
computational complexity, 2015Co-Authors: Irit Dinur, David Steurer, Thomas VidickAbstract:We study the behavior of the entangled value of two-player one-round projection games under parallel repetition. We show that for any projection game G of entangled value $${1- \epsilon < 1}$$ 1 - ϵ < 1 , the value of the k -fold repetition of G goes to zero as $${O((1-\epsilon^c)^k)}$$ O ( ( 1 - ϵ c ) k ) , for some universal constant $${c \geq 1}$$ c ≥ 1 . If furthermore the constraint graph of G is expanding, we obtain the optimal c = 1. Previously exponential decay of the entangled value under parallel repetition was only known for the case of XOR and unique games. To prove the theorem, we extend an analytical framework introduced by Dinur and Steurer for the study of the classical value of projection games under parallel repetition. Our proof, as theirs, relies on the introduction of a simple relaxation of the entangled value that is perfectly multiplicative. The main Technical Component of the proof consists in showing that the relaxed value remains tightly connected to the entangled value, thereby establishing the parallel repetition theorem. More generally, we obtain results on the behavior of the entangled value under products of arbitrary (not necessarily identical) projection games. Relating our relaxed value to the entangled value is done by giving an algorithm for converting a relaxed variant of quantum strategies that we call “vector quantum strategy” to a quantum strategy. The algorithm is considerably simpler in case the bipartite distribution of questions in the game has good expansion properties. When this is not the case, the algorithm relies on a quantum analogue of Holenstein’s correlated sampling lemma which may be of independent interest. Our “quantum correlated sampling lemma” generalizes results of van Dam and Hayden on universal embezzlement to the following approximate scenario: two non-communicating parties, given classical descriptions of bipartite states $${|{\psi}\rangle, |{\varphi}\rangle}$$ | ψ ⟩ , | φ ⟩ , respectively, such that $${|{\psi}\rangle \approx |{\varphi}\rangle}$$ | ψ ⟩ ≈ | φ ⟩ , are able to locally generate a joint entangled state $${|{\Psi}\rangle \approx |{\psi}\rangle \approx |{\varphi}\rangle}$$ | Ψ ⟩ ≈ | ψ ⟩ ≈ | φ ⟩ using an initial entangled state that is independent of their inputs.
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three player entangled xor games are np hard to approximate
Foundations of Computer Science, 2013Co-Authors: Thomas VidickAbstract:We show that for any e > 0 the problem of finding a factor (2 - e) approximation to the entangled value of a three-player XOR game is NP-hard. Equivalently, the problem of approximating the largest possible quantum violation of a tripartite Bell correlation inequality to within any multiplicative constant is NP-hard. These results are the first constant-factor hardness of approximation results for entangled games or quantum violations of Bell inequalities shown under the sole assumption that P≠NP. They can be thought of as an extension of Hastad's optimal hardness of approximation results for MAX-E3-LIN2 (JACM'01) to the entangled-player setting. The key Technical Component of our work is a soundness analysis of a point-vs-plane low-degree test against entangled players. This extends and simplifies the analysis of the multilinearity test by Ito and Vidick (FOCS'12). Our results demonstrate the possibility for efficient reductions between entangled-player games and our techniques may lead to further hardness of approximation results.
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a parallel repetition theorem for entangled projection games
arXiv: Quantum Physics, 2013Co-Authors: Irit Dinur, David Steurer, Thomas VidickAbstract:We study the behavior of the entangled value of two-player one-round projection games under parallel repetition. We show that for any projection game $G$ of entangled value 1-eps < 1, the value of the $k$-fold repetition of G goes to zero as O((1-eps^c)^k), for some universal constant c\geq 1. Previously parallel repetition with an exponential decay in $k$ was only known for the case of XOR and unique games. To prove the theorem we extend an analytical framework recently introduced by Dinur and Steurer for the study of the classical value of projection games under parallel repetition. Our proof, as theirs, relies on the introduction of a simple relaxation of the entangled value that is perfectly multiplicative. The main Technical Component of the proof consists in showing that the relaxed value remains tightly connected to the entangled value, thereby establishing the parallel repetition theorem. More generally, we obtain results on the behavior of the entangled value under products of arbitrary (not necessarily identical) projection games. Relating our relaxed value to the entangled value is done by giving an algorithm for converting a relaxed variant of quantum strategies that we call "vector quantum strategy" to a quantum strategy. The algorithm is considerably simpler in case the bipartite distribution of questions in the game has good expansion properties. When this is not the case, rounding relies on a quantum analogue of Holenstein's correlated sampling lemma which may be of independent interest. Our "quantum correlated sampling lemma" generalizes results of van Dam and Hayden on universal embezzlement.
