13,655 research outputs found
Entanglement area law from specific heat capacity
We study the scaling of entanglement in low-energy states of quantum
many-body models on lattices of arbitrary dimensions. We allow for unbounded
Hamiltonians such that systems with bosonic degrees of freedom are included. We
show that if at low enough temperatures the specific heat capacity of the model
decays exponentially with inverse temperature, the entanglement in every
low-energy state satisfies an area law (with a logarithmic correction). This
behaviour of the heat capacity is typically observed in gapped systems.
Assuming merely that the low-temperature specific heat decays polynomially with
temperature, we find a subvolume scaling of entanglement. Our results give
experimentally verifiable conditions for area laws, show that they are a
generic property of low-energy states of matter, and, to the best of our
knowledge, constitute the first proof of an area law for unbounded Hamiltonians
beyond those that are integrable.Comment: v3 now featuring bosonic system
Public Quantum Communication and Superactivation
Is there a meaningful quantum counterpart to public communication? We argue
that the symmetric-side channel -- which distributes quantum information
symmetrically between the receiver and the environment -- is a good candidate
for a notion of public quantum communication in entanglement distillation and
quantum error correction.
This connection is partially motivated by [Brand\~ao and Oppenheim,
arXiv:1004.3328], where it was found that if a sender would like to communicate
a secret message to a receiver through an insecure quantum channel using a
shared quantum state as a key, then the insecure quantum channel is only ever
used to simulate a symmetric-side channel, and can always be replaced by it
without altering the optimal rate. Here we further show, in complete analogy to
the role of public classical communication, that assistance by a symmetric-side
channel makes equal the distillable entanglement, the recently-introduced
mutual independence, and a generalization of the latter, which quantifies the
extent to which one of the parties can perform quantum privacy amplification.
Symmetric-side channels, and the closely related erasure channel, have been
recently harnessed to provide examples of superactivation of the quantum
channel capacity. Our findings give new insight into this non-additivity of the
channel capacity and its relation to quantum privacy. In particular, we show
that single-copy superactivation protocols with the erasure channel, which
encompasses all examples of non-additivity of the quantum capacity found to
date, can be understood as a conversion of mutual independence into distillable
entanglement.Comment: 10 page
Exponential Quantum Speed-ups are Generic
A central problem in quantum computation is to understand which quantum
circuits are useful for exponential speed-ups over classical computation. We
address this question in the setting of query complexity and show that for
almost any sufficiently long quantum circuit one can construct a black-box
problem which is solved by the circuit with a constant number of quantum
queries, but which requires exponentially many classical queries, even if the
classical machine has the ability to postselect.
We prove the result in two steps. In the first, we show that almost any
element of an approximate unitary 3-design is useful to solve a certain
black-box problem efficiently. The problem is based on a recent oracle
construction of Aaronson and gives an exponential separation between quantum
and classical bounded-error with postselection query complexities.
In the second step, which may be of independent interest, we prove that
linear-sized random quantum circuits give an approximate unitary 3-design. The
key ingredient in the proof is a technique from quantum many-body theory to
lower bound the spectral gap of local quantum Hamiltonians.Comment: 24 pages. v2 minor correction
Equivalence of Statistical Mechanical Ensembles for Non-Critical Quantum Systems
We consider the problem of whether the canonical and microcanonical ensembles
are locally equivalent for short-ranged quantum Hamiltonians of spins
arranged on a -dimensional lattices. For any temperature for which the
system has a finite correlation length, we prove that the canonical and
microcanonical state are approximately equal on regions containing up to
spins. The proof rests on a variant of the Berry--Esseen
theorem for quantum lattice systems and ideas from quantum information theory
The general structure of quantum resource theories
In recent years it was recognized that properties of physical systems such as
entanglement, athermality, and asymmetry, can be viewed as resources for
important tasks in quantum information, thermodynamics, and other areas of
physics. This recognition followed by the development of specific quantum
resource theories (QRTs), such as entanglement theory, determining how quantum
states that cannot be prepared under certain restrictions may be manipulated
and used to circumvent the restrictions. Here we discuss the general structure
of QRTs, and show that under a few assumptions (such as convexity of the set of
free states), a QRT is asymptotically reversible if its set of allowed
operations is maximal; that is, if the allowed operations are the set of all
operations that do not generate (asymptotically) a resource. In this case, the
asymptotic conversion rate is given in terms of the regularized relative
entropy of a resource which is the unique measure/quantifier of the resource in
the asymptotic limit of many copies of the state. This measure also equals the
smoothed version of the logarithmic robustness of the resource.Comment: 5 pages, no figures, few references added, published versio
One-shot rates for entanglement manipulation under non-entangling maps
We obtain expressions for the optimal rates of one- shot entanglement
manipulation under operations which generate a negligible amount of
entanglement. As the optimal rates for entanglement distillation and dilution
in this paradigm, we obtain the max- and min-relative entropies of
entanglement, the two logarithmic robustnesses of entanglement, and smoothed
versions thereof. This gives a new operational meaning to these entanglement
measures. Moreover, by considering the limit of many identical copies of the
shared entangled state, we partially recover the recently found reversibility
of entanglement manipu- lation under the class of operations which
asymptotically do not generate entanglement.Comment: 7 pages; no figure
Finite correlation length implies efficient preparation of quantum thermal states
Preparing quantum thermal states on a quantum computer is in general a
difficult task. We provide a procedure to prepare a thermal state on a quantum
computer with a logarithmic depth circuit of local quantum channels assuming
that the thermal state correlations satisfy the following two properties: (i)
the correlations between two regions are exponentially decaying in the distance
between the regions, and (ii) the thermal state is an approximate Markov state
for shielded regions. We require both properties to hold for the thermal state
of the Hamiltonian on any induced subgraph of the original lattice. Assumption
(ii) is satisfied for all commuting Gibbs states, while assumption (i) is
satisfied for every model above a critical temperature. Both assumptions are
satisfied in one spatial dimension. Moreover, both assumptions are expected to
hold above the thermal phase transition for models without any topological
order at finite temperature. As a building block, we show that exponential
decay of correlation (for thermal states of Hamiltonians on all induced
subgraph) is sufficient to efficiently estimate the expectation value of a
local observable. Our proof uses quantum belief propagation, a recent
strengthening of strong sub-additivity, and naturally breaks down for states
with topological order.Comment: 16 pages, 4 figure
- …