5 research outputs found
Certified Everlasting Zero-Knowledge Proof for QMA
In known constructions of classical zero-knowledge protocols for NP, either
of zero-knowledge or soundness holds only against computationally bounded
adversaries. Indeed, achieving both statistical zero-knowledge and statistical
soundness at the same time with classical verifier is impossible for NP unless
the polynomial-time hierarchy collapses, and it is also believed to be
impossible even with a quantum verifier. In this work, we introduce a novel
compromise, which we call the certified everlasting zero-knowledge proof for
QMA. It is a computational zero-knowledge proof for QMA, but the verifier
issues a classical certificate that shows that the verifier has deleted its
quantum information. If the certificate is valid, even unbounded malicious
verifier can no longer learn anything beyond the validity of the statement. We
construct a certified everlasting zero-knowledge proof for QMA. For the
construction, we introduce a new quantum cryptographic primitive, which we call
commitment with statistical binding and certified everlasting hiding, where the
hiding property becomes statistical once the receiver has issued a valid
certificate that shows that the receiver has deleted the committed information.
We construct commitment with statistical binding and certified everlasting
hiding from quantum encryption with certified deletion by Broadbent and Islam
[TCC 2020] (in a black box way), and then combine it with the quantum
sigma-protocol for QMA by Broadbent and Grilo [FOCS 2020] to construct the
certified everlasting zero-knowledge proof for QMA. Our constructions are
secure in the quantum random oracle model. Commitment with statistical binding
and certified everlasting hiding itself is of independent interest, and there
will be many other useful applications beyond zero-knowledge.Comment: 33 page
Nonlocality under Computational Assumptions
Nonlocality and its connections to entanglement are fundamental features of
quantum mechanics that have found numerous applications in quantum information
science. A set of correlations is said to be nonlocal if it cannot be
reproduced by spacelike-separated parties sharing randomness and performing
local operations. An important practical consideration is that the runtime of
the parties has to be shorter than the time it takes light to travel between
them. One way to model this restriction is to assume that the parties are
computationally bounded. We therefore initiate the study of nonlocality under
computational assumptions and derive the following results:
(a) We define the set (not-efficiently-local) as consisting of
all bipartite states whose correlations arising from local measurements cannot
be reproduced with shared randomness and \emph{polynomial-time} local
operations.
(b) Under the assumption that the Learning With Errors problem cannot be
solved in \emph{quantum} polynomial-time, we show that
, where is the set of \emph{all}
bipartite entangled states (pure and mixed). This is in contrast to the
standard notion of nonlocality where it is known that some entangled states,
e.g. Werner states, are local. In essence, we show that there exist (efficient)
local measurements producing correlations that cannot be reproduced through
shared randomness and quantum polynomial-time computation.
(c) We prove that if unconditionally, then
. In other words, the ability to certify all
bipartite entangled states against computationally bounded adversaries gives a
non-trivial separation of complexity classes.
(d) Using (c), we show that a certain natural class of 1-round delegated
quantum computation protocols that are sound against provers
cannot exist.Comment: 65 page
Post-quantum Zero Knowledge in Constant Rounds
We construct a constant-round zero-knowledge classical argument for NP secure
against quantum attacks. We assume the existence of Quantum Fully-Homomorphic
Encryption and other standard primitives, known based on the Learning with
Errors Assumption for quantum algorithms. As a corollary, we also obtain a
constant-round zero-knowledge quantum argument for QMA.
At the heart of our protocol is a new no-cloning non-black-box simulation
technique
Scheduling with Time Lags
Scheduling is essential when activities need to be allocated to scarce resources over time. Motivated by the problem of scheduling barges along container terminals in the Port of Rotterdam, this thesis designs and analyzes algorithms for various on-line and off-line scheduling problems with time lags. A time lag specifies a minimum time delay required between the execution of two consecutive operations of the same job. Time lags may be the result of transportation delays (like the time required for barges to sail from one terminal to the next), the duration of activities that do not require resources (like drying or cooling down), or intermediate processes on non-bottleneck machines between two bottleneck machines.
For the on-line flow shop, job shop and open shop problems of minimizing the makespan, we analyze the competitive ratio of a class of greedy algorithms. For the off-line parallel flow shop scheduling problem with time lags of minimizing the makespan, we design algorithms with fixed worst-case performance guarantees. For two special subsets of scheduling problems with time lags, we show that Polynomial-Time Approximation Schemes (PTAS) can be constructed under certain mild conditions. For the fixed interval scheduling problem, we show that the flow shop problem is solvable in polynomial time in the case of equal time lags but that it is NP-hard in the strong sense for general time lags. The fixed interval two-machine job shop and open shop problems are shown to be solvable in polynomial time if the time lags are smaller than the processing time of any operation