13,089 research outputs found
Unifying classical and quantum key distillation
Assume that two distant parties, Alice and Bob, as well as an adversary, Eve,
have access to (quantum) systems prepared jointly according to a tripartite
state. In addition, Alice and Bob can use local operations and authenticated
public classical communication. Their goal is to establish a key which is
unknown to Eve. We initiate the study of this scenario as a unification of two
standard scenarios: (i) key distillation (agreement) from classical
correlations and (ii) key distillation from pure tripartite quantum states.
Firstly, we obtain generalisations of fundamental results related to
scenarios (i) and (ii), including upper bounds on the key rate. Moreover, based
on an embedding of classical distributions into quantum states, we are able to
find new connections between protocols and quantities in the standard scenarios
(i) and (ii).
Secondly, we study specific properties of key distillation protocols. In
particular, we show that every protocol that makes use of pre-shared key can be
transformed into an equally efficient protocol which needs no pre-shared key.
This result is of practical significance as it applies to quantum key
distribution (QKD) protocols, but it also implies that the key rate cannot be
locked with information on Eve's side. Finally, we exhibit an arbitrarily large
separation between the key rate in the standard setting where Eve is equipped
with quantum memory and the key rate in a setting where Eve is only given
classical memory. This shows that assumptions on the nature of Eve's memory are
important in order to determine the correct security threshold in QKD.Comment: full versio
Quantum Reverse Shannon Theorem
Dual to the usual noisy channel coding problem, where a noisy (classical or
quantum) channel is used to simulate a noiseless one, reverse Shannon theorems
concern the use of noiseless channels to simulate noisy ones, and more
generally the use of one noisy channel to simulate another. For channels of
nonzero capacity, this simulation is always possible, but for it to be
efficient, auxiliary resources of the proper kind and amount are generally
required. In the classical case, shared randomness between sender and receiver
is a sufficient auxiliary resource, regardless of the nature of the source, but
in the quantum case the requisite auxiliary resources for efficient simulation
depend on both the channel being simulated, and the source from which the
channel inputs are coming. For tensor power sources (the quantum generalization
of classical IID sources), entanglement in the form of standard ebits
(maximally entangled pairs of qubits) is sufficient, but for general sources,
which may be arbitrarily correlated or entangled across channel inputs,
additional resources, such as entanglement-embezzling states or backward
communication, are generally needed. Combining existing and new results, we
establish the amounts of communication and auxiliary resources needed in both
the classical and quantum cases, the tradeoffs among them, and the loss of
simulation efficiency when auxiliary resources are absent or insufficient. In
particular we find a new single-letter expression for the excess forward
communication cost of coherent feedback simulations of quantum channels (i.e.
simulations in which the sender retains what would escape into the environment
in an ordinary simulation), on non-tensor-power sources in the presence of
unlimited ebits but no other auxiliary resource. Our results on tensor power
sources establish a strong converse to the entanglement-assisted capacity
theorem.Comment: 35 pages, to appear in IEEE-IT. v2 has a fixed proof of the Clueless
Eve result, a new single-letter formula for the "spread deficit", better
error scaling, and an improved strong converse. v3 and v4 each make small
improvements to the presentation and add references. v5 fixes broken
reference
Effect of nonstationarities on detrended fluctuation analysis
Detrended fluctuation analysis (DFA) is a scaling analysis method used to
quantify long-range power-law correlations in signals. Many physical and
biological signals are ``noisy'', heterogeneous and exhibit different types of
nonstationarities, which can affect the correlation properties of these
signals. We systematically study the effects of three types of
nonstationarities often encountered in real data. Specifically, we consider
nonstationary sequences formed in three ways: (i) stitching together segments
of data obtained from discontinuous experimental recordings, or removing some
noisy and unreliable parts from continuous recordings and stitching together
the remaining parts -- a ``cutting'' procedure commonly used in preparing data
prior to signal analysis; (ii) adding to a signal with known correlations a
tunable concentration of random outliers or spikes with different amplitude,
and (iii) generating a signal comprised of segments with different properties
-- e.g. different standard deviations or different correlation exponents. We
compare the difference between the scaling results obtained for stationary
correlated signals and correlated signals with these three types of
nonstationarities.Comment: 17 pages, 10 figures, corrected some typos, added one referenc
More Randomness from the Same Data
Correlations that cannot be reproduced with local variables certify the
generation of private randomness. Usually, the violation of a Bell inequality
is used to quantify the amount of randomness produced. Here, we show how
private randomness generated during a Bell test can be directly quantified from
the observed correlations, without the need to process these data into an
inequality. The frequency with which the different measurement settings are
used during the Bell test can also be taken into account. This improved
analysis turns out to be very relevant for Bell tests performed with a finite
collection efficiency. In particular, applying our technique to the data of a
recent experiment [Christensen et al., Phys. Rev. Lett. 111, 130406 (2013)], we
show that about twice as much randomness as previously reported can be
potentially extracted from this setup.Comment: 6 pages + appendices, 4 figures, v3: version close to the published
one. See also the related work arXiv:1309.393
EPR Paradox,Locality and Completeness of Quantum Theory
The quantum theory (QT) and new stochastic approaches have no deterministic
prediction for a single measurement or for a single time -series of events
observed for a trapped ion, electron or any other individual physical system.
