3,031 research outputs found
A framework for quantum-secure device-independent randomness expansion
A device-independent randomness expansion protocol aims to take an initial
random seed and generate a longer one without relying on details of how the
devices operate for security. A large amount of work to date has focussed on a
particular protocol based on spot-checking devices using the CHSH inequality.
Here we show how to derive randomness expansion rates for a wide range of
protocols, with security against a quantum adversary. Our technique uses
semidefinite programming and a recent improvement of the entropy accumulation
theorem. To support the work and facilitate its use, we provide code that can
generate lower bounds on the amount of randomness that can be output based on
the measured quantities in the protocol. As an application, we give a protocol
that robustly generates up to two bits of randomness per entangled qubit pair,
which is twice that established in existing analyses of the spot-checking CHSH
protocol in the low noise regime.Comment: 26 (+9) pages, 6 (+1) figures. v2: New result included (Fig. 7) and
several updates made based on referee comment
Security of practical private randomness generation
Measurements on entangled quantum systems necessarily yield outcomes that are
intrinsically unpredictable if they violate a Bell inequality. This property
can be used to generate certified randomness in a device-independent way, i.e.,
without making detailed assumptions about the internal working of the quantum
devices used to generate the random numbers. Furthermore these numbers are also
private, i.e., they appear random not only to the user, but also to any
adversary that might possess a perfect description of the devices. Since this
process requires a small initial random seed, one usually speaks of
device-independent randomness expansion.
The purpose of this paper is twofold. First, we point out that in most real,
practical situations, where the concept of device-independence is used as a
protection against unintentional flaws or failures of the quantum apparatuses,
it is sufficient to show that the generated string is random with respect to an
adversary that holds only classical-side information, i.e., proving randomness
against quantum-side information is not necessary. Furthermore, the initial
random seed does not need to be private with respect to the adversary, provided
that it is generated in a way that is independent from the measured systems.
The devices, though, will generate cryptographically-secure randomness that
cannot be predicted by the adversary and thus one can, given access to free
public randomness, talk about private randomness generation.
The theoretical tools to quantify the generated randomness according to these
criteria were already introduced in [S. Pironio et al, Nature 464, 1021
(2010)], but the final results were improperly formulated. The second aim of
this paper is to correct this inaccurate formulation and therefore lay out a
precise theoretical framework for practical device-independent randomness
expansion.Comment: 18 pages. v3: important changes: the present version focuses on
security against classical side-information and a discussion about the
significance of these results has been added. v4: minor changes. v5: small
typos correcte
Quantum-proof randomness extractors via operator space theory
Quantum-proof randomness extractors are an important building block for
classical and quantum cryptography as well as device independent randomness
amplification and expansion. Furthermore they are also a useful tool in quantum
Shannon theory. It is known that some extractor constructions are quantum-proof
whereas others are provably not [Gavinsky et al., STOC'07]. We argue that the
theory of operator spaces offers a natural framework for studying to what
extent extractors are secure against quantum adversaries: we first phrase the
definition of extractors as a bounded norm condition between normed spaces, and
then show that the presence of quantum adversaries corresponds to a completely
bounded norm condition between operator spaces. From this we show that very
high min-entropy extractors as well as extractors with small output are always
(approximately) quantum-proof. We also study a generalization of extractors
called randomness condensers. We phrase the definition of condensers as a
bounded norm condition and the definition of quantum-proof condensers as a
completely bounded norm condition. Seeing condensers as bipartite graphs, we
then find that the bounded norm condition corresponds to an instance of a well
studied combinatorial problem, called bipartite densest subgraph. Furthermore,
using the characterization in terms of operator spaces, we can associate to any
condenser a Bell inequality (two-player game) such that classical and quantum
strategies are in one-to-one correspondence with classical and quantum attacks
on the condenser. Hence, we get for every quantum-proof condenser (which
includes in particular quantum-proof extractors) a Bell inequality that can not
be violated by quantum mechanics.Comment: v3: 34 pages, published versio
Physical Randomness Extractors: Generating Random Numbers with Minimal Assumptions
How to generate provably true randomness with minimal assumptions? This
question is important not only for the efficiency and the security of
information processing, but also for understanding how extremely unpredictable
events are possible in Nature. All current solutions require special structures
in the initial source of randomness, or a certain independence relation among
two or more sources. Both types of assumptions are impossible to test and
difficult to guarantee in practice. Here we show how this fundamental limit can
be circumvented by extractors that base security on the validity of physical
laws and extract randomness from untrusted quantum devices. In conjunction with
the recent work of Miller and Shi (arXiv:1402:0489), our physical randomness
extractor uses just a single and general weak source, produces an arbitrarily
long and near-uniform output, with a close-to-optimal error, secure against
all-powerful quantum adversaries, and tolerating a constant level of
implementation imprecision. The source necessarily needs to be unpredictable to
the devices, but otherwise can even be known to the adversary.
Our central technical contribution, the Equivalence Lemma, provides a general
principle for proving composition security of untrusted-device protocols. It
implies that unbounded randomness expansion can be achieved simply by
cross-feeding any two expansion protocols. In particular, such an unbounded
expansion can be made robust, which is known for the first time. Another
significant implication is, it enables the secure randomness generation and key
distribution using public randomness, such as that broadcast by NIST's
Randomness Beacon. Our protocol also provides a method for refuting local
hidden variable theories under a weak assumption on the available randomness
for choosing the measurement settings.Comment: A substantial re-writing of V2, especially on model definitions. An
abstract model of robustness is added and the robustness claim in V2 is made
rigorous. Focuses on quantum-security. A future update is planned to address
non-signaling securit
Source-device-independent heterodyne-based quantum random number generator at 17 Gbps
For many applications, quantum random number generation should be fast and independent from assumptions on the apparatus. Here, the authors devise and implement an approach which assumes a trusted detector but not a trusted source, and allows random bit generations at ~17 Gbps using off-the-shelf components
Graphical Methods in Device-Independent Quantum Cryptography
We introduce a framework for graphical security proofs in device-independent
quantum cryptography using the methods of categorical quantum mechanics. We are
optimistic that this approach will make some of the highly complex proofs in
quantum cryptography more accessible, facilitate the discovery of new proofs,
and enable automated proof verification. As an example of our framework, we
reprove a previous result from device-independent quantum cryptography: any
linear randomness expansion protocol can be converted into an unbounded
randomness expansion protocol. We give a graphical proof of this result, and
implement part of it in the Globular proof assistant.Comment: Publishable version. Diagrams have been polished, minor revisions to
the text, and an appendix added with supplementary proof
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