Nonlocality and communication complexity

@article{Buhrman2010NonlocalityAC,
  title={Nonlocality and communication complexity},
  author={Harry Buhrman and Richard Cleve and Serge Massar and Ronald de Wolf},
  journal={Reviews of Modern Physics},
  year={2010},
  volume={82},
  pages={665-698}
}
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. Until recently the common notion of computing was based on classical mechanics, and did not take into account all the possibilities that physically-realizable computing devices offer in principle. The field gained momentum after Peter Shor developed an efficient algorithm for factoring… 

Figures from this paper

Experimental Quantum Switching for Exponentially Superior Quantum Communication Complexity.
TLDR
The results elucidate the crucial role of the coherence of communication direction in achieving the exponential separation for the one-way processing task, and open a new path for experimentally exploring the fundamentals and applications of advanced features of indefinite causal structures.
Quantum networks reveal quantum nonlocality.
TLDR
This work shows, using its framework, how any one-way entanglement distillable state leads to nonlocal correlations and proves that quantum nonlocality is a non-additive resource, which can be activated.
Contextuality supplies the ‘magic’ for quantum computation
TLDR
This work proves a remarkable equivalence between the onset of contextuality and the possibility of universal quantum computation via ‘magic state’ distillation, which is the leading model for experimentally realizing a fault-tolerant quantum computer.
Lower bounds on the communication complexity of two-party (quantum) processes
  • A. Montina, S. Wolf
  • Computer Science, Mathematics
    2014 IEEE International Symposium on Information Theory
  • 2014
TLDR
It is proved that this optimization problem is the dual of a geometric programming problem, which displays some appealing properties that imply that, once a feasible point is found, the computation of a lower bound on the communication cost in any two-party process is linearly complex.
High-Dimensional Quantum Communication Complexity beyond Strategies Based on Bell's Theorem.
TLDR
This work focuses on a family of CCPs, based on facet Bell inequalities, and finds that the advantages are tied to the use of measurements that are not rank-one projective, and provides an experimental semi-device-independent falsification of such measurements in Hilbert space dimension six.
Quantum Communication Complexity using the Quantum Zeno Effect
The quantum Zeno effect (QZE) is the phenomenon where the unitary evolution of a quantum state is suppressed e.g. due to frequent measurements. Here, we investigate the use of the QZE in a class of
Photonic quantum information processing: A concise review
TLDR
This concise review provides a flyover of some key aspects of the field, with a focus on experiment, and promises to out aside its reputation for requiring excessive resource overheads due to inefficient two-qubit gates.
Non-adaptive measurement-based quantum computation and multi-party Bell inequalities
TLDR
There are explicit connections between this model of computation and the question of non-classicality in quantum correlations and this is demonstrated by focusing on deterministic computation of Boolean functions, in which natural generalizations of the Greenberger–Horne–Zeilinger paradox emerge.
Quantum states cannot be transmitted efficiently classically
TLDR
Any classical two-way communication protocol with shared randomness that can approximately simulate the result of applying an arbitrary measurement to a quantum state of $n$ qubits, up to constant accuracy, must transmit at least $\Omega(2^n)$ bits.
Multi-party quantum fingerprinting with weak coherent pulses: circuit design and protocol analysis
Quantum communication has been leading the way of many remarkable theoretical results and experimental tests in physics. In this context, quantum communication complexity (QCC) has recently drawn
...
...

References

SHOWING 1-10 OF 157 REFERENCES
Quantum Pseudo-Telepathy
TLDR
Pseudo-telepathy is a surprising application of quantum information processing to communication complexity and a survey of recent and not-so-recent work on the subject is presented.
Quantum Communication Complexity
TLDR
It is well known that entanglement on its own is useless for the transmission of information, but there are distributed tasks that cannot be accomplished at all in a classical world when communication is not allowed, but that become possible if the non-communicating parties share prior entanglements.
Nonlocality & Communication Complexity
TLDR
It is shown that entanglement does not lead to a more efficient calculation of the inner prod uct function, and it is reached that nonlocality sometimes—but not al ways—allows a reduction in communication complexity.
Nonlocal correlations as an information-theoretic resource
It is well known that measurements performed on spatially separated entangled quantum systems can give rise to correlations that are nonlocal, in the sense that a Bell inequality is violated. They
Experimental quantum 'Guess my Number' protocol using multiphoton entanglement
TLDR
An experimental demonstration of a modified version of the entanglement-assisted “Guess my Number” protocol for the reduction of communication complexity among three separated parties and the results imply that the separated parties can compute a function of distributed inputs by exchanging less classical information than by using any classical strategy.
Feasible quantum communication complexity protocol
I show that a simple multi-party communication task can be performed more efficiently with quantum communication than with classical communication, even with low detection efficiency�. The task is a
Exponential separation of quantum and classical communication complexity
  • R. Raz
  • Computer Science
    STOC '99
  • 1999
TLDR
It is shown that for certain communication complezity problems quantum communication protocols are exponentially faster than classical ores and an ezponential gap between quantum communication complexity and classical probabilistic communication complexity is given.
On communication over an entanglement-assisted quantum channel
TLDR
This paper derives optimal bounds on the number of quantum bits required for this task, that of communicating classical bits from one party to another, for any given probability of error.
Most quantum States are too entangled to be useful as computational resources.
TLDR
It is shown that quantum states can be too entangled to be useful for the purpose of computation, in that high values of the geometric measure of entanglement preclude states from offering a universal quantum computational speedup.
Multiparty quantum communication complexity.
TLDR
This work constructs a function G such that for the one-round communication model and three parties, G can be computed with n+1 bits of communication when the parties share prior entanglement and if no entangled particles are provided, then F is roughly k*log(k).
...
...