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three player entangled xor games are np hard to approximate
arXiv: Quantum Physics, 2013Co-Authors: Thomas VidickAbstract:We show that for any eps>0 the problem of finding a factor (2-eps) approximation to the entangled value of a three-player XOR game is NP-hard. Equivalently, the problem of approximating the largest possible quantum violation of a tripartite Bell correlation inequality to within any multiplicative constant is NP-hard. These results are the first constant-factor hardness of approximation results for entangled games or quantum violations of Bell inequalities shown under the sole assumption that P \neq NP. They can be thought of as an extension of Hastad's optimal hardness of approximation results for MAX-E3-LIN2 (JACM'01) to the entangled-player setting. The key Technical Component of our work is a soundness analysis of a point-vs-plane low-degree test against entangled players. This extends and simplifies the analysis of the multilinearity test by Ito and Vidick (FOCS'12). Our results demonstrate the possibility for efficient reductions between entangled-player games and our techniques may lead to further hardness of approximation results.
Irit Dinur - One of the best experts on this subject based on the ideXlab platform.
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A parallel repetition theorem for entangled projection games
computational complexity, 2015Co-Authors: Irit Dinur, David Steurer, Thomas VidickAbstract:We study the behavior of the entangled value of two-player one-round projection games under parallel repetition. We show that for any projection game G of entangled value $${1- \epsilon < 1}$$ 1 - ϵ < 1 , the value of the k -fold repetition of G goes to zero as $${O((1-\epsilon^c)^k)}$$ O ( ( 1 - ϵ c ) k ) , for some universal constant $${c \geq 1}$$ c ≥ 1 . If furthermore the constraint graph of G is expanding, we obtain the optimal c = 1. Previously exponential decay of the entangled value under parallel repetition was only known for the case of XOR and unique games. To prove the theorem, we extend an analytical framework introduced by Dinur and Steurer for the study of the classical value of projection games under parallel repetition. Our proof, as theirs, relies on the introduction of a simple relaxation of the entangled value that is perfectly multiplicative. The main Technical Component of the proof consists in showing that the relaxed value remains tightly connected to the entangled value, thereby establishing the parallel repetition theorem. More generally, we obtain results on the behavior of the entangled value under products of arbitrary (not necessarily identical) projection games. Relating our relaxed value to the entangled value is done by giving an algorithm for converting a relaxed variant of quantum strategies that we call “vector quantum strategy” to a quantum strategy. The algorithm is considerably simpler in case the bipartite distribution of questions in the game has good expansion properties. When this is not the case, the algorithm relies on a quantum analogue of Holenstein’s correlated sampling lemma which may be of independent interest. Our “quantum correlated sampling lemma” generalizes results of van Dam and Hayden on universal embezzlement to the following approximate scenario: two non-communicating parties, given classical descriptions of bipartite states $${|{\psi}\rangle, |{\varphi}\rangle}$$ | ψ ⟩ , | φ ⟩ , respectively, such that $${|{\psi}\rangle \approx |{\varphi}\rangle}$$ | ψ ⟩ ≈ | φ ⟩ , are able to locally generate a joint entangled state $${|{\Psi}\rangle \approx |{\psi}\rangle \approx |{\varphi}\rangle}$$ | Ψ ⟩ ≈ | ψ ⟩ ≈ | φ ⟩ using an initial entangled state that is independent of their inputs.
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a parallel repetition theorem for entangled projection games
arXiv: Quantum Physics, 2013Co-Authors: Irit Dinur, David Steurer, Thomas VidickAbstract:We study the behavior of the entangled value of two-player one-round projection games under parallel repetition. We show that for any projection game $G$ of entangled value 1-eps < 1, the value of the $k$-fold repetition of G goes to zero as O((1-eps^c)^k), for some universal constant c\geq 1. Previously parallel repetition with an exponential decay in $k$ was only known for the case of XOR and unique games. To prove the theorem we extend an analytical framework recently introduced by Dinur and Steurer for the study of the classical value of projection games under parallel repetition. Our proof, as theirs, relies on the introduction of a simple relaxation of the entangled value that is perfectly multiplicative. The main Technical Component of the proof consists in showing that the relaxed value remains tightly connected to the entangled value, thereby establishing the parallel repetition theorem. More generally, we obtain results on the behavior of the entangled value under products of arbitrary (not necessarily identical) projection games. Relating our relaxed value to the entangled value is done by giving an algorithm for converting a relaxed variant of quantum strategies that we call "vector quantum strategy" to a quantum strategy. The algorithm is considerably simpler in case the bipartite distribution of questions in the game has good expansion properties. When this is not the case, rounding relies on a quantum analogue of Holenstein's correlated sampling lemma which may be of independent interest. Our "quantum correlated sampling lemma" generalizes results of van Dam and Hayden on universal embezzlement.
