2,579 research outputs found
Resource Destroying Maps
Resource theory is a widely-applicable framework for analyzing the physical
resources required for given tasks, such as computation, communication, and
energy extraction. In this paper, we propose a general scheme for analyzing
resource theories based on resource destroying maps, which leave resource-free
states unchanged but erase the resource stored in all other states. We
introduce a group of general conditions that determine whether a quantum
operation exhibits typical resource-free properties in relation to a given
resource destroying map. Our theory reveals fundamental connections among basic
elements of resource theories, in particular, free states, free operations, and
resource measures. In particular, we define a class of simple resource measures
that can be calculated without optimization, and that are monotone
nonincreasing under operations that commute with the resource destroying map.
We apply our theory to the resources of coherence and quantum correlations
(e.g., discord), two prominent features of nonclassicality.Comment: 12 pages including Supplemental Material, published versio
Diagonal quantum discord
Quantum discord measures quantum correlation by comparing the quantum mutual
information with the maximal amount of mutual information accessible to a
quantum measurement. This paper analyzes the properties of diagonal discord, a
simplified version of discord that compares quantum mutual information with the
mutual information revealed by a measurement that correspond to the eigenstates
of the local density matrices. In contrast to the optimized discord, diagonal
discord is easily computable; it also finds connections to thermodynamics and
resource theory. Here we further show that, for the generic case of
non-degenerate local density matrices, diagonal discord exhibits desirable
properties as a preferable discord measure. We employ the theory of resource
destroying maps [Liu/Hu/Lloyd, PRL 118, 060502 (2017)] to prove that diagonal
discord is monotonically nonincreasing under the operation of local discord
nongenerating qudit channels, , and provide numerical evidence that such
monotonicity holds for qubit channels as well. We also show that it is
continuous, and derive a Fannes-like continuity bound. Our results hold for a
variety of simple discord measures generalized from diagonal discord.Comment: 15 pages, 3 figures; published versio
Benchmarking one-shot distillation in general quantum resource theories
We study the one-shot distillation of general quantum resources, providing a
unified quantitative description of the maximal fidelity achievable in this
task, and revealing similarities shared by broad classes of resources. We
establish fundamental quantitative and qualitative limitations on resource
distillation applicable to all convex resource theories. We show that every
convex quantum resource theory admits a meaningful notion of a pure maximally
resourceful state which maximizes several monotones of operational relevance
and finds use in distillation. We endow the generalized robustness measure with
an operational meaning as an exact quantifier of performance in distilling such
maximal states in many classes of resources including bi- and multipartite
entanglement, multi-level coherence, as well as the whole family of affine
resource theories, which encompasses important examples such as asymmetry,
coherence, and thermodynamics.Comment: 8+5 pages, 1 figure. v3: fixed (inconsequential) error in Lemma 1
Entanglement, quantum randomness, and complexity beyond scrambling
Scrambling is a process by which the state of a quantum system is effectively
randomized due to the global entanglement that "hides" initially localized
quantum information. In this work, we lay the mathematical foundations of
studying randomness complexities beyond scrambling by entanglement properties.
We do so by analyzing the generalized (in particular R\'enyi) entanglement
entropies of designs, i.e. ensembles of unitary channels or pure states that
mimic the uniformly random distribution (given by the Haar measure) up to
certain moments. A main collective conclusion is that the R\'enyi entanglement
entropies averaged over designs of the same order are almost maximal. This
links the orders of entropy and design, and therefore suggests R\'enyi
entanglement entropies as diagnostics of the randomness complexity of
corresponding designs. Such complexities form a hierarchy between information
scrambling and Haar randomness. As a strong separation result, we prove the
existence of (state) 2-designs such that the R\'enyi entanglement entropies of
higher orders can be bounded away from the maximum. However, we also show that
the min entanglement entropy is maximized by designs of order only logarithmic
in the dimension of the system. In other words, logarithmic-designs already
achieve the complexity of Haar in terms of entanglement, which we also call
max-scrambling. This result leads to a generalization of the fast scrambling
conjecture, that max-scrambling can be achieved by physical dynamics in time
roughly linear in the number of degrees of freedom.Comment: 72 pages, 4 figures. Rewritten version with new title. v3: published
versio
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