3,094 research outputs found
Test for a large amount of entanglement, using few measurements
Bell-inequality violations establish that two systems share some quantum
entanglement. We give a simple test to certify that two systems share an
asymptotically large amount of entanglement, n EPR states. The test is
efficient: unlike earlier tests that play many games, in sequence or in
parallel, our test requires only one or two CHSH games. One system is directed
to play a CHSH game on a random specified qubit i, and the other is told to
play games on qubits {i,j}, without knowing which index is i.
The test is robust: a success probability within delta of optimal guarantees
distance O(n^{5/2} sqrt{delta}) from n EPR states. However, the test does not
tolerate constant delta; it breaks down for delta = Omega~(1/sqrt{n}). We give
an adversarial strategy that succeeds within delta of the optimum probability
using only O~(delta^{-2}) EPR states.Comment: 17 pages, 2 figures. Journal versio
Non-locality and Communication Complexity
Quantum information processing is the emerging field that defines and
realizes computing devices that make use of quantum mechanical principles, like
the superposition principle, entanglement, and interference. In this review we
study the information counterpart of computing. The abstract form of the
distributed computing setting is called communication complexity. It studies
the amount of information, in terms of bits or in our case qubits, that two
spatially separated computing devices need to exchange in order to perform some
computational task. Surprisingly, quantum mechanics can be used to obtain
dramatic advantages for such tasks.
We review the area of quantum communication complexity, and show how it
connects the foundational physics questions regarding non-locality with those
of communication complexity studied in theoretical computer science. The first
examples exhibiting the advantage of the use of qubits in distributed
information-processing tasks were based on non-locality tests. However, by now
the field has produced strong and interesting quantum protocols and algorithms
of its own that demonstrate that entanglement, although it cannot be used to
replace communication, can be used to reduce the communication exponentially.
In turn, these new advances yield a new outlook on the foundations of physics,
and could even yield new proposals for experiments that test the foundations of
physics.Comment: Survey paper, 63 pages LaTeX. A reformatted version will appear in
Reviews of Modern Physic
Quantum teleportation and entanglement swapping with linear optics logic gates
We report on the usage of a linear optics phase gate for distinguishing all
four Bell states simultaneously in a quantum teleportation and entanglement
swapping protocol. This is demonstrated by full state tomography of the one and
two qubit output states of the two protocols, yielding average state fidelities
of about 0.83 and 0.77, respectively. In addition, the performance of the
teleportation channel is characterised by quantum process tomography. The non
classical properties of the entanglement swapping output states are further
confirmed by the violation of a CHSH-type Bell inequality of 2.14 on average.Comment: 11 pages, 3 figure
Quantum de Finetti Theorems under Local Measurements with Applications
Quantum de Finetti theorems are a useful tool in the study of correlations in
quantum multipartite states. In this paper we prove two new quantum de Finetti
theorems, both showing that under tests formed by local measurements one can
get a much improved error dependence on the dimension of the subsystems. We
also obtain similar results for non-signaling probability distributions. We
give the following applications of the results:
We prove the optimality of the Chen-Drucker protocol for 3-SAT, under the
exponential time hypothesis.
We show that the maximum winning probability of free games can be estimated
in polynomial time by linear programming. We also show that 3-SAT with m
variables can be reduced to obtaining a constant error approximation of the
maximum winning probability under entangled strategies of O(m^{1/2})-player
one-round non-local games, in which the players communicate O(m^{1/2}) bits all
together.
We show that the optimization of certain polynomials over the hypersphere can
be performed in quasipolynomial time in the number of variables n by
considering O(log(n)) rounds of the Sum-of-Squares (Parrilo/Lasserre) hierarchy
of semidefinite programs. As an application to entanglement theory, we find a
quasipolynomial-time algorithm for deciding multipartite separability.
We consider a result due to Aaronson -- showing that given an unknown n qubit
state one can perform tomography that works well for most observables by
measuring only O(n) independent and identically distributed (i.i.d.) copies of
the state -- and relax the assumption of having i.i.d copies of the state to
merely the ability to select subsystems at random from a quantum multipartite
state.
The proofs of the new quantum de Finetti theorems are based on information
theory, in particular on the chain rule of mutual information.Comment: 39 pages, no figure. v2: changes to references and other minor
improvements. v3: added some explanations, mostly about Theorem 1 and
Conjecture 5. STOC version. v4, v5. small improvements and fixe
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