David Steurer - One of the best experts on this subject based on the ideXlab platform.
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A parallel repetition theorem for entangled projection games
computational complexity, 2015Co-Authors: Irit Dinur, David Steurer, Thomas VidickAbstract:We study the behavior of the entangled value of two-player one-round projection games under parallel repetition. We show that for any projection game G of entangled value $${1- \epsilon < 1}$$ 1 - ϵ < 1 , the value of the k -fold repetition of G goes to zero as $${O((1-\epsilon^c)^k)}$$ O ( ( 1 - ϵ c ) k ) , for some universal constant $${c \geq 1}$$ c ≥ 1 . If furthermore the constraint graph of G is expanding, we obtain the optimal c = 1. Previously exponential decay of the entangled value under parallel repetition was only known for the case of XOR and unique games. To prove the theorem, we extend an analytical framework introduced by Dinur and Steurer for the study of the classical value of projection games under parallel repetition. Our proof, as theirs, relies on the introduction of a simple relaxation of the entangled value that is perfectly multiplicative. The main Technical Component of the proof consists in showing that the relaxed value remains tightly connected to the entangled value, thereby establishing the parallel repetition theorem. More generally, we obtain results on the behavior of the entangled value under products of arbitrary (not necessarily identical) projection games. Relating our relaxed value to the entangled value is done by giving an algorithm for converting a relaxed variant of quantum strategies that we call “vector quantum strategy” to a quantum strategy. The algorithm is considerably simpler in case the bipartite distribution of questions in the game has good expansion properties. When this is not the case, the algorithm relies on a quantum analogue of Holenstein’s correlated sampling lemma which may be of independent interest. Our “quantum correlated sampling lemma” generalizes results of van Dam and Hayden on universal embezzlement to the following approximate scenario: two non-communicating parties, given classical descriptions of bipartite states $${|{\psi}\rangle, |{\varphi}\rangle}$$ | ψ ⟩ , | φ ⟩ , respectively, such that $${|{\psi}\rangle \approx |{\varphi}\rangle}$$ | ψ ⟩ ≈ | φ ⟩ , are able to locally generate a joint entangled state $${|{\Psi}\rangle \approx |{\psi}\rangle \approx |{\varphi}\rangle}$$ | Ψ ⟩ ≈ | ψ ⟩ ≈ | φ ⟩ using an initial entangled state that is independent of their inputs.
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a parallel repetition theorem for entangled projection games
arXiv: Quantum Physics, 2013Co-Authors: Irit Dinur, David Steurer, Thomas VidickAbstract:We study the behavior of the entangled value of two-player one-round projection games under parallel repetition. We show that for any projection game $G$ of entangled value 1-eps < 1, the value of the $k$-fold repetition of G goes to zero as O((1-eps^c)^k), for some universal constant c\geq 1. Previously parallel repetition with an exponential decay in $k$ was only known for the case of XOR and unique games. To prove the theorem we extend an analytical framework recently introduced by Dinur and Steurer for the study of the classical value of projection games under parallel repetition. Our proof, as theirs, relies on the introduction of a simple relaxation of the entangled value that is perfectly multiplicative. The main Technical Component of the proof consists in showing that the relaxed value remains tightly connected to the entangled value, thereby establishing the parallel repetition theorem. More generally, we obtain results on the behavior of the entangled value under products of arbitrary (not necessarily identical) projection games. Relating our relaxed value to the entangled value is done by giving an algorithm for converting a relaxed variant of quantum strategies that we call "vector quantum strategy" to a quantum strategy. The algorithm is considerably simpler in case the bipartite distribution of questions in the game has good expansion properties. When this is not the case, rounding relies on a quantum analogue of Holenstein's correlated sampling lemma which may be of independent interest. Our "quantum correlated sampling lemma" generalizes results of van Dam and Hayden on universal embezzlement.
