68 research outputs found
Asymptotic State Discrimination and a Strict Hierarchy in Distinguishability Norms
In this paper, we consider the problem of discriminating quantum states by
local operations and classical communication (LOCC) when an arbitrarily small
amount of error is permitted. This paradigm is known as asymptotic state
discrimination, and we derive necessary conditions for when two multipartite
states of any size can be discriminated perfectly by asymptotic LOCC. We use
this new criterion to prove a gap in the LOCC and separable distinguishability
norms. We then turn to the operational advantage of using two-way classical
communication over one-way communication in LOCC processing. With a simple
two-qubit product state ensemble, we demonstrate a strict majorization of the
two-way LOCC norm over the one-way norm.Comment: Corrected errors from the previous draft. Close to publication for
Round Complexity in the Local Transformations of Quantum and Classical States
A natural operational paradigm for distributed quantum and classical
information processing involves local operations coordinated by multiple rounds
of public communication. In this paper we consider the minimum number of
communication rounds needed to perform the locality-constrained task of
entanglement transformation and the analogous classical task of secrecy
manipulation. Specifically we address whether bipartite mixed entanglement can
always be converted into pure entanglement or whether unsecure classical
correlations can always be transformed into secret shared randomness using
local operations and a bounded number of communication exchanges. Our main
contribution in this paper is an explicit construction of quantum and classical
state transformations which, for any given , can be achieved using
rounds of classical communication exchanges but no fewer. Our results reveal
that highly complex communication protocols are indeed necessary to fully
harness the information-theoretic resources contained in general quantum and
classical states. The major technical contribution of this manuscript lies in
proving lower bounds for the required number of communication exchanges using
the notion of common information and various lemmas built upon it. We propose a
classical analog to the Schmidt rank of a bipartite quantum state which we call
the secrecy rank, and we show that it is a monotone under stochastic local
classical operations.Comment: Submitted to QIP 2017. Proof strategies have been streamlined and
differ from the submitted versio
Optimal Entanglement Transformations Among N-qubit W-Class States
We investigate the physically allowed probabilities for transforming one
N-partite W-class state to another by means of local operations assisted with
classical communication (LOCC). Recently, Kintas and Turgut have obtained an
upper bound for the maximum probability of transforming two such states
[arXiv:1003.2118v1]. Here, we provide a simple sufficient and necessary
condition for when this upper bound can be satisfied and thus when optimality
of state transformation can be achieved. Our discussion involves obtaining
lower bounds for the transformation of arbitrary W-class states and showing
precisely when this bound saturates the bound of [arXiv:1003.2118v1]. Finally,
we consider the question of transforming symmetric W-class states and find that
in general, the optimal one-shot procedure for converting two symmetric states
requires a non-symmetric filter by all the parties
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