101 research outputs found
Deriving tight error-trade-off relations for approximate joint measurements of incompatible quantum observables
The quantification of the "measurement uncertainty" aspect of Heisenberg's
Uncertainty Principle---that is, the study of trade-offs between accuracy and
disturbance, or between accuracies in an approximate joint measurement on two
incompatible observables---has regained a lot of interest recently. Several
approaches have been proposed and debated. In this paper we consider Ozawa's
definitions for inaccuracies (as root-mean-square errors) in approximate joint
measurements, and study how these are constrained in different cases, whether
one specifies certain properties of the approximations---namely their standard
deviations and/or their bias---or not. Extending our previous work [C.
Branciard, Proc. Natl. Acad. Sci. U.S.A. 110, 6742 (2013)], we derive new
error-trade-off relations, which we prove to be tight for pure states. We show
explicitly how all previously known relations for Ozawa's inaccuracies follow
from ours. While our relations are in general not tight for mixed states, we
show how these can be strengthened and how tight relations can still be
obtained in that case.Comment: 18 page
Detection Loophole in Bell experiments: How post-selected local correlations can look non-local
A common problem in Bell type experiments is the well-known detection
loophole: if the detection efficiencies are not perfect and if one simply
post-selects the conclusive events, one might observe a violation of a Bell
inequality, even though a local model could have explained the experimental
results. In this paper, we analyze the set of all post-selected correlations
that can be explained by a local model, and show that it forms a polytope,
larger than the Bell local polytope. We characterize the facets of this
post-selected local polytope in the CHSH scenario, where two parties have
binary inputs and outcomes. Our approach gives new insights on the detection
loophole problem.Comment: 9 pages, 3 figure
Witnesses of causal nonseparability: an introduction and a few case studies
It was recently realised that quantum theory allows for so-called causally
nonseparable processes, which are incompatible with any definite causal order.
This was first suggested on a rather abstract level by the formalism of process
matrices, which only assumes that quantum theory holds locally in some
observers' laboratories, but does not impose a global causal structure; it was
then shown, on a more practical level, that the quantum switch---a new resource
for quantum computation that goes beyond causally ordered circuits---provided
precisely a physical example of a causally nonseparable process. To demonstrate
that a given process is causally nonseparable, we introduced in [Ara\'ujo et
al., New J. Phys. 17, 102001 (2015)] the concept of witnesses of causal
nonseparability. Here we present a shorter introduction to this concept, and
concentrate on some explicit examples to show how to construct and use such
witnesses in practice.Comment: 15 pages, 7 figure
Noise and Disturbance of Qubit Measurements: An Information-Theoretic Characterisation
Information-theoretic definitions for the noise associated with a quantum
measurement and the corresponding disturbance to the state of the system have
recently been introduced [F. Buscemi et al., Phys. Rev. Lett. 112, 050401
(2014)]. These definitions are invariant under relabelling of measurement
outcomes, and lend themselves readily to the formulation of state-independent
uncertainty relations both for the joint estimate of observables (noise-noise
relations) and the noise-disturbance tradeoff. Here we derive such relations
for incompatible qubit observables, which we prove to be tight in the case of
joint estimates, and present progress towards fully characterising the
noise-disturbance tradeoff. In doing so, we show that the set of obtainable
noise-noise values for such observables is convex, whereas the conjectured form
for the set of obtainable noise-disturbance values is not. Furthermore,
projective measurements are not optimal with respect to the joint-measurement
noise or noise-disturbance tradeoffs. Interestingly, it seems that four-outcome
measurements are needed in the former case, whereas three-outcome measurements
are optimal in the latter.Comment: Minor changes, corresponds to final published version. 14 pages, 5
figure
How \psi-epistemic models fail at explaining the indistinguishability of quantum states
We study the extent to which \psi-epistemic models for quantum measurement
statistics---models where the quantum state does not have a real, ontic
status---can explain the indistinguishability of nonorthogonal quantum states.
