On the power of multipartite entanglement for pseudotelepathy

Abstract

As early as 1935, Schrödinger recognized entanglement as ``not one but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought''. Indeed, most remarkable phenomena in quantum information science, such as quantum computing and quantum teleportation, spring from clever uses of entanglement. Among them, pseudotelepathy enables two or more players to win systematically at some cooperative games with no need for communication between them, a restriction that would make the task impossible in a classical world. We investigate the power of multipartite entanglement for pseudotelepathy. Some known games that can be won with tripartite entanglement cannot be won with bipartite entanglement, but they can be won with bipartite nonsignalling resources such as the so-called Popescu--Rohrlich nonlocal box. We exhibit a five-player game that can be won with tripartite entanglement, but not with arbitrary bipartite nonsignalling resources even in the presence of arbitrary five-partite classical resources. This illustrates both the power of bipartite nonsignalling resources (over bipartite entanglement) and the even superior power of tripartite entanglement.

Figures (7)

• Figure 1: (a) Original scenario with three players (Alice, Bob and Charlie) sharing bipartite resources pairwise. (b) Inflated scenario obtained by duplicating and rearranging players and resources. Each duplicated player represents an indistinguishable copy of the same local input-output process as in the original scenario and each duplicated resource represents an independent copy of the corresponding original resource.
• Figure 2: Standard grid formulation of the magic square game. Each cell contains a bit. The parity of each row is required to be even, while the parity of each column is required to be odd.
• Figure 3: Hypergraph formulation of the magic square game. Each node corresponds to a cell of the $3 \times 3$ grid of Fig. \ref{['fig:msgGrid']}. Each row or column of the grid of Fig. \ref{['fig:msgGrid']} defines a hyperedge connecting the corresponding three nodes. Solid lines represent hyperedges whose parity must be even, while dashed lines represent ones whose parity must be odd.
• Figure 4: Hypergraph formulation of the magic pentagram game. Each straight line of the pentagram defines a hyperedge containing four nodes and carrying a parity constraint. Solid lines represent hyperedges whose parity must be even, while the dashed line corresponds to an odd parity.
• Figure 5: Modified magic pentagram game with three Alices. Each $\text{Alice}_i$ is assigned one node of a common hyperedge and receives as input the corresponding node label $x_i \in \{0,1\}$, with the promise that the three inputs belong to the same hyperedge. Bob is assigned the horizontal hyperedge and outputs the labels $b_1,b_2,b_3$ of its three leftmost nodes. Solid lines represent hyperedges whose parity must be even, while the dashed line corresponds to an odd parity. The value of the fourth node of each hyperedge is uniquely determined by the corresponding parity constraint.

Theorems & Definitions (15)

• Lemma 5.1
• Lemma 5.2
• proof
• Theorem 5.3
• proof
• Theorem B.1
• proof
• Theorem B.2
• proof
• Theorem B.3