1,368 research outputs found
Multipartite Quantum Correlation and Communication Complexities
The concepts of quantum correlation complexity and quantum communication
complexity were recently proposed to quantify the minimum amount of resources
needed in generating bipartite classical or quantum states in the single-shot
setting. The former is the minimum size of the initially shared state
on which local operations by the two parties (without communication) can
generate the target state , and the latter is the minimum amount of
communication needed when initially sharing nothing. In this paper, we
generalize these two concepts to multipartite cases, for both exact and
approximate state generation. Our results are summarized as follows. (1) For
multipartite pure states, the correlation complexity can be completely
characterized by local ranks of sybsystems. (2) We extend the notion of
PSD-rank of matrices to that of tensors, and use it to bound the quantum
correlation complexity for generating multipartite classical distributions. (3)
For generating multipartite mixed quantum states, communication complexity is
not always equal to correlation complexity (as opposed to bipartite case). But
they differ by at most a factor of 2. Generating a multipartite mixed quantum
state has the same communication complexity as generating its optimal
purification. But for correlation complexity of these two tasks can be
different (though still related by less than a factor of 2). (4) To generate a
bipartite classical distribution approximately, the quantum
communication complexity is completely characterized by the approximate
PSD-rank of . The quantum correlation complexity of approximately generating
multipartite pure states is bounded by approximate local ranks.Comment: 19 pages; some typos are correcte
Growth of graph states in quantum networks
We propose a scheme to distribute graph states over quantum networks in the
presence of noise in the channels and in the operations. The protocol can be
implemented efficiently for large graph sates of arbitrary (complex) topology.
We benchmark our scheme with two protocols where each connected component is
prepared in a node belonging to the component and subsequently distributed via
quantum repeaters to the remaining connected nodes. We show that the fidelity
of the generated graphs can be written as the partition function of a classical
Ising-type Hamiltonian. We give exact expressions of the fidelity of the linear
cluster and results for its decay rate in random graphs with arbitrary
(uncorrelated) degree distributions.Comment: 16 pages, 7 figure
Unifying classical and quantum key distillation
Assume that two distant parties, Alice and Bob, as well as an adversary, Eve,
have access to (quantum) systems prepared jointly according to a tripartite
state. In addition, Alice and Bob can use local operations and authenticated
public classical communication. Their goal is to establish a key which is
unknown to Eve. We initiate the study of this scenario as a unification of two
standard scenarios: (i) key distillation (agreement) from classical
correlations and (ii) key distillation from pure tripartite quantum states.
Firstly, we obtain generalisations of fundamental results related to
scenarios (i) and (ii), including upper bounds on the key rate. Moreover, based
on an embedding of classical distributions into quantum states, we are able to
find new connections between protocols and quantities in the standard scenarios
(i) and (ii).
Secondly, we study specific properties of key distillation protocols. In
particular, we show that every protocol that makes use of pre-shared key can be
transformed into an equally efficient protocol which needs no pre-shared key.
This result is of practical significance as it applies to quantum key
distribution (QKD) protocols, but it also implies that the key rate cannot be
locked with information on Eve's side. Finally, we exhibit an arbitrarily large
separation between the key rate in the standard setting where Eve is equipped
with quantum memory and the key rate in a setting where Eve is only given
classical memory. This shows that assumptions on the nature of Eve's memory are
important in order to determine the correct security threshold in QKD.Comment: full versio
Quantum information with continuous variables
Quantum information is a rapidly advancing area of interdisciplinary
research. It may lead to real-world applications for communication and
computation unavailable without the exploitation of quantum properties such as
nonorthogonality or entanglement. We review the progress in quantum information
based on continuous quantum variables, with emphasis on quantum optical
implementations in terms of the quadrature amplitudes of the electromagnetic
field.Comment: accepted for publication in Reviews of Modern Physic
Quantum Correlations and Global Coherence in Distributed Quantum Computing
Deviations from classical physics when distant quantum systems become
correlated are interesting both fundamentally and operationally. There exist
situations where the correlations enable collaborative tasks that are
impossible within the classical formalism. Here, we consider the efficiency of
quantum computation protocols compared to classical ones as a benchmark for
separating quantum and classical resources and argue that the computational
advantage of collaborative quantum protocols in the discrete variable domain
implies the nonclassicality of correlations. By analysing a toy model, it turns
out that this argument implies the existence of quantum correlations distinct
from entanglement and discord. We characterize such quantum correlations in
terms of the net global coherence resources inherent within quantum states and
show that entanglement and discord can be understood as special cases of our
general framework. Finally, we provide an operational interpretation of such
correlations as those allowing two distant parties to increase their respective
local quantum computational resources only using locally incoherent operations
and classical communication.Comment: Minor modifications and correction
Limitations on device independent secure key via squashed non-locality
We initiate a systematic study to provide upper bounds on device-independent
key, secure against a non-signaling adversary (NSDI), distilled by a wide class
of operations, currently used in both quantum and non-signaling
device-independent protocols. These operations consist of a direct measurements
on the devices followed by Local Operations and Public Communication (MDLOPC).
We employ the idea of "squashing" on the secrecy monotones, which provide upper
bounds on the key rate in secret key agreement (SKA) scenario, and show that
squashed secrecy monotones are the upper bounds on NSDI key. As an important
instance, an upper bound on NSDI key rate called "squashed non-locality", has
been constructed. It exhibits several important properties, including
convexity, monotonicity, additivity on tensor products, and asymptotic
continuity. Using this bound, we identify numerically a domain of two binary
inputs and two binary outputs non-local devices for which the squashed
non-locality is zero, and therefore one can not distil key from them via MDLOPC
operations. These are mixtures of Popescu-Rohrlich (PR) and anti-PR box with
the weight of PR box less than . This example confirms the intuition that
non-locality need not imply secrecy in the non-signaling scenario. The approach
is general, describing how to construct other tighter yet possibly less
computable upper bounds. Our technique for obtaining upper bounds is based on
the non-signaling analog of quantum purification: the complete extension, which
yields equivalent security conditions as previously known in the literature.Comment: 12 pages and 2 figures + supplemental materia
Quantum Correlations in Nonlocal BosonSampling
Determination of the quantum nature of correlations between two spatially
separated systems plays a crucial role in quantum information science. Of
particular interest is the questions of if and how these correlations enable
quantum information protocols to be more powerful. Here, we report on a
distributed quantum computation protocol in which the input and output quantum
states are considered to be classically correlated in quantum informatics.
Nevertheless, we show that the correlations between the outcomes of the
measurements on the output state cannot be efficiently simulated using
classical algorithms. Crucially, at the same time, local measurement outcomes
can be efficiently simulated on classical computers. We show that the only
known classicality criterion violated by the input and output states in our
protocol is the one used in quantum optics, namely, phase-space
nonclassicality. As a result, we argue that the global phase-space
nonclassicality inherent within the output state of our protocol represents
true quantum correlations.Comment: 5 pages, 1 figure, comments are very welcome
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