3,057 research outputs found
Implementation of two-party protocols in the noisy-storage model
The noisy-storage model allows the implementation of secure two-party
protocols under the sole assumption that no large-scale reliable quantum
storage is available to the cheating party. No quantum storage is thereby
required for the honest parties. Examples of such protocols include bit
commitment, oblivious transfer and secure identification. Here, we provide a
guideline for the practical implementation of such protocols. In particular, we
analyze security in a practical setting where the honest parties themselves are
unable to perform perfect operations and need to deal with practical problems
such as errors during transmission and detector inefficiencies. We provide
explicit security parameters for two different experimental setups using weak
coherent, and parametric down conversion sources. In addition, we analyze a
modification of the protocols based on decoy states.Comment: 41 pages, 33 figures, this is a companion paper to arXiv:0906.1030
considering practical aspects, v2: published version, title changed in
accordance with PRA guideline
Quantum de Finetti Theorems under Local Measurements with Applications
Quantum de Finetti theorems are a useful tool in the study of correlations in
quantum multipartite states. In this paper we prove two new quantum de Finetti
theorems, both showing that under tests formed by local measurements one can
get a much improved error dependence on the dimension of the subsystems. We
also obtain similar results for non-signaling probability distributions. We
give the following applications of the results:
We prove the optimality of the Chen-Drucker protocol for 3-SAT, under the
exponential time hypothesis.
We show that the maximum winning probability of free games can be estimated
in polynomial time by linear programming. We also show that 3-SAT with m
variables can be reduced to obtaining a constant error approximation of the
maximum winning probability under entangled strategies of O(m^{1/2})-player
one-round non-local games, in which the players communicate O(m^{1/2}) bits all
together.
We show that the optimization of certain polynomials over the hypersphere can
be performed in quasipolynomial time in the number of variables n by
considering O(log(n)) rounds of the Sum-of-Squares (Parrilo/Lasserre) hierarchy
of semidefinite programs. As an application to entanglement theory, we find a
quasipolynomial-time algorithm for deciding multipartite separability.
We consider a result due to Aaronson -- showing that given an unknown n qubit
state one can perform tomography that works well for most observables by
measuring only O(n) independent and identically distributed (i.i.d.) copies of
the state -- and relax the assumption of having i.i.d copies of the state to
merely the ability to select subsystems at random from a quantum multipartite
state.
The proofs of the new quantum de Finetti theorems are based on information
theory, in particular on the chain rule of mutual information.Comment: 39 pages, no figure. v2: changes to references and other minor
improvements. v3: added some explanations, mostly about Theorem 1 and
Conjecture 5. STOC version. v4, v5. small improvements and fixe
Security of Quantum Bit-String Generation
We consider the cryptographic task of bit-string generation. This is a
generalisation of coin tossing in which two mistrustful parties wish to
generate a string of random bits such that an honest party can be sure that the
other cannot have biased the string too much. We consider a quantum protocol
for this task, originally introduced in Phys. Rev. A {\bf 69}, 022322 (2004),
that is feasible with present day technology. We introduce security conditions
based on the average bias of the bits and the Shannon entropy of the string.
For each, we prove rigorous security bounds for this protocol in both noiseless
and noisy conditions under the most general attacks allowed by quantum
mechanics. Roughly speaking, in the absence of noise, a cheater can only bias
significantly a vanishing fraction of the bits, whereas in the presence of
noise, a cheater can bias a constant fraction, with this fraction depending
quantitatively on the level of noise. We also discuss classical protocols for
the same task, deriving upper bounds on how well a classical protocol can
perform. This enables the determination of how much noise the quantum protocol
can tolerate while still outperforming classical protocols. We raise several
conjectures concerning both quantum and classical possibilities for large n
cryptography. An experiment corresponding to the scheme analysed in this paper
has been performed and is reported elsewhere.Comment: 16 pages. No figures. Accepted for publication in Phys. Rev. A. A
corresponding experiment is reported in quant-ph/040812
A Framework for Efficient Adaptively Secure Composable Oblivious Transfer in the ROM
Oblivious Transfer (OT) is a fundamental cryptographic protocol that finds a
number of applications, in particular, as an essential building block for
two-party and multi-party computation. We construct a round-optimal (2 rounds)
universally composable (UC) protocol for oblivious transfer secure against
active adaptive adversaries from any OW-CPA secure public-key encryption scheme
with certain properties in the random oracle model (ROM). In terms of
computation, our protocol only requires the generation of a public/secret-key
pair, two encryption operations and one decryption operation, apart from a few
calls to the random oracle. In~terms of communication, our protocol only
requires the transfer of one public-key, two ciphertexts, and three binary
strings of roughly the same size as the message. Next, we show how to
instantiate our construction under the low noise LPN, McEliece, QC-MDPC, LWE,
and CDH assumptions. Our instantiations based on the low noise LPN, McEliece,
and QC-MDPC assumptions are the first UC-secure OT protocols based on coding
assumptions to achieve: 1) adaptive security, 2) optimal round complexity, 3)
low communication and computational complexities. Previous results in this
setting only achieved static security and used costly cut-and-choose
techniques.Our instantiation based on CDH achieves adaptive security at the
small cost of communicating only two more group elements as compared to the
gap-DH based Simplest OT protocol of Chou and Orlandi (Latincrypt 15), which
only achieves static security in the ROM
The Multi-round Process Matrix
We develop an extension of the process matrix (PM) framework for correlations
between quantum operations with no causal order that allows multiple rounds of
information exchange for each party compatibly with the assumption of
well-defined causal order of events locally. We characterise the higher-order
process describing such correlations, which we name the multi-round process
matrix (MPM), and formulate a notion of causal nonseparability for it that
extends the one for standard PMs. We show that in the multi-round case there
are novel manifestations of causal nonseparability that are not captured by a
naive application of the standard PM formalism: we exhibit an instance of an
operator that is both a valid PM and a valid MPM, but is causally separable in
the first case and can violate causal inequalities in the second case due to
the possibility of using a side channel.Comment: 24 pages with 6 figures, various improvements and corrections,
accepted in Quantu
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