374 research outputs found
Unconditional Security of Three State Quantum Key Distribution Protocols
Quantum key distribution (QKD) protocols are cryptographic techniques with
security based only on the laws of quantum mechanics. Two prominent QKD schemes
are the BB84 and B92 protocols that use four and two quantum states,
respectively. In 2000, Phoenix et al. proposed a new family of three state
protocols that offers advantages over the previous schemes. Until now, an error
rate threshold for security of the symmetric trine spherical code QKD protocol
has only been shown for the trivial intercept/resend eavesdropping strategy. In
this paper, we prove the unconditional security of the trine spherical code QKD
protocol, demonstrating its security up to a bit error rate of 9.81%. We also
discuss on how this proof applies to a version of the trine spherical code QKD
protocol where the error rate is evaluated from the number of inconclusive
events.Comment: 4 pages, published versio
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
Spherical Code Key Distribution Protocols for Qubits
Recently spherical codes were introduced as potentially more capable
ensembles for quantum key distribution. Here we develop specific key creation
protocols for the two qubit-based spherical codes, the trine and tetrahedron,
and analyze them in the context of a suitably-tailored intercept/resend attack,
both in standard form, and a ``gentler'' version whose back-action on the
quantum state is weaker. When compared to the standard unbiased basis
protocols, BB84 and six-state, two distinct advantages are found. First, they
offer improved tolerance of eavesdropping, the trine besting its counterpart
BB84 and the tetrahedron the six-state protocol. Second, the key error rate may
be computed from the sift rate of the protocol itself, removing the need to
sacrifice key bits for this purpose. This simplifies the protocol and improves
the overall key rate.Comment: 4 pages revtex, 2 figures; clarified security analysis. Final version
for publicatio
Minimal Informationally Complete Measurements for Pure States
We consider measurements, described by a positive-operator-valued measure
(POVM), whose outcome probabilities determine an arbitrary pure state of a
D-dimensional quantum system. We call such a measurement a pure-state
informationally complete (PSI-complete) POVM. We show that a measurement with
2D-1 outcomes cannot be PSI-complete, and then we construct a POVM with 2D
outcomes that suffices, thus showing that a minimal PSI-complete POVM has 2D
outcomes. We also consider PSI-complete POVMs that have only rank-one POVM
elements and construct an example with 3D-2 outcomes, which is a generalization
of the tetrahedral measurement for a qubit. The question of the minimal number
of elements in a rank-one PSI-complete POVM is left open.Comment: 2 figures, submitted for the Asher Peres festschrif
A simple construction of complex equiangular lines
A set of vectors of equal norm in represents equiangular lines
if the magnitudes of the inner product of every pair of distinct vectors in the
set are equal. The maximum size of such a set is , and it is conjectured
that sets of this maximum size exist in for every . We
describe a new construction for maximum-sized sets of equiangular lines,
exposing a previously unrecognized connection with Hadamard matrices. The
construction produces a maximum-sized set of equiangular lines in dimensions 2,
3 and 8.Comment: 11 pages; minor revisions and comments added in section 1 describing
a link to previously known results; correction to Theorem 1 and updates to
reference
A prolonged ICU stay after interhospital transport?
Transport of critically ill patients can be complicated [1-3]. Barratt and colleagues studied patients transferred for nonclinical reasons to evaluate the consequences of transportation [4]. Th ere was no diff erence in mortality but the ICU length of stay (LOS) increased by 3Â days, which was explained as a negative impact of the transport on patient physiology. We disagree with this conclusion. First, by including only transports to level 3 ICUs the received level of care for transported patients will increase, introducing a bias. Second, the increase in LOS can be interpreted as a result of selection bias, because patients with a short expected LOS would often not be considered eligible for transport. Also, since there was no increase in mortality, which would have been expected with an increased LOS, we might be looking at a mortality reduction as a result of the transfer to a higher-level ICU. Th ird, Barrett and colleagues suggest that deterioration of patient physiology during transport is probably respon sible for the increase in LOS. However, the reported Intensive Care National Audit and Research Centre scores before and after transport (although not validated for sequential patient assessments) do not support this assumption. Fourth, the method of transportation should have been included in this study. Specialised transport teams deliver patients with a better acute physiology compared with nonspecialised teams [2,5], making a need for regaining physiological stability unlikely. In conclusion, we congratulate Barratt and colleagues for their research. However, we think their conclusion is premature because multiple possible confounders were not taken into account
The Lie Algebraic Significance of Symmetric Informationally Complete Measurements
Examples of symmetric informationally complete positive operator valued
measures (SIC-POVMs) have been constructed in every dimension less than or
equal to 67. However, it remains an open question whether they exist in all
finite dimensions. A SIC-POVM is usually thought of as a highly symmetric
structure in quantum state space. However, its elements can equally well be
regarded as a basis for the Lie algebra gl(d,C). In this paper we examine the
resulting structure constants, which are calculated from the traces of the
triple products of the SIC-POVM elements and which, it turns out, characterize
the SIC-POVM up to unitary equivalence. We show that the structure constants
have numerous remarkable properties. In particular we show that the existence
of a SIC-POVM in dimension d is equivalent to the existence of a certain
structure in the adjoint representation of gl(d,C). We hope that transforming
the problem in this way, from a question about quantum state space to a
question about Lie algebras, may help to make the existence problem tractable.Comment: 56 page
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