This is done by comparing the overlap of any two quantum states with the
overlap of the corresponding classical probability distributions over ontic
states in a \psi-epistemic model. It is shown that in Hilbert spaces of
dimension , the ratio between the classical and quantum overlaps in
any \psi-epistemic model must be arbitrarily small for certain nonorthogonal
states, suggesting that such models are arbitrarily bad at explaining the
indistinguishability of quantum states. For dimensions = 3 and 4, we
construct explicit states and measurements that can be used experimentally to
put stringent bounds on the ratio of classical-to-quantum overlaps in
\psi-epistemic models, allowing one in particular to rule out maximally
\psi-epistemic models more efficiently than previously proposed.Comment: 8 page
Simulation of equatorial von Neumann measurements on GHZ states using nonlocal resources
Reproducing with elementary resources the correlations that arise when a
quantum system is measured (quantum state simulation), allows one to get
insight on the operational and computational power of quantum correlations. We
propose a family of models that can simulate von Neumann measurements in the
x-y plane of the Bloch sphere on n-partite GHZ states using only bipartite
nonlocal boxes. For the tripartite and fourpartite states, the models use only
bipartite nonlocal boxes; they can be translated into classical communication
schemes with finite average communication cost.Comment: 15 pages, 4 figures, published versio
On the definition and characterisation of multipartite causal (non)separability
The concept of causal nonseparability has been recently introduced, in
opposition to that of causal separability, to qualify physical processes that
locally abide by the laws of quantum theory, but cannot be embedded in a
well-defined global causal structure. While the definition is unambiguous in
the bipartite case, its generalisation to the multipartite case is not so
straightforward. Two seemingly different generalisations have been proposed,
one for a restricted tripartite scenario and one for the general multipartite
case. Here we compare the two, showing that they are in fact inequivalent. We
propose our own definition of causal (non)separability for the general case,
which---although a priori subtly different---turns out to be equivalent to the
concept of "extensible causal (non)separability" introduced before, and which
we argue is a more natural definition for general multipartite scenarios. We
then derive necessary, as well as sufficient conditions to characterise
causally (non)separable processes in practice. These allow one to devise
practical tests, by generalising the tool of witnesses of causal
nonseparability
Evaluation of two different entanglement measures on a bound entangled state
We consider the mixed three-qubit bound entangled state defined as the
normalized projector on the subspace that is complementary to an Unextendible
Product Basis [C. H. Bennett et. al., Phys. Rev. Lett. 82, 5385 (1999)]. Using
the fact that no product state lies in the support of that state, we compute
its entanglement by providing a basis of its subspace formed by
"minimally-entangled" states. The approach is in principle applicable to any
entanglement measure; here we provide explicit values for both the geometric
measure of entanglement and a generalized concurrence.Comment: 6 pages, 1 figur
Zero-Error Attacks and Detection Statistics in the Coherent One-Way Protocol for Quantum Cryptography
This is a study of the security of the Coherent One-Way (COW) protocol for
quantum cryptography, proposed recently as a simple and fast experimental
scheme. In the zero-error regime, the eavesdropper Eve can only take advantage
of the losses in the transmission. We consider new attacks, based on
unambiguous state discrimination, which perform better than the basic
beam-splitting attack, but which can be detected by a careful analysis of the
detection statistics. These results stress the importance of testing several
statistical parameters in order to achieve higher rates of secret bits
Device-dependent and device-independent quantum key distribution without a shared reference frame
Standard quantum key distribution (QKD) protocols typically assume that the
distant parties share a common reference frame. In practice, however,
establishing and maintaining a good alignment between distant observers is
rarely a trivial issue, which may significantly restrain the implementation of
long-distance quantum communication protocols. Here we propose simple QKD
protocols that do not require the parties to share any reference frame, and
study their security and feasibility in both the usual device-dependent
case--in which the two parties use well characterized measurement devices--as
well as in the device-independent case--in which the measurement devices can be
untrusted, and the security relies on the violation of a Bell inequality. To
illustrate the practical relevance of these ideas, we present a
proof-of-principle demonstration of our protocols using polarization entangled
photons distributed over a coiled 10-km-long optical fiber. We consider two
situations, in which either the fiber spool freely drifts, or randomly chosen
polarization transformations are applied. The correlations obtained from
measurements allow, with high probability, to generate positive asymptotic
secret key rates in both the device-dependent and device-independent scenarios
(under the fair-sampling assumption for the latter case).Comment: 12 pages, 11 figure
- …