331 research outputs found
Mutual information area laws for thermal free fermions
We provide a rigorous and asymptotically exact expression of the mutual
information of translationally invariant free fermionic lattice systems in a
Gibbs state. In order to arrive at this result, we introduce a novel
frameworkfor computing determinants of Toeplitz operators with smooth symbols,
and for treating Toeplitz matrices with system size dependent entries. The
asymptotically exact mutual information for a partition of the one-dimensional
lattice satisfies an area law, with a prefactor which we compute explicitly. As
examples, we discuss the fermionic XX model in one dimension and free fermionic
models on the torus in higher dimensions in detail. Special emphasis is put
onto the discussion of the temperature dependence of the mutual information,
scaling like the logarithm of the inverse temperature, hence confirming an
expression suggested by conformal field theory. We also comment on the
applicability of the formalism to treat open systems driven by quantum noise.
In the appendix, we derive useful bounds to the mutual information in terms of
purities. Finally, we provide a detailed error analysis for finite system
sizes. This analysis is valuable in its own right for the abstract theory of
Toeplitz determinants.Comment: 42 pages, 4 figures, replaced by final versio
Dissipative preparation of entanglement in optical cavities
We propose a novel scheme for the preparation of a maximally entangled state
of two atoms in an optical cavity. Starting from an arbitrary initial state, a
singlet state is prepared as the unique fixed point of a dissipative quantum
dynamical process. In our scheme, cavity decay is no longer undesirable, but
plays an integral part in the dynamics. As a result, we get a qualitative
improvement in the scaling of the fidelity with the cavity parameters. Our
analysis indicates that dissipative state preparation is more than just a new
conceptual approach, but can allow for significant improvement as compared to
preparation protocols based on coherent unitary dynamics.Comment: 4 pages, 2 figure
Locality of temperature
This work is concerned with thermal quantum states of Hamiltonians on spin
and fermionic lattice systems with short range interactions. We provide results
leading to a local definition of temperature, thereby extending the notion of
"intensivity of temperature" to interacting quantum models. More precisely, we
derive a perturbation formula for thermal states. The influence of the
perturbation is exactly given in terms of a generalized covariance. For this
covariance, we prove exponential clustering of correlations above a universal
critical temperature that upper bounds physical critical temperatures such as
the Curie temperature. As a corollary, we obtain that above the critical
temperature, thermal states are stable against distant Hamiltonian
perturbations. Moreover, our results imply that above the critical temperature,
local expectation values can be approximated efficiently in the error and the
system size.Comment: 11 pages + 6 pages appendix, 6 figures; proof of the clustering
theorem corrected, improved presentatio
Hilbert's projective metric in quantum information theory
We introduce and apply Hilbert's projective metric in the context of quantum
information theory. The metric is induced by convex cones such as the sets of
positive, separable or PPT operators. It provides bounds on measures for
statistical distinguishability of quantum states and on the decrease of
entanglement under LOCC protocols or other cone-preserving operations. The
results are formulated in terms of general cones and base norms and lead to
contractivity bounds for quantum channels, for instance improving Ruskai's
trace-norm contraction inequality. A new duality between distinguishability
measures and base norms is provided. For two given pairs of quantum states we
show that the contraction of Hilbert's projective metric is necessary and
sufficient for the existence of a probabilistic quantum operation that maps one
pair onto the other. Inequalities between Hilbert's projective metric and the
Chernoff bound, the fidelity and various norms are proven.Comment: 32 pages including 3 appendices and 3 figures; v2: minor changes,
published versio
Precisely timing dissipative quantum information processing
Dissipative engineering constitutes a framework within which quantum
information processing protocols are powered by system-environment interaction
rather than by unitary dynamics alone. This framework embraces noise as a
resource, and consequently, offers a number of advantages compared to one based
on unitary dynamics alone, e.g., that the protocols are typically independent
of the initial state of the system. However, the time independent nature of
this scheme makes it difficult to imagine precisely timed sequential
operations, conditional measurements or error correction. In this work, we
provide a path around these challenges, by introducing basic dissipative
gadgets which allow us to precisely initiate, trigger and time dissipative
operations, while keeping the system Liouvillian time-independent. These
gadgets open up novel perspectives for thinking of timed dissipative quantum
information processing. As an example, we sketch how measurement based
computation can be simulated in the dissipative setting.Comment: 5+5 pages, material adde
The - divergence and Mixing times of quantum Markov processes
We introduce quantum versions of the -divergence, provide a detailed
analysis of their properties, and apply them in the investigation of mixing
times of quantum Markov processes. An approach similar to the one presented in
[1-3] for classical Markov chains is taken to bound the trace-distance from the
steady state of a quantum processes. A strict spectral bound to the convergence
rate can be given for time-discrete as well as for time-continuous quantum
Markov processes. Furthermore the contractive behavior of the
-divergence under the action of a completely positive map is
investigated and contrasted to the contraction of the trace norm. In this
context we analyse different versions of quantum detailed balance and, finally,
give a geometric conductance bound to the convergence rate for unital quantum
Markov processes
Cellular-automaton decoders for topological quantum memories
We introduce a new framework for constructing topological quantum memories, by recasting error recovery as a dynamical process
on a field generating cellular automaton. We envisage quantum systems controlled by a classical hardware composed of small local
memories, communicating with neighbours and repeatedly performing identical simple update rules. This approach does not
require any global operations or complex decoding algorithms. Our cellular automata draw inspiration from classical field theories,
with a Coulomb-like potential naturally emerging from the local dynamics. For a 3D automaton coupled to a 2D toric code, we
present evidence of an error correction threshold above 6.1% for uncorrelated noise. A 2D automaton equipped with a more
complex update rule yields a threshold above 8.2%. Our framework provides decisive new tools in the quest for realising a passive
dissipative quantum memory
A dissipative quantum Church-Turing theorem
We show that the time evolution of an open quantum system, described by a
possibly time dependent Liouvillian, can be simulated by a unitary quantum
circuit of a size scaling polynomially in the simulation time and the size of
the system. An immediate consequence is that dissipative quantum computing is
no more powerful than the unitary circuit model. Our result can be seen as a
dissipative Church-Turing theorem, since it implies that under natural
assumptions, such as weak coupling to an environment, the dynamics of an open
quantum system can be simulated efficiently on a quantum computer. Formally, we
introduce a Trotter decomposition for Liouvillian dynamics and give explicit
error bounds. This constitutes a practical tool for numerical simulations,
e.g., using matrix-product operators. We also demonstrate that most quantum
states cannot be prepared efficiently.Comment: 4 pages + 5 pages appendix, Implication 3 correcte
Driving two atoms in an optical cavity into an entangled steady state using engineered decay
We propose various schemes for the dissipative preparation of a maximally
entangled steady state of two atoms in an optical cavity. Harnessing the
natural decay processes of cavity photon loss and spontaneous emission, we use
an effective operator formalism to identify and engineer effective decay
processes, which reach an entangled steady state of two atoms as the unique
fixed point of the dissipative time evolution. We investigate various aspects
that are crucial for the experimental implementation of our schemes in
present-day and future cavity quantum electrodynamics systems and analytically
derive the optimal parameters, the error scaling and the speed of convergence
of our protocols. Our study shows promising performance of our schemes for
existing cavity experiments and favorable scaling of fidelity and speed with
respect to the cavity parameters.Comment: 37 pages, 14 figure
Guest editorial
International audienc
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