2,424 research outputs found
Certified randomness in quantum physics
The concept of randomness plays an important role in many disciplines. On one
hand, the question of whether random processes exist is fundamental for our
understanding of nature. On the other hand, randomness is a resource for
cryptography, algorithms and simulations. Standard methods for generating
randomness rely on assumptions on the devices that are difficult to meet in
practice. However, quantum technologies allow for new methods for generating
certified randomness. These methods are known as device-independent because do
not rely on any modeling of the devices. Here we review the efforts and
challenges to design device-independent randomness generators.Comment: 18 pages, 3 figure
High speed self-testing quantum random number generation without detection loophole
Quantum mechanics provides means of generating genuine randomness that is
impossible with deterministic classical processes. Remarkably, the
unpredictability of randomness can be certified in a self-testing manner that
is independent of implementation devices. Here, we present an experimental
demonstration of self-testing quantum random number generation based on an
detection-loophole free Bell test with entangled photons. In the randomness
analysis, without the assumption of independent identical distribution, we
consider the worst case scenario that the adversary launches the most powerful
attacks against quantum adversary. After considering statistical fluctuations
and applying an 80 Gb 45.6 Mb Toeplitz matrix hashing, we achieve a
final random bit rate of 114 bits/s, with a failure probability less than
. Such self-testing random number generators mark a critical step
towards realistic applications in cryptography and fundamental physics tests.Comment: 34 pages, 10 figure
Experimental device-independent certified randomness generation with an instrumental causal structure
The intrinsic random nature of quantum physics offers novel tools for the
generation of random numbers, a central challenge for a plethora of fields.
Bell non-local correlations obtained by measurements on entangled states allow
for the generation of bit strings whose randomness is guaranteed in a
device-independent manner, i.e. without assumptions on the measurement and
state-generation devices. Here, we generate this strong form of certified
randomness on a new platform: the so-called instrumental scenario, which is
central to the field of causal inference. First, we theoretically show that
certified random bits, private against general quantum adversaries, can be
extracted exploiting device-independent quantum instrumental-inequality
violations. To that end, we adapt techniques previously developed for the Bell
scenario. Then, we experimentally implement the corresponding
randomness-generation protocol using entangled photons and active feed-forward
of information. Moreover, we show that, for low levels of noise, our protocol
offers an advantage over the simplest Bell-nonlocality protocol based on the
Clauser-Horn-Shimony-Holt inequality.Comment: Modified Supplementary Information: removed description of extractor
algorithm introduced by arXiv:1212.0520. Implemented security of the protocol
against general adversarial attack
Quantifying randomness from Bell nonlocality
The twentieth century was marked by two scientific revolutions. On the one hand, quantum mechanics questioned our understanding of nature and physics. On the other hand, came the realisation that information could be treated as a mathematical quantity. They together brought forward the age of information.
A conceptual leap took place in the 1980's, that consisted in treating information in a quantum way as well. The idea that the intuitive notion of information could be governed by the counter-intuitive laws of quantum mechanics proved extremely fruitful, both from fundamental and applied points of view.
The notion of randomness plays a central role in that respect. Indeed, the laws of quantum physics are probabilistic: that contrasts with thousands of years of physical theories that aimed to derive deterministic laws of nature. This, in turn, provides us with sources of random numbers, a crucial resource for information protocols.
The fact that quantum theory only describes probabilistic behaviours was for some time regarded as a form of incompleteness. But nonlocality, in the sense of Bell, showed that this was not the case: the laws of quantum physics are inherently random, i.e., the randomness they imply cannot be traced back to a lack of knowledge.
This observation has practical consequences: the outputs of a nonlocal physical process are necessarily unpredictable. Moreover, the random character of these outputs does not depend on the physical system, but only of its nonlocal character. For that reason, nonlocality-based randomness is certified in a device-independent manner.
In this thesis, we quantify nonlocality-based randomness in various frameworks. In the first scenario, we quantify randomness without relying on the quantum formalism. We consider a nonlocal process and assume that it has a specific causal structure that is only due to how it evolves with time. We provide trade-offs between nonlocality and randomness for the various causal structures that we consider.
Nonlocality-based randomness is usually defined in a theoretical framework. In the second scenario, we take a practical approach and ask how much randomness can be certified in a practical situation, where only partial information can be gained from an experiment. We describe a method to optimise how much randomness can be certified in such a situation.
Trade-offs between nonlocality and randomness are usually studied in the bipartite case, as two agents is the minimal requirement to define nonlocality. In the third scenario, we quantify how much randomness can be certified for a tripartite process.
