2,790 research outputs found
The Quantum Frontier
The success of the abstract model of computation, in terms of bits, logical
operations, programming language constructs, and the like, makes it easy to
forget that computation is a physical process. Our cherished notions of
computation and information are grounded in classical mechanics, but the
physics underlying our world is quantum. In the early 80s researchers began to
ask how computation would change if we adopted a quantum mechanical, instead of
a classical mechanical, view of computation. Slowly, a new picture of
computation arose, one that gave rise to a variety of faster algorithms, novel
cryptographic mechanisms, and alternative methods of communication. Small
quantum information processing devices have been built, and efforts are
underway to build larger ones. Even apart from the existence of these devices,
the quantum view on information processing has provided significant insight
into the nature of computation and information, and a deeper understanding of
the physics of our universe and its connections with computation.
We start by describing aspects of quantum mechanics that are at the heart of
a quantum view of information processing. We give our own idiosyncratic view of
a number of these topics in the hopes of correcting common misconceptions and
highlighting aspects that are often overlooked. A number of the phenomena
described were initially viewed as oddities of quantum mechanics. It was
quantum information processing, first quantum cryptography and then, more
dramatically, quantum computing, that turned the tables and showed that these
oddities could be put to practical effect. It is these application we describe
next. We conclude with a section describing some of the many questions left for
future work, especially the mysteries surrounding where the power of quantum
information ultimately comes from.Comment: Invited book chapter for Computation for Humanity - Information
Technology to Advance Society to be published by CRC Press. Concepts
clarified and style made more uniform in version 2. Many thanks to the
referees for their suggestions for improvement
Quantum Cryptography Beyond Quantum Key Distribution
Quantum cryptography is the art and science of exploiting quantum mechanical
effects in order to perform cryptographic tasks. While the most well-known
example of this discipline is quantum key distribution (QKD), there exist many
other applications such as quantum money, randomness generation, secure two-
and multi-party computation and delegated quantum computation. Quantum
cryptography also studies the limitations and challenges resulting from quantum
adversaries---including the impossibility of quantum bit commitment, the
difficulty of quantum rewinding and the definition of quantum security models
for classical primitives. In this review article, aimed primarily at
cryptographers unfamiliar with the quantum world, we survey the area of
theoretical quantum cryptography, with an emphasis on the constructions and
limitations beyond the realm of QKD.Comment: 45 pages, over 245 reference
Complexity Theory
Computational Complexity Theory is the mathematical study of the intrinsic power and limitations of computational resources like time, space, or randomness. The current workshop focused on recent developments in various sub-areas including arithmetic complexity, Boolean complexity, communication complexity, cryptography, probabilistic proof systems, pseudorandomness, and quantum computation. Many of the developements are related to diverse mathematical fields such as algebraic geometry, combinatorial number theory, probability theory, quantum mechanics, representation theory, and the theory of error-correcting codes
Some Applications of Coding Theory in Computational Complexity
Error-correcting codes and related combinatorial constructs play an important
role in several recent (and old) results in computational complexity theory. In
this paper we survey results on locally-testable and locally-decodable
error-correcting codes, and their applications to complexity theory and to
cryptography.
Locally decodable codes are error-correcting codes with sub-linear time
error-correcting algorithms. They are related to private information retrieval
(a type of cryptographic protocol), and they are used in average-case
complexity and to construct ``hard-core predicates'' for one-way permutations.
Locally testable codes are error-correcting codes with sub-linear time
error-detection algorithms, and they are the combinatorial core of
probabilistically checkable proofs
The Prom Problem: Fair and Privacy-Enhanced Matchmaking with Identity Linked Wishes
In the Prom Problem (TPP), Alice wishes to attend a school dance with Bob and needs a risk-free, privacy preserving way to find out whether Bob shares that same wish. If not, no one should know that she inquired about it, not even Bob. TPP represents a special class of matchmaking challenges, augmenting the properties of privacy-enhanced matchmaking, further requiring fairness and support for identity linked wishes (ILW) – wishes involving specific identities that are only valid if all involved parties have those same wishes.
The Horne-Nair (HN) protocol was proposed as a solution to TPP along with a sample pseudo-code embodiment leveraging an untrusted matchmaker. Neither identities nor pseudo-identities are included in any messages or stored in the matchmaker’s database. Privacy relevant data stay within user control. A security analysis and proof-of-concept implementation validated the approach, fairness was quantified, and a feasibility analysis demonstrated practicality in real-world networks and systems, thereby bounding risk prior to incurring the full costs of development.
The SecretMatch™ Prom app leverages one embodiment of the patented HN protocol to achieve privacy-enhanced and fair matchmaking with ILW. The endeavor led to practical lessons learned and recommendations for privacy engineering in an era of rapidly evolving privacy legislation. Next steps include design of SecretMatch™ apps for contexts like voting negotiations in legislative bodies and executive recruiting. The roadmap toward a quantum resistant SecretMatch™ began with design of a Hybrid Post-Quantum Horne-Nair (HPQHN) protocol. Future directions include enhancements to HPQHN, a fully Post Quantum HN protocol, and more
A new hardware-assisted PIR with O(n) shuffle cost
Ministry of Education, Singapore under its Academic Research Funding Tier
Shadow Tomography of Quantum States
We introduce the problem of *shadow tomography*: given an unknown
-dimensional quantum mixed state , as well as known two-outcome
measurements , estimate the probability that
accepts , to within additive error , for each of the
measurements. How many copies of are needed to achieve this, with high
probability? Surprisingly, we give a procedure that solves the problem by
measuring only copies. This means, for example, that we can learn the behavior of an
arbitrary -qubit state, on all accepting/rejecting circuits of some fixed
polynomial size, by measuring only copies of the state.
This resolves an open problem of the author, which arose from his work on
private-key quantum money schemes, but which also has applications to quantum
copy-protected software, quantum advice, and quantum one-way communication.
Recently, building on this work, Brand\~ao et al. have given a different
approach to shadow tomography using semidefinite programming, which achieves a
savings in computation time.Comment: 29 pages, extended abstract appeared in Proceedings of STOC'2018,
revised to give slightly better upper bound (1/eps^4 rather than 1/eps^5) and
lower bounds with explicit dependence on the dimension
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