62 research outputs found
Improved Lower Bounds for Locally Decodable Codes and Private Information Retrieval
We prove new lower bounds for locally decodable codes and private information
retrieval. We show that a 2-query LDC encoding n-bit strings over an l-bit
alphabet, where the decoder only uses b bits of each queried position of the
codeword, needs code length m = exp(Omega(n/(2^b Sum_{i=0}^b {l choose i})))
Similarly, a 2-server PIR scheme with an n-bit database and t-bit queries,
where the user only needs b bits from each of the two l-bit answers, unknown to
the servers, satisfies t = Omega(n/(2^b Sum_{i=0}^b {l choose i})). This
implies that several known PIR schemes are close to optimal. Our results
generalize those of Goldreich et al. who proved roughly the same bounds for
linear LDCs and PIRs. Like earlier work by Kerenidis and de Wolf, our classical
lower bounds are proved using quantum computational techniques. In particular,
we give a tight analysis of how well a 2-input function can be computed from a
quantum superposition of both inputs.Comment: 12 pages LaTeX, To appear in ICALP '0
Quantum Circulant Preconditioner for Linear System of Equations
We consider the quantum linear solver for with the circulant
preconditioner . The main technique is the singular value estimation (SVE)
introduced in [I. Kerenidis and A. Prakash, Quantum recommendation system, in
ITCS 2017]. However, some modifications of SVE should be made to solve the
preconditioned linear system . Moreover, different from
the preconditioned linear system considered in [B. D. Clader, B. C. Jacobs, C.
R. Sprouse, Preconditioned quantum linear system algorithm, Phys. Rev. Lett.,
2013], the circulant preconditioner is easy to construct and can be directly
applied to general dense non-Hermitian cases. The time complexity depends on
the condition numbers of and , as well as the Frobenius norm
Tight bounds for classical and quantum coin flipping
Coin flipping is a cryptographic primitive for which strictly better
protocols exist if the players are not only allowed to exchange classical, but
also quantum messages. During the past few years, several results have appeared
which give a tight bound on the range of implementable unconditionally secure
coin flips, both in the classical as well as in the quantum setting and for
both weak as well as strong coin flipping. But the picture is still incomplete:
in the quantum setting, all results consider only protocols with perfect
correctness, and in the classical setting tight bounds for strong coin flipping
are still missing. We give a general definition of coin flipping which unifies
the notion of strong and weak coin flipping (it contains both of them as
special cases) and allows the honest players to abort with a certain
probability. We give tight bounds on the achievable range of parameters both in
the classical and in the quantum setting.Comment: 18 pages, 2 figures; v2: published versio
Secure certification of mixed quantum states with application to two-party randomness generation
We investigate sampling procedures that certify that an arbitrary quantum
state on subsystems is close to an ideal mixed state
for a given reference state , up to errors on a few positions. This
task makes no sense classically: it would correspond to certifying that a given
bitstring was generated according to some desired probability distribution.
However, in the quantum case, this is possible if one has access to a prover
who can supply a purification of the mixed state.
In this work, we introduce the concept of mixed-state certification, and we
show that a natural sampling protocol offers secure certification in the
presence of a possibly dishonest prover: if the verifier accepts then he can be
almost certain that the state in question has been correctly prepared, up to a
small number of errors.
We then apply this result to two-party quantum coin-tossing. Given that
strong coin tossing is impossible, it is natural to ask "how close can we get".
This question has been well studied and is nowadays well understood from the
perspective of the bias of individual coin tosses. We approach and answer this
question from a different---and somewhat orthogonal---perspective, where we do
not look at individual coin tosses but at the global entropy instead. We show
how two distrusting parties can produce a common high-entropy source, where the
entropy is an arbitrarily small fraction below the maximum (except with
negligible probability)
Fully Distrustful Quantum Cryptography
In the distrustful quantum cryptography model the different parties have
conflicting interests and do not trust one another. Nevertheless, they trust
the quantum devices in their labs. The aim of the device-independent approach
to cryptography is to do away with the necessity of making this assumption,
and, consequently, significantly increase security. In this paper we enquire
whether the scope of the device-independent approach can be extended to the
distrustful cryptography model, thereby rendering it `fully' distrustful. We
answer this question in the affirmative by presenting a device-independent
(imperfect) bit-commitment protocol, which we then use to construct a
device-independent coin flipping protocol
Experimental verification of multipartite entanglement in quantum networks
Multipartite entangled states are a fundamental resource for a wide range of
quantum information processing tasks. In particular, in quantum networks it is
essential for the parties involved to be able to verify if entanglement is
present before they carry out a given distributed task. Here we design and
experimentally demonstrate a protocol that allows any party in a network to
check if a source is distributing a genuinely multipartite entangled state,
even in the presence of untrusted parties. The protocol remains secure against
dishonest behaviour of the source and other parties, including the use of
system imperfections to their advantage. We demonstrate the verification
protocol in a three- and four-party setting using polarization-entangled
photons, highlighting its potential for realistic photonic quantum
communication and networking applications.Comment: 8 pages, 4 figure
Secure certification of mixed quantum states with application to two-party randomness generation
We investigate sampling procedures that certify that an arbitrary quantum state on n subsystems is close to an ideal mixed state ⊗ for a given reference state , up to errors on a few positions. This task makes no sense classically: it would correspond to certifying that a given bitstring was generated according to some desired probability distribution. However, in the quantum case, this is possible if one has access to a prover who can supply a purification of the mixed state.
In this work, we introduce the concept of mixed-state certification, and we show that a natural sampling protocol offers secure certification in the presence of a possibly dishonest prover: if the verifier accepts then he can be almost certain that the state in question has been correctly prepared, up to a small number of errors.
We then apply this result to two-party quantum coin-tossing. Given that strong coin tossing is impossible, it is natural to ask “how close can we get”. This question has been well studied and is nowadays well understood from the perspective of the bias of individual coin tosses. We approach and answer this question from a different—and somewhat orthogonal—perspective, where we do not look at individual coin tosses but at the global entropy instead. We show how two distrusting parties can produce a common high-entropy source, where the entropy is an arbitrarily small fraction below the maximum
Do Israelis understand the Hebrew bible?
The Hebrew Bible should be taught like a foreign language in Israel too, argues Ghil'ad Zuckermann, inter alia endorsing Avraham Ahuvia’s recently-launched translation of the Old Testament into what Zuckermann calls high-register 'Israeli'. According to Zuckermann, Tanakh RAM fulfills the mission of 'red 'el ha'am' not only in its Hebrew meaning (Go down to the people) but also – more importantly – in its Yiddish meaning ('red' meaning 'speak!', as opposed to its colorful communist sense). Ahuvia's translation is most useful and dignified. Given its high register, however, Zuckermann predicts that the future promises consequent translations into more colloquial forms of Israeli, a beautifully multi-layered and intricately multi-sourced language, of which to be proud.Ghil'ad Zuckerman
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