5,469 research outputs found
Generalized Entropies
We study an entropy measure for quantum systems that generalizes the von
Neumann entropy as well as its classical counterpart, the Gibbs or Shannon
entropy. The entropy measure is based on hypothesis testing and has an elegant
formulation as a semidefinite program, a type of convex optimization. After
establishing a few basic properties, we prove upper and lower bounds in terms
of the smooth entropies, a family of entropy measures that is used to
characterize a wide range of operational quantities. From the formulation as a
semidefinite program, we also prove a result on decomposition of hypothesis
tests, which leads to a chain rule for the entropy.Comment: 21 page
A de Finetti representation for finite symmetric quantum states
Consider a symmetric quantum state on an n-fold product space, that is, the
state is invariant under permutations of the n subsystems. We show that,
conditioned on the outcomes of an informationally complete measurement applied
to a number of subsystems, the state in the remaining subsystems is close to
having product form. This immediately generalizes the so-called de Finetti
representation to the case of finite symmetric quantum states.Comment: 22 pages, LaTe
Unconditional privacy over channels which cannot convey quantum information
By sending systems in specially prepared quantum states, two parties can
communicate without an eavesdropper being able to listen. The technique, called
quantum cryptography, enables one to verify that the state of the quantum
system has not been tampered with, and thus one can obtain privacy regardless
of the power of the eavesdropper. All previous protocols relied on the ability
to faithfully send quantum states. In fact, until recently, they could all be
reduced to a single protocol where security is ensured though sharing maximally
entangled states. Here we show this need not be the case -- one can obtain
verifiable privacy even through some channels which cannot be used to reliably
send quantum states.Comment: Related to quant-ph/0608195 and for a more general audienc
An All-But-One Entropic Uncertainty Relation, and Application to Password-based Identification
Entropic uncertainty relations are quantitative characterizations of
Heisenberg's uncertainty principle, which make use of an entropy measure to
quantify uncertainty. In quantum cryptography, they are often used as
convenient tools in security proofs. We propose a new entropic uncertainty
relation. It is the first such uncertainty relation that lower bounds the
uncertainty in the measurement outcome for all but one choice for the
measurement from an arbitrarily large (but specifically chosen) set of possible
measurements, and, at the same time, uses the min-entropy as entropy measure,
rather than the Shannon entropy. This makes it especially suited for quantum
cryptography. As application, we propose a new quantum identification scheme in
the bounded quantum storage model. It makes use of our new uncertainty relation
at the core of its security proof. In contrast to the original quantum
identification scheme proposed by Damg{\aa}rd et al., our new scheme also
offers some security in case the bounded quantum storage assumption fails hold.
Specifically, our scheme remains secure against an adversary that has unbounded
storage capabilities but is restricted to non-adaptive single-qubit operations.
The scheme by Damg{\aa}rd et al., on the other hand, completely breaks down
under such an attack.Comment: 33 pages, v
A measure of majorisation emerging from single-shot statistical mechanics
The use of the von Neumann entropy in formulating the laws of thermodynamics
has recently been challenged. It is associated with the average work whereas
the work guaranteed to be extracted in any single run of an experiment is the
more interesting quantity in general. We show that an expression that
quantifies majorisation determines the optimal guaranteed work. We argue it
should therefore be the central quantity of statistical mechanics, rather than
the von Neumann entropy. In the limit of many identical and independent
subsystems (asymptotic i.i.d) the von Neumann entropy expressions are recovered
but in the non-equilbrium regime the optimal guaranteed work can be radically
different to the optimal average. Moreover our measure of majorisation governs
which evolutions can be realized via thermal interactions, whereas the
nondecrease of the von Neumann entropy is not sufficiently restrictive. Our
results are inspired by single-shot information theory.Comment: 54 pages (15+39), 9 figures. Changed title / changed presentation,
same main results / added minor result on pure bipartite state entanglement
(appendix G) / near to published versio
Noisy pre-processing facilitating a photonic realisation of device-independent quantum key distribution
Device-independent quantum key distribution provides security even when the
equipment used to communicate over the quantum channel is largely
uncharacterized. An experimental demonstration of device-independent quantum
key distribution is however challenging. A central obstacle in photonic
implementations is that the global detection efficiency, i.e., the probability
that the signals sent over the quantum channel are successfully received, must
be above a certain threshold. We here propose a method to significantly relax
this threshold, while maintaining provable device-independent security. This is
achieved with a protocol that adds artificial noise, which cannot be known or
controlled by an adversary, to the initial measurement data (the raw key).
Focusing on a realistic photonic setup using a source based on spontaneous
parametric down conversion, we give explicit bounds on the minimal required
global detection efficiency.Comment: 5+16 pages, 4 figure
Decoupling with unitary approximate two-designs
Consider a bipartite system, of which one subsystem, A, undergoes a physical
evolution separated from the other subsystem, R. One may ask under which
conditions this evolution destroys all initial correlations between the
subsystems A and R, i.e. decouples the subsystems. A quantitative answer to
this question is provided by decoupling theorems, which have been developed
recently in the area of quantum information theory. This paper builds on
preceding work, which shows that decoupling is achieved if the evolution on A
consists of a typical unitary, chosen with respect to the Haar measure,
followed by a process that adds sufficient decoherence. Here, we prove a
generalized decoupling theorem for the case where the unitary is chosen from an
approximate two-design. A main implication of this result is that decoupling is
physical, in the sense that it occurs already for short sequences of random
two-body interactions, which can be modeled as efficient circuits. Our
decoupling result is independent of the dimension of the R system, which shows
that approximate 2-designs are appropriate for decoupling even if the dimension
of this system is large.Comment: Published versio
Multi-Prover Commitments Against Non-Signaling Attacks
We reconsider the concept of multi-prover commitments, as introduced in the
late eighties in the seminal work by Ben-Or et al. As was recently shown by
Cr\'{e}peau et al., the security of known two-prover commitment schemes not
only relies on the explicit assumption that the provers cannot communicate, but
also depends on their information processing capabilities. For instance, there
exist schemes that are secure against classical provers but insecure if the
provers have quantum information processing capabilities, and there are schemes
that resist such quantum attacks but become insecure when considering general
so-called non-signaling provers, which are restricted solely by the requirement
that no communication takes place.
This poses the natural question whether there exists a two-prover commitment
scheme that is secure under the sole assumption that no communication takes
place; no such scheme is known.
In this work, we give strong evidence for a negative answer: we show that any
single-round two-prover commitment scheme can be broken by a non-signaling
attack. Our negative result is as bad as it can get: for any candidate scheme
that is (almost) perfectly hiding, there exists a strategy that allows the
dishonest provers to open a commitment to an arbitrary bit (almost) as
successfully as the honest provers can open an honestly prepared commitment,
i.e., with probability (almost) 1 in case of a perfectly sound scheme. In the
case of multi-round schemes, our impossibility result is restricted to
perfectly hiding schemes.
On the positive side, we show that the impossibility result can be
circumvented by considering three provers instead: there exists a three-prover
commitment scheme that is secure against arbitrary non-signaling attacks
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