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research
A doubly exponential upper bound on noisy EPR states for binary games
Authors
Penghui Yao
Publication date
1 January 2011
Publisher
View
on
arXiv
Abstract
This paper initiates the study of a class of entangled games, mono-state games, denoted by
(
G
,
ψ
)
(G,\psi)
(
G
,
ψ
)
, where
G
G
G
is a two-player one-round game and
ψ
\psi
ψ
is a bipartite state independent of the game
G
G
G
. In the mono-state game
(
G
,
ψ
)
(G,\psi)
(
G
,
ψ
)
, the players are only allowed to share arbitrary copies of
ψ
\psi
ψ
. This paper provides a doubly exponential upper bound on the copies of
ψ
\psi
ψ
for the players to approximate the value of the game to an arbitrarily small constant precision for any mono-state binary game
(
G
,
ψ
)
(G,\psi)
(
G
,
ψ
)
, if
ψ
\psi
ψ
is a noisy EPR state, which is a two-qubit state with completely mixed states as marginals and maximal correlation less than
1
1
1
. In particular, it includes
(
1
−
ϵ
)
∣
Ψ
⟩
⟨
Ψ
∣
+
ϵ
I
2
2
⊗
I
2
2
(1-\epsilon)|\Psi\rangle\langle\Psi|+\epsilon\frac{I_2}{2}\otimes\frac{I_2}{2}
(
1
−
ϵ
)
∣Ψ
⟩
⟨
Ψ∣
+
ϵ
2
I
2
​
​
⊗
2
I
2
​
​
, an EPR state with an arbitrary depolarizing noise
ϵ
>
0
\epsilon>0
ϵ
>
0
.The structure of the proofs is built the recent framework about the decidability of the non-interactive simulation of joint distributions, which is completely different from all previous optimization-based approaches or "Tsirelson's problem"-based approaches. This paper develops a series of new techniques about the Fourier analysis on matrix spaces and proves a quantum invariance principle and a hypercontractive inequality of random operators. This novel approach provides a new angle to study the decidability of the complexity class MIP
∗
^*
∗
, a longstanding open problem in quantum complexity theory.Comment: The proof of Lemma C.9 is corrected. The presentation is improved. Some typos are correcte
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University of Richmond
See this paper in CORE
Go to the repository landing page
Download from data provider
oai:scholarship.richmond.edu:l...
Last time updated on 29/10/2019