283 research outputs found
Variable Bias Coin Tossing
Alice is a charismatic quantum cryptographer who believes her parties are
unmissable; Bob is a (relatively) glamorous string theorist who believes he is
an indispensable guest. To prevent possibly traumatic collisions of
self-perception and reality, their social code requires that decisions about
invitation or acceptance be made via a cryptographically secure variable bias
coin toss (VBCT). This generates a shared random bit by the toss of a coin
whose bias is secretly chosen, within a stipulated range, by one of the
parties; the other party learns only the random bit. Thus one party can
secretly influence the outcome, while both can save face by blaming any
negative decisions on bad luck.
We describe here some cryptographic VBCT protocols whose security is
guaranteed by quantum theory and the impossibility of superluminal signalling,
setting our results in the context of a general discussion of secure two-party
computation. We also briefly discuss other cryptographic applications of VBCT.Comment: 14 pages, minor correction
Tomographic Quantum Cryptography Protocols are Reference Frame Independent
We consider the class of reference frame independent protocols in d
dimensions for quantum key distribution, in which Alice and Bob have one
natural basis that is aligned and the rest of their frames are unaligned. We
relate existing approaches to tomographically complete protocols. We comment on
two different approaches to finite key bounds in this setting, one direct and
one using the entropic uncertainty relation and suggest that the existing
finite key bounds can still be improved.Comment: Published version. 8 pages, 1 figur
Keyring models: an approach to steerability
If a measurement is made on one half of a bipartite system, then, conditioned
on the outcome, the other half has a new reduced state. If these reduced states
defy classical explanation -- that is, if shared randomness cannot produce
these reduced states for all possible measurements -- the bipartite state is
said to be steerable. Determining which states are steerable is a challenging
problem even for low dimensions. In the case of two-qubit systems a criterion
is known for T-states (that is, those with maximally mixed marginals) under
projective measurements. In the current work we introduce the concept of
keyring models -- a special class of local hidden state models. When the
measurements made correspond to real projectors, these allow us to study
steerability beyond T-states.
Using keyring models, we completely solve the steering problem for real
projective measurements when the state arises from mixing a pure two-qubit
state with uniform noise. We also give a partial solution in the case when the
uniform noise is replaced by independent depolarizing channels.Comment: 15(+4) pages, 5 figures. v2: references added, v3: minor change
Causality - Complexity - Consistency: Can Space-Time Be Based on Logic and Computation?
The difficulty of explaining non-local correlations in a fixed causal
structure sheds new light on the old debate on whether space and time are to be
seen as fundamental. Refraining from assuming space-time as given a priori has
a number of consequences. First, the usual definitions of randomness depend on
a causal structure and turn meaningless. So motivated, we propose an intrinsic,
physically motivated measure for the randomness of a string of bits: its length
minus its normalized work value, a quantity we closely relate to its Kolmogorov
complexity (the length of the shortest program making a universal Turing
machine output this string). We test this alternative concept of randomness for
the example of non-local correlations, and we end up with a reasoning that
leads to similar conclusions as in, but is conceptually more direct than, the
probabilistic view since only the outcomes of measurements that can actually
all be carried out together are put into relation to each other. In the same
context-free spirit, we connect the logical reversibility of an evolution to
the second law of thermodynamics and the arrow of time. Refining this, we end
up with a speculation on the emergence of a space-time structure on bit strings
in terms of data-compressibility relations. Finally, we show that logical
consistency, by which we replace the abandoned causality, it strictly weaker a
constraint than the latter in the multi-party case.Comment: 17 pages, 16 figures, small correction
Bell inequalities from no-signaling distributions
A Bell inequality is a constraint on a set of correlations whose violation
can be used to certify non-locality. They are instrumental for
device-independent tasks such as key distribution or randomness expansion. In
this work we consider bipartite Bell inequalities where two parties have
and possible inputs and give and possible outputs, referring
to this as the scenario. By exploiting knowledge of the
set of extremal no-signalling distributions, we find all 175 Bell inequality
classes in the (4, 4, 2, 2) scenario, as well as providing a partial list of
18277 classes in the (4, 5, 2, 2) scenario. We also use a probabilistic
algorithm to obtain 5 classes of inequality in the (2, 3, 3, 2) scenario, which
we confirmed to be complete, 25 classes in the (3, 3, 2, 3) scenario, and a
partial list of 21170 classes in the (3, 3, 3, 3) scenario. Our inequalities
are given in supplementary files. Finally, we discuss the application of these
inequalities to the detection loophole problem, and provide new lower bounds on
the detection efficiency threshold for small numbers of inputs and outputs.Comment: 15 + 7 pages. v2: more scenarios are covered and more analysis has
been done. v3: shorter title and a few additional updates, including summary
table
Entropic uncertainty relations for extremal unravelings of super-operators
A way to pose the entropic uncertainty principle for trace-preserving
super-operators is presented. It is based on the notion of extremal unraveling
of a super-operator. For given input state, different effects of each
unraveling result in some probability distribution at the output. As it is
shown, all Tsallis' entropies of positive order as well as some of Renyi's
entropies of this distribution are minimized by the same unraveling of a
super-operator. Entropic relations between a state ensemble and the generated
density matrix are revisited in terms of both the adopted measures. Using
Riesz's theorem, we obtain two uncertainty relations for any pair of
generalized resolutions of the identity in terms of the Renyi and Tsallis
entropies. The inequality with Renyi's entropies is an improvement of the
previous one, whereas the inequality with Tsallis' entropies is a new relation
of a general form. The latter formulation is explicitly shown for a pair of
complementary observables in a -level system and for the angle and the
angular momentum. The derived general relations are immediately applied to
extremal unravelings of two super-operators.Comment: 8 pages, one figure. More explanations are given for Eq. (2.19) and
Example III.5. One reference is adde
The Intrinsic Quantum Nature of Nash Equilibrium Mixtures
Every undergraduate textbook in game theory has a chapter discussing the difficulty to interpret the mixed Nash equilibrium strategies. Unlike the usual suggested interpretations made in those textbooks, here we prove that these randomised strategies neither imply that players use some coin flips to make their decisions, nor that the mixtures represent the uncertainty of each player about the others' actions.Instead, the paper demonstrates a fundamental connection between the Nash equilibrium 'randomised' or 'mixed' strategies of classical game theory and the pure quantum states of quantum theory in physics. This link has some key consequences for the meaning of randomised strategies:In the main theorem, I prove that in every mixed Nash equilibrium, each player state of knowledge about his/her own future rational choices is represented by a pure quantum state. This indicates that prior making his/her actual choice, each player must be in a quantum superposition over her/his possible rational choices (in the support of his probability measure). This result notably permits to show that the famous 'indifference condition' that must be satisfied by each player in an equilibrium is actually the condition that ensures each player is in a 'rational epistemic state of ignorance' about her/his own future choice of an action
On thermalization in Kitaev's 2D model
The thermalization process of the 2D Kitaev model is studied within the
Markovian weak coupling approximation. It is shown that its largest relaxation
time is bounded from above by a constant independent of the system size and
proportional to where is an energy gap over the
4-fold degenerate ground state. This means that the 2D Kitaev model is not an
example of a memory, neither quantum nor classical.Comment: 26 page
- …