The predictions of QT being of probabilistic character apply to the statistical
distribution of the results obtained in various experiments. The probability
distribution is not an attribute of a dice but it is a characteristic of a
whole random experiment : '' rolling a dice''. and statistical long range
correlations between two random variables X and Y are not a proof of any causal
relation between these variable. Moreover any probabilistic model used to
describe a random experiment is consistent only with a specific protocol
telling how the random experiment has to be performed.In this sense the quantum
theory is a statistical and contextual theory of phenomena. In this paper we
discuss these important topics in some detail. Besides we discuss in historical
perspective various prerequisites used in the proofs of Bell and CHSH
inequalities concluding that the violation of these inequalities in spin
polarization correlation experiments is neither a proof of the completeness of
QT nor of its nonlocality. The question whether QT is predictably complete is
still open and it should be answered by a careful and unconventional analysis
of the experimental data. It is sufficient to analyze more in detail the
existing experimental data by using various non-parametric purity tests and
other specific statistical tools invented to study the fine structure of the
time-series. The correct understanding of statistical and contextual character
of QT has far reaching consequences for the quantum information and quantum
computing.Comment: 16 pages, 59 references,the contribution to the conference QTRF-4
held in Vaxjo, Sweden, 11-16 june 2007. To be published in the Proceeding
Intrinsic randomness in non-local theories: quantification and amplification
Quantum mechanics was developed as a response to the inadequacy of classical physics in explaining certain physical phenomena. While it has proved immensely successful, it also presents several features that severely challenge our classicality based intuition. Randomness in quantum theory is one such and is the central theme of this dissertation.
Randomness is a notion we have an intuitive grasp on since it appears to abound in nature. It a icts weather systems and nancial markets and is explicitly used in sport and gambling. It is used in a wide range of scienti c applications such as the simulation of genetic drift, population dynamics and molecular motion in fluids. Randomness (or the lack of it) is also central to philosophical concerns such as the existence of free will and anthropocentric notions of ethics and morality. The conception of randomness has evolved dramatically along with physical theory. While all randomness in classical theory can be fully attributed to a lack of knowledge of the observer, quantum theory qualitatively departs by allowing the existence of objective or intrinsic randomness. It is now known that intrinsic randomness is a generic feature of hypothetical theories larger than quantum theory called the non-signalling theories. They are usually studied with regards to a potential future completion of quantum mechanics or from the perspective of recognizing new physical principles describing nature. While several aspects have been studied to date, there has been little work in globally characterizing and quantifying randomness in quantum and non-signalling theories and the relationship between them. This dissertation is an attempt to ll this gap. Beginning with the unavoidable assumption of a weak source of randomness in the universe, we characterize upper bounds on quantum and non-signalling randomness. We develop a simple symmetry argument that helps identify maximal randomness in quantum theory and demonstrate its use in several explicit examples. Furthermore, we show that maximal randomness is forbidden within general non-signalling theories and constitutes a quantitative departure from quantum theory. We next address (what was) an open question about randomness ampli cation. It is known that a single source of randomness cannot be ampli ed using classical resources alone. We show that using quantum resources on the
other hand allows a full ampli cation of the weakest sources of randomness to maximal randomness even in the presence of supra-quantum adversaries. The signi cance of this result spans practical cryptographic scenarios as well as foundational concerns. It demonstrates that conditional on the smallest set of assumptions, the existence of the weakest randomness in the universe guarantees the existence of maximal randomness. The next question we address is the quanti cation of intrinsic randomness in non-signalling correlations. While this is intractable in general, we identify cases where this can be quanti ed. We nd that in these cases all observed randomness is intrinsic even relaxing the measurement independence assumption. We nally turn to the study of the only known resource that allows generating certi able intrinsic randomness in the laboratory i.e. entanglement. We address noisy quantum systems and calculate their entanglement dynamics under decoherence. We identify exact results for several realistic noise models and provide tight bounds in some other cases. We conclude by putting our results into perspective, pointing out some drawbacks and future avenues of work in addressing these concerns
Distributed Channel Synthesis
Two familiar notions of correlation are rediscovered as the extreme operating
points for distributed synthesis of a discrete memoryless channel, in which a
stochastic channel output is generated based on a compressed description of the
channel input. Wyner's common information is the minimum description rate
needed. However, when common randomness independent of the input is available,
the necessary description rate reduces to Shannon's mutual information. This
work characterizes the optimal trade-off between the amount of common
randomness used and the required rate of description. We also include a number
of related derivations, including the effect of limited local randomness, rate
requirements for secrecy, applications to game theory, and new insights into
common information duality.
Our proof makes use of a soft covering lemma, known in the literature for its
role in quantifying the resolvability of a channel. The direct proof
(achievability) constructs a feasible joint distribution over all parts of the
system using a soft covering, from which the behavior of the encoder and
decoder is inferred, with no explicit reference to joint typicality or binning.
Of auxiliary interest, this work also generalizes and strengthens this soft
covering tool.Comment: To appear in IEEE Trans. on Information Theory (submitted Aug., 2012,
accepted July, 2013), 26 pages, using IEEEtran.cl
How Quantum Computers Fail: Quantum Codes, Correlations in Physical Systems, and Noise Accumulation
The feasibility of computationally superior quantum computers is one of the
most exciting and clear-cut scientific questions of our time. The question
touches on fundamental issues regarding probability, physics, and
computability, as well as on exciting problems in experimental physics,
engineering, computer science, and mathematics. We propose three related
directions towards a negative answer. The first is a conjecture about physical
realizations of quantum codes, the second has to do with correlations in
stochastic physical systems, and the third proposes a model for quantum
evolutions when noise accumulates. The paper is dedicated to the memory of
Itamar Pitowsky.Comment: 16 page
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