1,214 research outputs found
On Variational Expressions for Quantum Relative Entropies
Distance measures between quantum states like the trace distance and the
fidelity can naturally be defined by optimizing a classical distance measure
over all measurement statistics that can be obtained from the respective
quantum states. In contrast, Petz showed that the measured relative entropy,
defined as a maximization of the Kullback-Leibler divergence over projective
measurement statistics, is strictly smaller than Umegaki's quantum relative
entropy whenever the states do not commute. We extend this result in two ways.
First, we show that Petz' conclusion remains true if we allow general positive
operator valued measures. Second, we extend the result to Renyi relative
entropies and show that for non-commuting states the sandwiched Renyi relative
entropy is strictly larger than the measured Renyi relative entropy for , and strictly smaller for . The
latter statement provides counterexamples for the data-processing inequality of
the sandwiched Renyi relative entropy for . Our main tool is
a new variational expression for the measured Renyi relative entropy, which we
further exploit to show that certain lower bounds on quantum conditional mutual
information are superadditive.Comment: v2: final published versio
Witnessing eigenstates for quantum simulation of Hamiltonian spectra
The efficient calculation of Hamiltonian spectra, a problem often intractable
on classical machines, can find application in many fields, from physics to
chemistry. Here, we introduce the concept of an "eigenstate witness" and
through it provide a new quantum approach which combines variational methods
and phase estimation to approximate eigenvalues for both ground and excited
states. This protocol is experimentally verified on a programmable silicon
quantum photonic chip, a mass-manufacturable platform, which embeds entangled
state generation, arbitrary controlled-unitary operations, and projective
measurements. Both ground and excited states are experimentally found with
fidelities >99%, and their eigenvalues are estimated with 32-bits of precision.
We also investigate and discuss the scalability of the approach and study its
performance through numerical simulations of more complex Hamiltonians. This
result shows promising progress towards quantum chemistry on quantum computers.Comment: 9 pages, 4 figures, plus Supplementary Material [New version with
minor typos corrected.
Variational neural network ansatz for steady states in open quantum systems
We present a general variational approach to determine the steady state of
open quantum lattice systems via a neural network approach. The steady-state
density matrix of the lattice system is constructed via a purified neural
network ansatz in an extended Hilbert space with ancillary degrees of freedom.
The variational minimization of cost functions associated to the master
equation can be performed using a Markov chain Monte Carlo sampling. As a first
application and proof-of-principle, we apply the method to the dissipative
quantum transverse Ising model.Comment: 6 pages, 4 figures, 54 references, 5 pages of Supplemental
Information
Quantum enigma machines and the locking capacity of a quantum channel
The locking effect is a phenomenon which is unique to quantum information
theory and represents one of the strongest separations between the classical
and quantum theories of information. The Fawzi-Hayden-Sen (FHS) locking
protocol harnesses this effect in a cryptographic context, whereby one party
can encode n bits into n qubits while using only a constant-size secret key.
The encoded message is then secure against any measurement that an eavesdropper
could perform in an attempt to recover the message, but the protocol does not
necessarily meet the composability requirements needed in quantum key
distribution applications. In any case, the locking effect represents an
extreme violation of Shannon's classical theorem, which states that
information-theoretic security holds in the classical case if and only if the
secret key is the same size as the message. Given this intriguing phenomenon,
it is of practical interest to study the effect in the presence of noise, which
can occur in the systems of both the legitimate receiver and the eavesdropper.
This paper formally defines the locking capacity of a quantum channel as the
maximum amount of locked information that can be reliably transmitted to a
legitimate receiver by exploiting many independent uses of a quantum channel
and an amount of secret key sublinear in the number of channel uses. We provide
general operational bounds on the locking capacity in terms of other well-known
capacities from quantum Shannon theory. We also study the important case of
bosonic channels, finding limitations on these channels' locking capacity when
coherent-state encodings are employed and particular locking protocols for
these channels that might be physically implementable.Comment: 37 page
On variational expressions for quantum relative entropies
© 2017, Springer Science+Business Media B.V. Distance measures between quantum states like the trace distance and the fidelity can naturally be defined by optimizing a classical distance measure over all measurement statistics that can be obtained from the respective quantum states. In contrast, Petz showed that the measured relative entropy, defined as a maximization of the KullbackâLeibler divergence over projective measurement statistics, is strictly smaller than Umegakiâs quantum relative entropy whenever the states do not commute. We extend this result in two ways. First, we show that Petzâ conclusion remains true if we allow general positive operator-valued measures. Second, we extend the result to RĂ©nyi relative entropies and show that for non-commuting states the sandwiched RĂ©nyi relative entropy is strictly larger than the measured RĂ©nyi relative entropy for αâ(12,â) and strictly smaller for αâ[0,12). The latter statement provides counterexamples for the data processing inequality of the sandwiched RĂ©nyi relative entropy for α<12. Our main tool is a new variational expression for the measured RĂ©nyi relative entropy, which we further exploit to show that certain lower bounds on quantum conditional mutual information are superadditive
Residual entropy and critical behavior of two interacting boson species in a double well
Motivated by the importance of entanglement and correlation indicators in the
analysis of quantum systems, we study the equilibrium and the bipartite
residual entropy in a two-species Bose Hubbard dimer when the spatial phase
separation of the two species takes place. We consider both the zero and
non-zero-temperature regime. We present different kinds of residual entropies
(each one associated to a different way of partitioning the system), and we
show that they strictly depend on the specific quantum phase characterizing the
two species (supermixed, mixed or demixed) even at finite temperature. To
provide a deeper physical insight into the zero-temperature scenario, we apply
the fully-analytical variational approach based on su(2) coherent states and
provide a considerably good approximation of the entanglement entropy. Finally,
we show that the effectiveness of bipartite residual entropy as a critical
indicator at non-zero temperature is unchanged when considering a restricted
combination of energy eigenstates.Comment: 18 pages, 9 figure
Entanglement Entropy from the Truncated Conformal Space
A new numerical approach to entanglement entropies of the Renyi type is
proposed for one-dimensional quantum field theories. The method extends the
truncated conformal spectrum approach and we will demonstrate that it is
especially suited to study the crossover from massless to massive behavior when
the subsystem size is comparable to the correlation length. We apply it to
different deformations of massless free fermions, corresponding to the scaling
limit of the Ising model in transverse and longitudinal fields. For massive
free fermions the exactly known crossover function is reproduced already in
very small system sizes. The new method treats ground states and excited states
on the same footing, and the applicability for excited states is illustrated by
reproducing Renyi entropies of low-lying states in the transverse field Ising
model.Comment: 8 pages, 3 figures; v3: some typos corrected, figures replaced; v2:
discussion in Sec. 2 expanded, some typos corrected, one new reference adde
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