1,591 research outputs found
Identifying the Information Gain of a Quantum Measurement
We show that quantum-to-classical channels, i.e., quantum measurements, can
be asymptotically simulated by an amount of classical communication equal to
the quantum mutual information of the measurement, if sufficient shared
randomness is available. This result generalizes Winter's measurement
compression theorem for fixed independent and identically distributed inputs
[Winter, CMP 244 (157), 2004] to arbitrary inputs, and more importantly, it
identifies the quantum mutual information of a measurement as the information
gained by performing it, independent of the input state on which it is
performed. Our result is a generalization of the classical reverse Shannon
theorem to quantum-to-classical channels. In this sense, it can be seen as a
quantum reverse Shannon theorem for quantum-to-classical channels, but with the
entanglement assistance and quantum communication replaced by shared randomness
and classical communication, respectively. The proof is based on a novel
one-shot state merging protocol for "classically coherent states" as well as
the post-selection technique for quantum channels, and it uses techniques
developed for the quantum reverse Shannon theorem [Berta et al., CMP 306 (579),
2011].Comment: v2: new result about non-feedback measurement simulation, 45 pages, 4
figure
Optimizing Memory-Bounded Controllers for Decentralized POMDPs
We present a memory-bounded optimization approach for solving
infinite-horizon decentralized POMDPs. Policies for each agent are represented
by stochastic finite state controllers. We formulate the problem of optimizing
these policies as a nonlinear program, leveraging powerful existing nonlinear
optimization techniques for solving the problem. While existing solvers only
guarantee locally optimal solutions, we show that our formulation produces
higher quality controllers than the state-of-the-art approach. We also
incorporate a shared source of randomness in the form of a correlation device
to further increase solution quality with only a limited increase in space and
time. Our experimental results show that nonlinear optimization can be used to
provide high quality, concise solutions to decentralized decision problems
under uncertainty.Comment: Appears in Proceedings of the Twenty-Third Conference on Uncertainty
in Artificial Intelligence (UAI2007
Trevisan's extractor in the presence of quantum side information
Randomness extraction involves the processing of purely classical information
and is therefore usually studied in the framework of classical probability
theory. However, such a classical treatment is generally too restrictive for
applications, where side information about the values taken by classical random
variables may be represented by the state of a quantum system. This is
particularly relevant in the context of cryptography, where an adversary may
make use of quantum devices. Here, we show that the well known construction
paradigm for extractors proposed by Trevisan is sound in the presence of
quantum side information.
We exploit the modularity of this paradigm to give several concrete extractor
constructions, which, e.g, extract all the conditional (smooth) min-entropy of
the source using a seed of length poly-logarithmic in the input, or only
require the seed to be weakly random.Comment: 20+10 pages; v2: extract more min-entropy, use weakly random seed;
v3: extended introduction, matches published version with sections somewhat
reordere
Linear list-approximation for short programs (or the power of a few random bits)
A -short program for a string is a description of of length at
most , where is the Kolmogorov complexity of . We show that
there exists a randomized algorithm that constructs a list of elements that
contains a -short program for . We also show a polynomial-time
randomized construction that achieves the same list size for -short programs. These results beat the lower bounds shown by Bauwens et al.
\cite{bmvz:c:shortlist} for deterministic constructions of such lists. We also
prove tight lower bounds for the main parameters of our result. The
constructions use only ( for the polynomial-time
result) random bits . Thus using only few random bits it is possible to do
tasks that cannot be done by any deterministic algorithm regardless of its
running time
Unforgeable Quantum Encryption
We study the problem of encrypting and authenticating quantum data in the
presence of adversaries making adaptive chosen plaintext and chosen ciphertext
queries. Classically, security games use string copying and comparison to
detect adversarial cheating in such scenarios. Quantumly, this approach would
violate no-cloning. We develop new techniques to overcome this problem: we use
entanglement to detect cheating, and rely on recent results for characterizing
quantum encryption schemes. We give definitions for (i.) ciphertext
unforgeability , (ii.) indistinguishability under adaptive chosen-ciphertext
attack, and (iii.) authenticated encryption. The restriction of each definition
to the classical setting is at least as strong as the corresponding classical
notion: (i) implies INT-CTXT, (ii) implies IND-CCA2, and (iii) implies AE. All
of our new notions also imply QIND-CPA privacy. Combining one-time
authentication and classical pseudorandomness, we construct schemes for each of
these new quantum security notions, and provide several separation examples.
Along the way, we also give a new definition of one-time quantum authentication
which, unlike all previous approaches, authenticates ciphertexts rather than
plaintexts.Comment: 22+2 pages, 1 figure. v3: error in the definition of QIND-CCA2 fixed,
some proofs related to QIND-CCA2 clarifie
Pseudorandomness for Regular Branching Programs via Fourier Analysis
We present an explicit pseudorandom generator for oblivious, read-once,
permutation branching programs of constant width that can read their input bits
in any order. The seed length is , where is the length of the
branching program. The previous best seed length known for this model was
, which follows as a special case of a generator due to
Impagliazzo, Meka, and Zuckerman (FOCS 2012) (which gives a seed length of
for arbitrary branching programs of size ). Our techniques
also give seed length for general oblivious, read-once branching
programs of width , which is incomparable to the results of
Impagliazzo et al.Our pseudorandom generator is similar to the one used by
Gopalan et al. (FOCS 2012) for read-once CNFs, but the analysis is quite
different; ours is based on Fourier analysis of branching programs. In
particular, we show that an oblivious, read-once, regular branching program of
width has Fourier mass at most at level , independent of the
length of the program.Comment: RANDOM 201
Quantum Cryptography Beyond Quantum Key Distribution
Quantum cryptography is the art and science of exploiting quantum mechanical
effects in order to perform cryptographic tasks. While the most well-known
example of this discipline is quantum key distribution (QKD), there exist many
other applications such as quantum money, randomness generation, secure two-
and multi-party computation and delegated quantum computation. Quantum
cryptography also studies the limitations and challenges resulting from quantum
adversaries---including the impossibility of quantum bit commitment, the
difficulty of quantum rewinding and the definition of quantum security models
for classical primitives. In this review article, aimed primarily at
cryptographers unfamiliar with the quantum world, we survey the area of
theoretical quantum cryptography, with an emphasis on the constructions and
limitations beyond the realm of QKD.Comment: 45 pages, over 245 reference
- …