4,416 research outputs found
Quantum bounds on multiplayer linear games and device-independent witness of genuine tripartite entanglement
Here we study multiplayer linear games, a natural generalization of XOR games
to multiple outcomes. We generalize a recently proposed efficiently computable
bound, in terms of the norm of a game matrix, on the quantum value of 2-player
games to linear games with players. As an example, we bound the quantum
value of a generalization of the well-known CHSH game to players and
outcomes. We also apply the bound to show in a simple manner that any
nontrivial functional box, that could lead to trivialization of communication
complexity in a multiparty scenario, cannot be realized in quantum mechanics.
We then present a systematic method to derive device-independent witnesses of
genuine tripartite entanglement.Comment: 7+8 page
Monogamy of nonlocal quantum correlations
We describe a new technique for obtaining Tsirelson bounds, or upper bounds
on the quantum value of a Bell inequality. Since quantum correlations do not
allow signaling, we obtain a Tsirelson bound by maximizing over all
no-signaling probability distributions. This maximization can be cast as a
linear program. In a setting where three parties, A, B, and C, share an
entangled quantum state of arbitrary dimension, we: (i) bound the trade-off
between AB's and AC's violation of the CHSH inequality, and (ii) demonstrate
that forcing B and C to be classically correlated prevents A and B from
violating certain Bell inequalities, relevant for interactive proof systems and
cryptography.Comment: This is the submitted version. The refereed version, which contains
an additional result about strong parallel repetition and corrects some
typos, is available on my personal web site at
http://bentoner.com/papers/monogamyrs.pdf [PDF
Tsirelson's bound and supersymmetric entangled states
A superqubit, belonging to a -dimensional super-Hilbert space,
constitutes the minimal supersymmetric extension of the conventional qubit. In
order to see whether superqubits are more nonlocal than ordinary qubits, we
construct a class of two-superqubit entangled states as a nonlocal resource in
the CHSH game. Since super Hilbert space amplitudes are Grassmann numbers, the
result depends on how we extract real probabilities and we examine three
choices of map: (1) DeWitt (2) Trigonometric (3) Modified Rogers. In cases (1)
and (2) the winning probability reaches the Tsirelson bound
of standard quantum mechanics. Case (3)
crosses Tsirelson's bound with . Although all states used
in the game involve probabilities lying between 0 and 1, case (3) permits other
changes of basis inducing negative transition probabilities.Comment: Updated to match published version. Minor modifications. References
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Unbounded entanglement in nonlocal games
Quantum entanglement is known to provide a strong advantage in many two-party
distributed tasks. We investigate the question of how much entanglement is
needed to reach optimal performance. For the first time we show that there
exists a purely classical scenario for which no finite amount of entanglement
suffices. To this end we introduce a simple two-party nonlocal game ,
inspired by Lucien Hardy's paradox. In our game each player has only two
possible questions and can provide bit strings of any finite length as answer.
We exhibit a sequence of strategies which use entangled states in increasing
dimension and succeed with probability for some .
On the other hand, we show that any strategy using an entangled state of local
dimension has success probability at most . In addition,
we show that any strategy restricted to producing answers in a set of
cardinality at most has success probability at most .
Finally, we generalize our construction to derive similar results starting from
any game with two questions per player and finite answers sets in which
quantum strategies have an advantage.Comment: We have removed the inaccurate discussion of infinite-dimensional
strategies in Section 5. Other minor correction
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