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Consequences and Limits of Nonlocal Strategies
, 2010
"... Thispaperinvestigatesthepowersandlimitationsofquantum entanglementinthecontext of cooperative games of incomplete information. We give several examples of such nonlocal games where strategies that make use of entanglement outperform all possible classical strategies. One implication ofthese examples ..."
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Cited by 120 (20 self)
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Thispaperinvestigatesthepowersandlimitationsofquantum entanglementinthecontext of cooperative games of incomplete information. We give several examples of such nonlocal games where strategies that make use of entanglement outperform all possible classical strategies. One implication ofthese examplesis that entanglement canprofoundly affectthesoundness property of twoprover interactive proof systems. We then establish limits on the probability with which strategies making use of entanglement can win restricted types of nonlocal games. These upperbounds mayberegardedasgeneralizationsof Tsirelsontypeinequalities, which place bounds on the extent to which quantum information can allow for the violation of Bell inequalities. We also investigate the amount of entanglement required by optimal and nearly optimal quantum strategies forsome games.
Polynomialspace approximation of nosignaling provers
 In 37th international colloquium conference on Automata, languages and programming (ICALP
, 2010
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Tsirelson’s Problem
, 2008
"... The situation of two independent observers conducting measurements on a joint quantum system is usually modelled using a Hilbert space of tensor product form, each factor associated to one observer. Correspondingly, the operators describing the observables are then acting nontrivially only on one t ..."
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Cited by 7 (1 self)
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The situation of two independent observers conducting measurements on a joint quantum system is usually modelled using a Hilbert space of tensor product form, each factor associated to one observer. Correspondingly, the operators describing the observables are then acting nontrivially only on one tensor factor. However, the same situation can also be modelled by just using one joint Hilbert space, and requiring that all two operators associated to different observers commute, i.e. are jointly measurable without causing disturbance. The problem of Tsirelson is now to decide the question whether all quantum correlation functions between two independent observers derived from by commuting observables can also be expressed using observables defined on a Hilbert space of tensor product form. Tsirelson showed already that the distinction is irrelevant in the case that the ambient Hilbert space is of finite dimension [17]. We show here that the problem is equivalent to the question whether all quantum correlation functions can be approximated by correlation function derived form finitedimensional systems. We also discuss some physical examples which fulfill this requirement. 1 1
Abstract
, 2007
"... The central question in quantum multiprover interactive proof systems is whether or not entanglement shared between provers affects the verification power of the proof system. We study for the first time positive aspects of prior entanglement and show that entanglement is useful even for honest pro ..."
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The central question in quantum multiprover interactive proof systems is whether or not entanglement shared between provers affects the verification power of the proof system. We study for the first time positive aspects of prior entanglement and show that entanglement is useful even for honest provers. We show how to use shared entanglement to parallelize any multiprover quantum interactive proof system to a oneround system with perfect completeness, with one extra prover. Alternatively, we can also parallelize to a threeturn system with the same number of provers, where the verifier only broadcasts the outcome of a coin flip. This “publiccoin ” property is somewhat surprising, since in the classical case publiccoin multiprover interactive proofs are equivalent to single prover ones.
PolynomialSpace Approximation of NoSignaling Provers Tsuyoshi Ito
, 908
"... In twoprover oneround interactive proof systems, nosignaling provers are those who are allowed to use arbitrary strategies, not limited to local operations, as long as their strategies cannot be used for communication between them. Study of multiprover interactive proof systems with nosignaling ..."
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In twoprover oneround interactive proof systems, nosignaling provers are those who are allowed to use arbitrary strategies, not limited to local operations, as long as their strategies cannot be used for communication between them. Study of multiprover interactive proof systems with nosignaling provers is motivated by study of those with provers sharing quantum states. The relation between them is that nosignaling strategies include all the strategies realizable by provers sharing arbitrary entangled quantum states, and more. This paper shows that twoprover oneround interactive proof systems with nosignaling provers only accept languages in PSPACE. Combined with the protocol for PSPACE by Ito, Kobayashi and Matsumoto (CCC 2009), this implies MIP ns (2, 1) = PSPACE, where MIP ns (2, 1) is the class of languages having a twoprover oneround interactive proof system with nosignaling provers. The proof uses the fast parallel algorithm for the mixed packing and covering problem by Young (FOCS 2001). 1
Oracularization and TwoProver OneRound Interactive Proofs against Nonlocal Strategies
, 2008
"... A central problem in quantum computational complexity is how to prevent entanglementassisted cheating in multiprover interactive proof systems. It is wellknown that the standard oracularization technique completely fails in some proof systems under the existence of prior entanglement. This paper ..."
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A central problem in quantum computational complexity is how to prevent entanglementassisted cheating in multiprover interactive proof systems. It is wellknown that the standard oracularization technique completely fails in some proof systems under the existence of prior entanglement. This paper studies two constructions of twoprover oneround interactive proof systems based on oracularization. First, it is proved that the twoprover oneround interactive proof system for PSPACE by Cai, Condon, and Lipton still achieves exponentially small soundness error in the existence of prior entanglement between dishonest provers (and more strongly, even if dishonest provers are allowed to use arbitrary nosignaling strategies). It follows that, unless the polynomialtime hierarchy collapses to the second level, twoprover systems are still advantageous to singleprover systems even when only malicious provers can use quantum information. Second, it is proved that the twoprover oneround interactive proof system obtained by oracularizing a threequery probabilistically checkable proof system becomes sound in a weak sense even against dishonest entangled provers with the help of a dummy question. As a consequence, every language in NEXP has a twoprover oneround interactive proof system of perfect completeness, albeit with exponentially small gap between completeness and soundness, in which each prover responds with only two bits. In other words, it is NPhard to approximate within an inversepolynomial the value
c © Rinton Press ENTANGLEMENTRESISTANT TWOPROVER INTERACTIVE PROOF SYSTEMS AND NONADAPTIVE PIR’S
, 2008
"... We show that every language in NP is recognized by a twoprover interactive proof system with the following properties. The proof system is entanglementresistant (i.e., its soundness is robust against provers who have prior shared entanglement), it has one round of interaction, the provers ’ answer ..."
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We show that every language in NP is recognized by a twoprover interactive proof system with the following properties. The proof system is entanglementresistant (i.e., its soundness is robust against provers who have prior shared entanglement), it has one round of interaction, the provers ’ answers are single bits, and the completenesssoundness gap is constant (formally, NP ⊆ ⊕MIP∗1−ε,1/2+ε[2], for any ε such that 0 < ε < 1/4). Our result is based on the “oracularizing ” property of a particular private information retrieval scheme (PIR), and it suggests that investigating related properties of other PIRs might bear further fruit.