Quantum Multi-Prover Interactive Proof Systems with Limited Prior Entanglement

This paper gives the first formal treatment of a quantum analogue of multi-prover interactive proof systems. It is proved that the class of languages having quantum multi-prover interactive proof systems is necessarily contained in NEXP, under the assumption that provers are allowed to share at most polynomially many prior-entangled qubits. This implies that, in particular, if provers do not share any prior entanglement with each other, the class of languages having quantum multi-prover interactive proof systems is equal to NEXP. Related to these, it is shown that, in the case a prover does not have his private qubits, the class of languages having quantum single-prover interactive proof systems is also equal to NEXP.Comment: LaTeX2e, 19 pages, 2 figures, title changed, some of the sections are fully revised, journal version in Journal of Computer and System Science

Computing on Anonymous Quantum Network

This paper considers distributed computing on an anonymous quantum network, a network in which no party has a unique identifier and quantum communication and computation are available. It is proved that the leader election problem can exactly (i.e., without error in bounded time) be solved with at most the same complexity up to a constant factor as that of exactly computing symmetric functions (without intermediate measurements for a distributed and superposed input), if the number of parties is given to every party. A corollary of this result is a more efficient quantum leader election algorithm than existing ones: the new quantum algorithm runs in O(n) rounds with bit complexity O(mn^2), on an anonymous quantum network with n parties and m communication links. Another corollary is the first quantum algorithm that exactly computes any computable Boolean function with round complexity O(n) and with smaller bit complexity than that of existing classical algorithms in the worst case over all (computable) Boolean functions and network topologies. More generally, any n-qubit state can be shared with that complexity on an anonymous quantum network with n parties.Comment: 25 page

Entangled Games Are Hard to Approximate

We establish the first hardness results for the problem of computing the value of one-round games played by a verifier and a team of provers who can share quantum entanglement. In particular, we show that it is NP-hard to approximate within an inverse polynomial the value of a one-round game with (i) a quantum verifier and two entangled provers or (ii) a classical verifier and three entangled provers. Previously it was not even known if computing the value exactly is NP-hard. We also describe a mathematical conjecture, which, if true, would imply hardness of approximation of entangled-prover games to within a constant. Using our techniques we also show that every language in PSPACE has a two-prover one-round interactive proof system with perfect completeness and soundness 1-1/poly even against entangled provers. We start our proof by describing two ways to modify classical multiprover games to make them resistant to entangled provers. We then show that a strategy for the modified game that uses entanglement can be “rounded” to one that does not. The results then follow from classical inapproximability bounds. Our work implies that, unless P=NP, the values of entangled-prover games cannot be computed by semidefinite programs that are polynomial in the size of the verifier's system, a method that has been successful for more restricted quantum games

骨転移を有しない前立腺がん患者へのアンドロゲン除去療法による骨粗鬆症に対する経口ビスフォスフォネート製剤の予防効果について

We studied the short-term efficacy of alendronate, an oral bisphosphonates, on bone mineral density (BMD) during androgen deprivation therapy (ADT) in 45 nonmetastatic prostate cancer patients at the beginning of ADT (treatment group). All received alendronate five mg daily from the initiation of ADT. Lumber BMD was evaluated by dual energy X-ray absorptiometry, at baseline and after six months of treatment. Historical data on 24 patients with prostate cancer who received ADT without bisphosphonate administration were studied as controls (control group). BMD decreased in 13.9 and 45.8% of the patients in the treatment and control groups, respectively. Mean BMD changes in the lumber spine were +1.6 +/- 3.0% in the treatment group and -1.1 +/- 2.7% in the control group (p = 0.006). No pathological fractures occurred during the study period. No severe adverse effects were observed, but three patients could not continue alendronate treatment because of adverse events. Despite the short-term of this evaluation, our results showed that oral alendronate is an effective and safe treatment for preventing bone loss and increasing BMD in patients receiving ADT for prostate cancer.目的:アンドロゲン除去療法は骨塩減少とそれに伴う病的骨折の潜在的な危険因子である。点滴ビスフォスフォネート製剤はアンドロゲン除去療法を受けている前立腺がん患者に対する骨塩量の減少を予防することが示されているが経口ビスフォスフォネート製剤については評価されていない。今回, われわれは経口ビスフォスフォネート製剤の1つであるアレンドン酸を骨転移を有しない前立腺がん患者に投与して骨塩量を測定し短期間での効果を検討した。対象と方法:治療群として45人の骨転移を有しない前立腺がん患者について検討した。アレンドロン酸を1日5mg経口投与し治療前, 治療半年後に腰椎の骨塩量を測定し比較検討した。対照群として24人の骨転移を有しない前立腺がん患者についても同様に検討を行った。結果:骨塩量の減少は治療群で13.9%, 対照群で45.8%に見られた。腰椎における骨塩量の変化は治療群で平均1.6%, 対照群で-1.1%であった(p=0.006)。治療期間内において病的骨折は認められず, 有害事象として重篤なものは認めなかったが副作用のため3例が内服継続困難であった。結語:短期間の検討であるにもかかわらず経口ビスフォスフォネート製剤であるアレンドロン酸は前立腺がん患者に対するアンドロゲン除去療法による骨塩量減少を予防するのに有効で安全な治療法であることが示唆された。(著者抄録