James S. Harrop - One of the best experts on this subject based on the ideXlab platform.
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simulated spinal cerebrospinal fluid leak repair an educational model with didactic and Technical Components
Neurosurgery, 2013Co-Authors: George M. Ghobrial, Rohan Chitale, Darlene A. Lobel, Paul A Anderson, Peter G Campbell, James S. HarropAbstract:BACKGROUND: In the era of surgical resident work hour restrictions, the traditional apprenticeship model may provide fewer hours for neurosurgical residents to hone Technical skills. Spinal dura mater closure or repair is 1 skill that is infrequently encountered, and persistent cerebrospinal fluid leaks are a potential morbidity. OBJECTIVE: To establish an educational curriculum to train residents in spinal dura mater closure with a novel durotomy repair model. METHODS: The Congress of Neurological Surgeons has developed a simulation-based model for durotomy closure with the ongoing efforts of their simulation educational committee. The core curriculum consists of didactic training materials and a Technical simulation model of dural repair for the lumbar spine. RESULTS: Didactic pretest scores ranged from 4/11 (36%) to 10/11 (91%). Posttest scores ranged from 8/11 (73%) to 11/11 (100%). Overall, didactic improvements were demonstrated by all participants, with a mean improvement between pre- and posttest scores of 1.17 (18.5%; P = .02). The Technical Component consisted of 11 durotomy closures by 6 participants, where 4 participants performed multiple durotomies. Mean time to closure of the durotomy ranged from 490 to 546 seconds in the first and second closures, respectively (P = .66), whereby the median leak rate improved from 14 to 7 (P = .34). There were also demonstrative Technical improvements by all. CONCLUSION: Simulated spinal dura mater repair appears to be a potentially valuable tool in the education of neurosurgery residents. The combination of a didactic and Technical assessment appears to be synergistic in terms of educational development.
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a didactic and hands on module enhances resident microsurgical knowledge and Technical skill
Neurosurgery, 2013Co-Authors: Tarek El Y Ahmadieh, James S. Harrop, Salah G Aoun, Najib El E Tecle, Allan D Nanney, Marc R Daou, Hunt H Batjer, Bernard R BendokAbstract:BACKGROUND Simulation has been adopted as a powerful training tool in many areas of health care. However, it has not yet been systematically embraced in neurosurgery because of the absence of validated tools, assessment scales, and curricula. OBJECTIVE To use our validated microanastomosis module and scale to evaluate the effects of an educational intervention on the performance of neurosurgery residents at the 2012 Congress of Neurological Surgeons Annual Meeting. METHODS The module consisted of an end-to-end microanastomosis of a 3-mm vessel and was divided into 3 phases: (1) a cognitive and microsuture prelecture testing phase, (2) a didactic lecture, and (3) a cognitive and microsuture postlecture testing phase. We compared resident knowledge and Technical proficiency from the pretesting and posttesting phases. RESULTS One neurosurgeon and 7 neurosurgery residents participated in the study. None had previous experience in microsurgery. The average score on the microsuture prelecture and postlecture tests, as measured by our assessment scale, was 32.50 and 39.75, respectively (P = .001). The number of completed sutures at the end of each procedure was higher for 75% of participants in the postlecture testing phase (P = .03). The average score on the cognitive postlecture test (12.75) was significantly better than that of the cognitive prelecture test (8.38; P = .001). CONCLUSION Simulation has the potential to enhance resident education and to elevate proficiency levels. Our data suggest that a focused microsurgical module that incorporates a didactic Component and a Technical Component can enhance resident knowledge and Technical proficiency in microsurgical anastomosis.
Gary S Rose - One of the best experts on this subject based on the ideXlab platform.
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toward a theory of motivational interviewing
American Psychologist, 2009Co-Authors: William R Miller, Gary S RoseAbstract:The widely disseminated clinical method of motivational interviewing (MI) arose through a convergence of science and practice. Beyond a large base of clinical trials, advances have been made toward "looking under the hood" of MI to understand the underlying mechanisms by which it affects behavior change. Such specification of outcome-relevant aspects of practice is vital to theory development and can inform both treatment delivery and clinical training. An emergent theory of MI is proposed that emphasizes two specific active Components: a relational Component focused on empathy and the interpersonal spirit of MI, and a Technical Component involving the differential evocation and reinforcement of client change talk. A resulting causal chain model links therapist training, therapist and client responses during treatment sessions, and posttreatment outcomes.
