695 research outputs found
Properties of thermal quantum states: locality of temperature, decay of correlations, and more
We review several properties of thermal states of spin Hamiltonians with
short range interactions. In particular, we focus on those aspects in which the
application of tools coming from quantum information theory has been specially
successful in the recent years. This comprises the study of the correlations at
finite and zero temperature, the stability against distant and/or weak
perturbations, the locality of temperature and their classical simulatability.
For the case of states with a finite correlation length, we overview the
results on their energy distribution and the equivalence of the canonical and
microcanonical ensemble.Comment: v1: 10 pages, 4 figures; v2: minor changes, close to published
versio
Lieb-Robinson bounds and the simulation of time evolution of local observables in lattice systems
This is an introductory text reviewing Lieb-Robinson bounds for open and
closed quantum many-body systems. We introduce the Heisenberg picture for
time-dependent local Liouvillians and state a Lieb-Robinson bound that gives
rise to a maximum speed of propagation of correlations in many body systems of
locally interacting spins and fermions. Finally, we discuss a number of
important consequences concerning the simulation of time evolution and
properties of ground states and stationary states.Comment: 13 pages, 2 figures; book chapte
Reliable quantum certification for photonic quantum technologies
A major roadblock for large-scale photonic quantum technologies is the lack
of practical reliable certification tools. We introduce an experimentally
friendly - yet mathematically rigorous - certification test for experimental
preparations of arbitrary m-mode pure Gaussian states, pure non-Gaussian states
generated by linear-optical circuits with n-boson Fock-basis states as inputs,
and states of these two classes subsequently post-selected with local
measurements on ancillary modes. The protocol is efficient in m and the inverse
post-selection success probability for all Gaussian states and all mentioned
non-Gaussian states with constant n. We follow the mindset of an untrusted
prover, who prepares the state, and a skeptic certifier, with classical
computing and single-mode homodyne-detection capabilities only. No assumptions
are made on the type of noise or capabilities of the prover. Our technique
exploits an extremality-based fidelity bound whose estimation relies on
non-Gaussian state nullifiers, which we introduce on the way as a byproduct
result. The certification of many-mode photonic networks, as those used for
photonic quantum simulations, boson samplers, and quantum metrology, is now
within reach.Comment: 8 pages + 20 pages appendix, 2 figures, results generalized to
scenarios with post-selection, presentation improve
Improving compressed sensing with the diamond norm
In low-rank matrix recovery, one aims to reconstruct a low-rank matrix from a
minimal number of linear measurements. Within the paradigm of compressed
sensing, this is made computationally efficient by minimizing the nuclear norm
as a convex surrogate for rank.
In this work, we identify an improved regularizer based on the so-called
diamond norm, a concept imported from quantum information theory. We show that
-for a class of matrices saturating a certain norm inequality- the descent cone
of the diamond norm is contained in that of the nuclear norm. This suggests
superior reconstruction properties for these matrices. We explicitly
characterize this set of matrices. Moreover, we demonstrate numerically that
the diamond norm indeed outperforms the nuclear norm in a number of relevant
applications: These include signal analysis tasks such as blind matrix
deconvolution or the retrieval of certain unitary basis changes, as well as the
quantum information problem of process tomography with random measurements.
The diamond norm is defined for matrices that can be interpreted as order-4
tensors and it turns out that the above condition depends crucially on that
tensorial structure. In this sense, this work touches on an aspect of the
notoriously difficult tensor completion problem.Comment: 25 pages + Appendix, 7 Figures, published versio
Direct certification of a class of quantum simulations
One of the main challenges in the field of quantum simulation and computation
is to identify ways to certify the correct functioning of a device when a
classical efficient simulation is not available. Important cases are situations
in which one cannot classically calculate local expectation values of state
preparations efficiently. In this work, we develop weak-membership formulations
of the certification of ground state preparations. We provide a non-interactive
protocol for certifying ground states of frustration-free Hamiltonians based on
simple energy measurements of local Hamiltonian terms. This certification
protocol can be applied to classically intractable analog quantum simulations:
For example, using Feynman-Kitaev Hamiltonians, one can encode universal
quantum computation in such ground states. Moreover, our certification protocol
is applicable to ground states encodings of IQP circuits demonstration of
quantum supremacy. These can be certified efficiently when the error is
polynomially bounded.Comment: 10 pages, corrected a small error in Eqs. (2) and (5
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