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37
Polynomial time quantum computation with advice
 Inform. Proc. Lett., 90:195–204, 2003. ECCC
"... Abstract. Advice is supplementary information that enhances the computational power of an underlying computation. This paper focuses on advice that is given in the form of a pure quantum state. The notion of advised quantum computation has a direct connection to nonuniform quantum circuits and tall ..."
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Abstract. Advice is supplementary information that enhances the computational power of an underlying computation. This paper focuses on advice that is given in the form of a pure quantum state. The notion of advised quantum computation has a direct connection to nonuniform quantum circuits and tally languages. The paper examines the influence of such advice on the behaviors of an underlying polynomialtime quantum computation with boundederror probability and shows a power and a limitation of advice. Key Words: computational complexity, quantum circuit, advice function 1
Certifiable quantum dice  or, true random number generation . . . (Extended Anstract)
"... We introduce a protocol through which a pair of quantum mechanical devices may be used to generate n bits that are εclose in statistical distance from n uniformly distributed bits, starting from a seed of O(lognlog1/ε) uniform bits. The bits generated are certifiably random based only on a simple s ..."
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We introduce a protocol through which a pair of quantum mechanical devices may be used to generate n bits that are εclose in statistical distance from n uniformly distributed bits, starting from a seed of O(lognlog1/ε) uniform bits. The bits generated are certifiably random based only on a simple statistical test that can be performed by the user, and on the assumption that the devices do not communicate in the middle of each phase of the protocol. No other assumptions are placed on the devices’ inner workings. A modified protocol uses a seed of O(log 3 n) uniformly random bits to generate n bits that are poly −1 (n)indistinguishable from uniform even from the point of view of a quantum adversary who may have had prior access to the devices, and may be entangled with them.
Improved constructions of quantum automata
, 805
"... Abstract. We present a simple construction of quantum automata which achieve an exponential advantage over classical finite automata. Our automata use 4 log 2p + O(1) states to recognize a language that requires ǫ p states classically. The construction is both substantially simpler and achieves a be ..."
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Abstract. We present a simple construction of quantum automata which achieve an exponential advantage over classical finite automata. Our automata use 4 log 2p + O(1) states to recognize a language that requires ǫ p states classically. The construction is both substantially simpler and achieves a better constant in the front of log p than the previously known construction of [2]. Similarly to [2], our construction is by a probabilistic argument. We consider the possibility to derandomize it and present some results in this direction. 1
(4,1)quantum random access coding does not exist—one qubit is not enough to recover one of four bits,”
 New J. Phys.,
, 2006
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Short seed extractors against quantum storage
, 2008
"... Some, but not all, extractors resist adversaries with limited quantum storage. In this paper we show that Trevisan’s extractor has this property, thereby showing an extractor against quantum storage with logarithmic seed length. 1 ..."
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Some, but not all, extractors resist adversaries with limited quantum storage. In this paper we show that Trevisan’s extractor has this property, thereby showing an extractor against quantum storage with logarithmic seed length. 1
Optimal direct sum and privacy tradeoff results for quantum and classical communication complexity
 CoRR
"... Abstract. We show optimal Direct Sum result for the oneway entanglementassisted quantum communication complexity for any relation f ⊆ X × Y × Z. We show: Q 1,pub (f ⊕m) = Ω(m · Q 1,pub (f)), where Q 1,pub (f), represents the oneway entanglementassisted quantum communication complexity of f with ..."
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Abstract. We show optimal Direct Sum result for the oneway entanglementassisted quantum communication complexity for any relation f ⊆ X × Y × Z. We show: Q 1,pub (f ⊕m) = Ω(m · Q 1,pub (f)), where Q 1,pub (f), represents the oneway entanglementassisted quantum communication complexity of f with error at most 1/3 and f ⊕m represents mcopies of f. Similarly for the oneway publiccoin classical communication complexity we show: R 1,pub (f ⊕m) = Ω(m · R 1,pub (f)), where R 1,pub (f), represents the oneway publiccoin classical communication complexity of f with error at most 1/3. We show similar optimal Direct Sum results for the Simultaneous Message Passing (SMP) quantum and classical models. For twoparty twoway protocols we present optimal Privacy Tradeoff results leading to a Weak Direct Sum result for such protocols. We show our Direct Sum and Privacy Tradeoff results via message compression arguments. These arguments also imply a new round elimination lemma in quantum communication, which allows us to extend classical lower bounds on the cell probe complexity of some data structure problems, e.g. Approximate Nearest Neighbor Searching (ANN) on the Hamming cube {0, 1} n and Predecessor Search to the quantum setting. In a separate result we show that Newman’s [New91] technique of reducing the number of publiccoins in a classical protocol cannot be lifted to the quantum setting. We do this by defining a general notion of blackbox reduction of prior entanglement that subsumes Newman’s technique. We prove that such a blackbox reduction is impossible for quantum protocols by exhibiting a particular oneround quantum protocol for the Equality function where the blackbox technique fails to reduce the amount of prior entanglement by more than a constant factor. In the final result in the theme of message compression, we provide an upper bound on the problem of Exact Remote State Preparation (ERSP). 1
Quantum communication for wireless widearea networks
 IEEE Journal on Selected Areas in Communications
, 2005
"... Abstract—In this paper, a quantum routing mechanism is proposed to teleport a quantum state from one quantum device to another wirelessly even though these two devices do not share EPR pairs mutually. This results in the proposed quantum routing mechanism that can be used to construct the quantum wi ..."
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Abstract—In this paper, a quantum routing mechanism is proposed to teleport a quantum state from one quantum device to another wirelessly even though these two devices do not share EPR pairs mutually. This results in the proposed quantum routing mechanism that can be used to construct the quantum wireless networks. In terms of time complexity, the proposed mechanism transports a quantum bit in time almost the same as the quantum teleportation does regardless of the number of hops between the source and destination. From this point of view, the quantum routing mechanism is close to optimal in data transmission time. In addition, in order to realize the wireless communication in the quantum domain, a hierarchical network architecture and its corresponding communication protocol are developed. Based on these network components, a scalable quantum wireless communication can be achieved. Index Terms—EPR pair, handover, quantum bit (qubit), quantum entanglement, quantum routing, quantum teleportation, wireless widearea network (WAN). I.