Though nonlocality-based randomness is device-independent, the process from which randomness is certified is actually realised with a physical state. In the fourth scenario, we ask what physical requirements should be imposed on the physical state for maximal randomness to be certified, and more specifically, how entangled the underlying state should be. We show that maximal randomness can be certified from any level of entanglement.El siglo XX estuvo marcado por dos revoluciones científicas. Por un lado, la mecánica cuántica cuestionó nuestro entendimiento de la naturaleza y de la física. Por otro lado, quedó claro que la información podía ser tratada como un objeto matemático. Juntos, ambas revoluciones dieron inicio a la era de la información. Un salto conceptual ocurrió en los años 80: se descubrió que la información podía ser tratada de manera cuántica. La idea de que la noción intuitiva de información podía ser gobernada por las leyes contra intuitivas de la mecánica cuántica resultó extremadamente fructífera tanto desde un punto de vista teórico como práctico. El concepto de aleatoriedad desempeña un papel central en este respecto. En efecto, las leyes de la física cuántica son probabilistas, lo que contrasta con siglos de teorías físicas cuyo objetivo era elaborar leyes deterministas de la naturaleza. Además, esto constituye una fuente de números aleatorios, un recurso crucial para criptografía. El hecho de que la física cuántica solo describe comportamientos aleatorios fue a veces considerado como una forma de incompletitud en la teoría. Pero la no-localidad, en el sentido de Bell, probó que no era el caso: las leyes cuánticas son intrínsecamente probabilistas, es decir, el azar que contienen no puede ser atribuido a una falta de conocimiento. Esta observación tiene consecuencias prácticas: los datos procedentes de un proceso físico no-local son necesariamente impredecibles. Además, el carácter aleatorio de estos datos no depende del sistema físico, sino solo de su carácter no-local. Por esta razón, el azar basado en la no-localidad está certificado independientemente del dispositivo físico. En esta tesis, cuantificamos el azar basado en la no-localidad en varios escenarios. En el primero, no utilizamos el formalismo cuántico. Estudiamos un proceso no-local dotado de varias estructuras causales en relación con su evolución temporal, y calculamos las relaciones entre aleatoriedad y no-localidad para estas diferentes estructuras causales. El azar basado en la no-localidad suele ser definido en un marco teórico. En el segundo escenario, adoptamos un enfoque práctico, y examinamos la relación entre aleatoriedad y no-localidad en una situación real, donde solo tenemos una información parcial, procedente de un experimento, sobre el proceso. Proponemos un método para optimizar la aleatoriedad en este caso. Hasta ahora, las relaciones entre aleatoriedad y no-localidad han sido estudiadas en el caso bipartito, dado que dos agentes forman el requisito mínimo para definir el concepto de no-localidad. En el tercer escenario, estudiamos esta relación en el caso tripartito. Aunque el azar basado en la no-localidad no depende del dispositivo físico, el proceso que sirve para generar azar debe sin embargo ser implementado con un estado cuántico. En el cuarto escenario, preguntamos si hay que imponer requisitos sobre el estado para poder certificar una máxima aleatoriedad de los resultados. Mostramos que se puede obtener la cantidad máxima de aleatoriedad indiferentemente del nivel de entrelazamiento del estado cuántico.Postprint (published version
Maximal randomness expansion from steering inequality violations using qudits
We consider the generation of randomness based upon the observed violation of
an Einstein-Podolsky-Rosen (EPR) steering inequality, known as one-sided
device-independent randomness expansion. We show that in the simplest scenario
-- involving only two parties applying two measurements with outcomes each
-- that there exist EPR steering inequalities whose maximal violation certifies
the maximal amount of randomness, equal to log(d) bits. We further show that
all pure partially entangled full-Schmidt-rank states in all dimensions can
achieve maximal violation of these inequalities, and thus lead to maximal
randomness expansion in the one-sided device-independent setting. More
generally, the amount of randomness that can be certified is given by a
semidefinite program, which we use to study the behaviour for non-maximal
violations of the inequalities.Comment: 6 pages, 1 figur
Randomness in post-selected events
Bell inequality violations can be used to certify private randomness for use
in cryptographic applications. In photonic Bell experiments, a large amount of
the data that is generated comes from no-detection events and presumably
contains little randomness. This raises the question as to whether randomness
can be extracted only from the smaller post-selected subset corresponding to
proper detection events, instead of from the entire set of data. This could in
principle be feasible without opening an analogue of the detection loophole as
long as the min-entropy of the post-selected data is evaluated by taking all
the information into account, including no-detection events. The possibility of
extracting randomness from a short string has a practical advantage, because it
reduces the computational time of the extraction.
Here, we investigate the above idea in a simple scenario, where the devices
and the adversary behave according to i.i.d. strategies. We show that indeed
almost all the randomness is present in the pair of outcomes for which at least
one detection happened. We further show that in some cases applying a
pre-processing on the data can capture features that an analysis based on
global frequencies only misses, thus resulting in the certification of more
randomness. We then briefly consider non-i.i.d strategies and provide an
explicit example of such a strategy that is more powerful than any i.i.d. one
even in the asymptotic limit of infinitely many measurement rounds, something
that was not reported before in the context of Bell inequalities.Comment: similar to published version, new section (III) on photonic
experiment
Optimal randomness generation from optical Bell experiments
Genuine randomness can be certified from Bell tests without any detailed
assumptions on the working of the devices with which the test is implemented.
An important class of experiments for implementing such tests is optical setups
based on polarisation measurements of entangled photons distributed from a
spontaneous parametric down conversion source. Here we compute the maximal
amount of randomness which can be certified in such setups under realistic
conditions. We provide relevant yet unexpected numerical values for the
physical parameters and achieve four times more randomness than previous
methods.Comment: 15 pages, 4 figure
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