437 research outputs found
Multiparty Quantum Communication Complexity of Triangle Finding
Triangle finding (deciding if a graph contains a triangle or not) is a central problem in quantum query complexity. The quantum communication complexity of this problem, where the edges of the graph are distributed among the players, was considered recently by Ivanyos et al. in the two- party setting. In this paper we consider its k-party quantum communication complexity with k >= 3. Our main result is a ~O(m^(7/12))-qubit protocol, for any constant number of players k, deciding with high probability if a graph with m edges contains a triangle or not. Our approach makes connections between the multiparty quantum communication complexity of triangle finding and the quantum query complexity of graph collision, a well-studied problem in quantum query complexity
Converses for Secret Key Agreement and Secure Computing
We consider information theoretic secret key agreement and secure function
computation by multiple parties observing correlated data, with access to an
interactive public communication channel. Our main result is an upper bound on
the secret key length, which is derived using a reduction of binary hypothesis
testing to multiparty secret key agreement. Building on this basic result, we
derive new converses for multiparty secret key agreement. Furthermore, we
derive converse results for the oblivious transfer problem and the bit
commitment problem by relating them to secret key agreement. Finally, we derive
a necessary condition for the feasibility of secure computation by trusted
parties that seek to compute a function of their collective data, using an
interactive public communication that by itself does not give away the value of
the function. In many cases, we strengthen and improve upon previously known
converse bounds. Our results are single-shot and use only the given joint
distribution of the correlated observations. For the case when the correlated
observations consist of independent and identically distributed (in time)
sequences, we derive strong versions of previously known converses
Continuous variable tangle, monogamy inequality, and entanglement sharing in Gaussian states of continuous variable systems
For continuous-variable systems, we introduce a measure of entanglement, the
continuous variable tangle ({\em contangle}), with the purpose of quantifying
the distributed (shared) entanglement in multimode, multipartite Gaussian
states. This is achieved by a proper convex roof extension of the squared
logarithmic negativity. We prove that the contangle satisfies the
Coffman-Kundu-Wootters monogamy inequality in all three--mode Gaussian states,
and in all fully symmetric --mode Gaussian states, for arbitrary . For
three--mode pure states we prove that the residual entanglement is a genuine
tripartite entanglement monotone under Gaussian local operations and classical
communication. We show that pure, symmetric three--mode Gaussian states allow a
promiscuous entanglement sharing, having both maximum tripartite residual
entanglement and maximum couplewise entanglement between any pair of modes.
These states are thus simultaneous continuous-variable analogs of both the GHZ
and the states of three qubits: in continuous-variable systems monogamy
does not prevent promiscuity, and the inequivalence between different classes
of maximally entangled states, holding for systems of three or more qubits, is
removed.Comment: 13 pages, 1 figure. Replaced with published versio
Bounds on oblivious multiparty quantum communication complexity
The main conceptual contribution of this paper is investigating quantum
multiparty communication complexity in the setting where communication is
\emph{oblivious}. This requirement, which to our knowledge is satisfied by all
quantum multiparty protocols in the literature, means that the communication
pattern, and in particular the amount of communication exchanged between each
pair of players at each round is fixed \emph{independently of the input} before
the execution of the protocol. We show, for a wide class of functions, how to
prove strong lower bounds on their oblivious quantum -party communication
complexity using lower bounds on their \emph{two-party} communication
complexity. We apply this technique to prove tight lower bounds for all
symmetric functions with \textsf{AND} gadget, and in particular obtain an
optimal lower bound on the oblivious quantum -party
communication complexity of the -bit Set-Disjointness function. We also show
the tightness of these lower bounds by giving (nearly) matching upper bounds.Comment: 13 pages, an accepted paper of LATIN 202
Simultaneous Multiparty Communication Protocols for Composed Functions
In the Number On the Forehead (NOF) multiparty communication model,
players want to evaluate a function on some input by broadcasting bits according to a
predetermined protocol. The input is distributed in such a way that each player
sees all of it except . In the simultaneous setting, the players
cannot speak to each other but instead send information to a referee. The
referee does not know the players' input, and cannot give any information back.
At the end, the referee must be able to recover from what
she obtained.
A central open question, called the barrier, is to find a function
which is hard to compute for or more players (where the 's
have size ) in the simultaneous NOF model. This has important
applications in circuit complexity, as it could help to separate from
other complexity classes. One of the candidates belongs to the family of
composed functions. The input to these functions is represented by a boolean matrix , whose row is the input and is a
block-width parameter. A symmetric composed function acting on is specified
by two symmetric - and -variate functions and , that output
where is the -th block of width
of . As the majority function is conjectured to be outside of
, Babai et. al. suggested to study , with large
enough.
So far, it was only known that is not enough for to
break the barrier in the simultaneous deterministic NOF model. In this
paper, we extend this result to any constant block-width , by giving a
protocol of cost for any symmetric composed
function when there are players.Comment: 17 pages, 1 figure; v2: improved introduction, better cost analysis
for the 2nd protoco
Graph states as ground states of many-body spin-1/2 Hamiltonians
We consider the problem whether graph states can be ground states of local
interaction Hamiltonians. For Hamiltonians acting on n qubits that involve at
most two-body interactions, we show that no n-qubit graph state can be the
exact, non-degenerate ground state. We determine for any graph state the
minimal d such that it is the non-degenerate ground state of a d-body
interaction Hamiltonian, while we show for d'-body Hamiltonians H with d'<d
that the resulting ground state can only be close to the graph state at the
cost of H having a small energy gap relative to the total energy. When allowing
for ancilla particles, we show how to utilize a gadget construction introduced
in the context of the k-local Hamiltonian problem, to obtain n-qubit graph
states as non-degenerate (quasi-)ground states of a two-body Hamiltonian acting
on n'>n spins.Comment: 10 pages, 1 figur
Survey of Distributed Decision
We survey the recent distributed computing literature on checking whether a
given distributed system configuration satisfies a given boolean predicate,
i.e., whether the configuration is legal or illegal w.r.t. that predicate. We
consider classical distributed computing environments, including mostly
synchronous fault-free network computing (LOCAL and CONGEST models), but also
asynchronous crash-prone shared-memory computing (WAIT-FREE model), and mobile
computing (FSYNC model)
Quantum network communication -- the butterfly and beyond
We study the k-pair communication problem for quantum information in networks
of quantum channels. We consider the asymptotic rates of high fidelity quantum
communication between specific sender-receiver pairs. Four scenarios of
classical communication assistance (none, forward, backward, and two-way) are
considered. (i) We obtain outer and inner bounds of the achievable rate regions
in the most general directed networks. (ii) For two particular networks
(including the butterfly network) routing is proved optimal, and the free
assisting classical communication can at best be used to modify the directions
of quantum channels in the network. Consequently, the achievable rate regions
are given by counting edge avoiding paths, and precise achievable rate regions
in all four assisting scenarios can be obtained. (iii) Optimality of routing
can also be proved in classes of networks. The first class consists of directed
unassisted networks in which (1) the receivers are information sinks, (2) the
maximum distance from senders to receivers is small, and (3) a certain type of
4-cycles are absent, but without further constraints (such as on the number of
communicating and intermediate parties). The second class consists of arbitrary
backward-assisted networks with 2 sender-receiver pairs. (iv) Beyond the k-pair
communication problem, observations are made on quantum multicasting and a
static version of network communication related to the entanglement of
assistance.Comment: 15 pages, 17 figures. Final versio
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