260 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
Full security of quantum key distribution from no-signaling constraints
We analyze a cryptographic protocol for generating a distributed secret key
from correlations that violate a Bell inequality by a sufficient amount, and
prove its security against eavesdroppers, constrained only by the assumption
that any information accessible to them must be compatible with the
non-signaling principle. The claim holds with respect to the state-of-the-art
security definition used in cryptography, known as universally-composable
security. The non-signaling assumption only refers to the statistics of
measurement outcomes depending on the choices of measurements; hence security
is independent of the internal workings of the devices --- they do not even
need to follow the laws of quantum theory. This is relevant for practice as a
correct and complete modeling of realistic devices is generally impossible. The
techniques developed are general and can be applied to other Bell
inequality-based protocols. In particular, we provide a scheme for estimating
Bell-inequality violations when the samples are not independent and identically
distributed.Comment: 15 pages, 2 figur
On Nonzero Kronecker Coefficients and their Consequences for Spectra
A triple of spectra (r^A, r^B, r^{AB}) is said to be admissible if there is a
density operator rho^{AB} with (Spec rho^A, Spec rho^B, Spec rho^{AB})=(r^A,
r^B, r^{AB}). How can we characterise such triples? It turns out that the
admissible spectral triples correspond to Young diagrams (mu, nu, lambda) with
nonzero Kronecker coefficient [M. Christandl and G. Mitchison, to appear in
Comm. Math. Phys., quant-ph/0409016; A. Klyachko, quant-ph/0409113]. This means
that the irreducible representation V_lambda is contained in the tensor product
of V_mu and V_nu. Here, we show that such triples form a finitely generated
semigroup, thereby resolving a conjecture of Klyachko. As a consequence we are
able to obtain stronger results than in [M. Ch. and G. M. op. cit.] and give a
complete information-theoretic proof of the correspondence between triples of
spectra and representations. Finally, we show that spectral triples form a
convex polytope.Comment: 13 page
Upper bound on the secret key rate distillable from effective quantum correlations with imperfect detectors
We provide a simple method to obtain an upper bound on the secret key rate
that is particularly suited to analyze practical realizations of quantum key
distribution protocols with imperfect devices. We consider the so-called
trusted device scenario where Eve cannot modify the actual detection devices
employed by Alice and Bob. The upper bound obtained is based on the available
measurements results, but it includes the effect of the noise and losses
present in the detectors of the legitimate users.Comment: 9 pages, 1 figure; suppress sifting effect in the figure, final
versio
Nondeterministic quantum communication complexity:The cyclic equality game and iterated matrix multiplication
Finite de Finetti theorem for conditional probability distributions describing physical theories
Recoupling Coefficients and Quantum Entropies
We prove that the asymptotic behavior of the recoupling coefficients of the symmetric group S_k is characterized by a quantum marginal problem: they decay polynomially in k if there exists a quantum state of three particles with given eigenvalues for their reduced density operators and exponentially otherwise. As an application, we deduce solely from symmetry considerations of the coefficients the strong subadditivity property of the von Neumann entropy, first proved by Lieb and Ruskai (J Math Phys 14:1938–1941, 1973). Our work may be seen as a non-commutative generalization of the representation-theoretic aspect of the recently found connection between the quantum marginal problem and the Kronecker coefficient of the symmetric group, which has applications in quantum information theory and algebraic complexity theory. This connection is known to generalize the correspondence between Weyl’s problem on the addition of Hermitian matrices and the Littlewood–Richardson coefficients of SU(d). In this sense, our work may also be regarded as a generalization of Wigner’s famous observation of the semiclassical behavior of the recoupling coefficients (here also known as 6j or Racah coefficients), which decay polynomially whenever a tetrahedron with given edge lengths exists. More precisely, we show that our main theorem contains a characterization of the possible eigenvalues of partial sums of Hermitian matrices thus presenting a representation-theoretic characterization of a generalization of Weyl’s problem. The appropriate geometric objects to SU(d) recoupling coefficients are thus tuples of Hermitian matrices and to S_k recoupling coefficients they are three-particle quantum states
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