109 research outputs found
N-representability is QMA-complete
We study the computational complexity of the N-representability problem in
quantum chemistry. We show that this problem is QMA-complete, which is the
quantum generalization of NP-complete. Our proof uses a simple mapping from
spin systems to fermionic systems, as well as a convex optimization technique
that reduces the problem of finding ground states to N-representability
Dynamics of entanglement of bosonic modes on symmetric graphs
We investigate the dynamics of an initially disentangled Gaussian state on a
general finite symmetric graph. As concrete examples we obtain properties of
this dynamics on mean field graphs of arbitrary sizes. In the same way that
chains can be used for transmitting entanglement by their natural dynamics,
these graphs can be used to store entanglement. We also consider two kinds of
regular polyhedron which show interesting features of entanglement sharing.Comment: 14 pages, 11 figures, Accepted for publication in Physics Letters
Detection of Multiparticle Entanglement: Quantifying the Search for Symmetric Extensions
We provide quantitative bounds on the characterisation of multiparticle
separable states by states that have locally symmetric extensions. The bounds
are derived from two-particle bounds and relate to recent studies on quantum
versions of de Finetti's theorem. We discuss algorithmic applications of our
results, in particular a quasipolynomial-time algorithm to decide whether a
multiparticle quantum state is separable or entangled (for constant number of
particles and constant error in the LOCC or Frobenius norm). Our results
provide a theoretical justification for the use of the Search for Symmetric
Extensions as a practical test for multiparticle entanglement.Comment: 5 pages, 1 figur
Secure certification of mixed quantum states with application to two-party randomness generation
We investigate sampling procedures that certify that an arbitrary quantum
state on subsystems is close to an ideal mixed state
for a given reference state , up to errors on a few positions. This
task makes no sense classically: it would correspond to certifying that a given
bitstring was generated according to some desired probability distribution.
However, in the quantum case, this is possible if one has access to a prover
who can supply a purification of the mixed state.
In this work, we introduce the concept of mixed-state certification, and we
show that a natural sampling protocol offers secure certification in the
presence of a possibly dishonest prover: if the verifier accepts then he can be
almost certain that the state in question has been correctly prepared, up to a
small number of errors.
We then apply this result to two-party quantum coin-tossing. Given that
strong coin tossing is impossible, it is natural to ask "how close can we get".
This question has been well studied and is nowadays well understood from the
perspective of the bias of individual coin tosses. We approach and answer this
question from a different---and somewhat orthogonal---perspective, where we do
not look at individual coin tosses but at the global entropy instead. We show
how two distrusting parties can produce a common high-entropy source, where the
entropy is an arbitrarily small fraction below the maximum (except with
negligible probability)
The Quantum Reverse Shannon Theorem based on One-Shot Information Theory
The Quantum Reverse Shannon Theorem states that any quantum channel can be
simulated by an unlimited amount of shared entanglement and an amount of
classical communication equal to the channel's entanglement assisted classical
capacity. In this paper, we provide a new proof of this theorem, which has
previously been proved by Bennett, Devetak, Harrow, Shor, and Winter. Our proof
has a clear structure being based on two recent information-theoretic results:
one-shot Quantum State Merging and the Post-Selection Technique for quantum
channels.Comment: 30 pages, 4 figures, published versio
Catalytic Decoupling of Quantum Information
The decoupling technique is a fundamental tool in quantum information theory with applications ranging from quantum thermodynamics to quantum many body physics to the study of black hole radiation. In this work we introduce the notion of catalytic decoupling, that is, decoupling in the presence of an uncorrelated ancilla system. This removes a restriction on the standard notion of decoupling, which becomes important for structureless resources, and yields a tight characterization in terms of the max-mutual information. Catalytic decoupling naturally unifies various tasks like the erasure of correlations and quantum state merging, and leads to a resource theory of decoupling
Asymptotic performance of port-based teleportation
Quantum teleportation is one of the fundamental building blocks of quantum Shannon theory. While ordinary teleportation is simple and efficient, port-based teleportation (PBT) enables applications such as universal programmable quantum processors, instantaneous non-local quantum computation and attacks on position-based quantum cryptography. In this work, we determine the fundamental limit on the performance of PBT: for arbitrary fixed input dimension and a large number N of ports, the error of the optimal protocol is proportional to the inverse square of N. We prove this by deriving an achievability bound, obtained by relating the corresponding optimization problem to the lowest Dirichlet eigenvalue of the Laplacian on the ordered simplex. We also give an improved converse bound of matching order in the number of ports. In addition, we determine the leading-order asymptotics of PBT variants defined in terms of maximally entangled resource states. The proofs of these results rely on connecting recently-derived representation-theoretic formulas to random matrix theory. Along the way, we refine a convergence result for the fluctuations of the Schur-Weyl distribution by Johansson, which might be of independent interest
Quantum Computational Complexity of the N-Representability Problem: QMA Complete
We study the computational complexity of the N-representability problem in quantum chemistry. We show that this problem is quantum Merlin-Arthur complete, which is the quantum generalization of nondeterministic polynomial time complete. Our proof uses a simple mapping from spin systems to fermionic systems, as well as a convex optimization technique that reduces the problem of finding ground states to N representability
Quantum marginal problem and N-representability
A variant of the quantum marginal problem was known from early sixties as
N-representability problem. In 1995 it was designated by National Research
Council of USA as one of ten most prominent research challenges in quantum
chemistry. In spite of this recognition the progress was very slow, until a
couple of years ago the problem came into focus again, now in framework of
quantum information theory. In the paper I give an account of the recent
development.Comment: A talk at 12 Central European workshop on Quantum Optics, July 2005,
Bilkent University, Turke
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