200 research outputs found
Revisiting the optimal detection of quantum information
In 1991, Peres and Wootters wrote a seminal paper on the nonlocal processing of quantum information [Phys. Rev. Lett. 66, 1119 (1991)]. We return to their classic problem and solve it in various contexts. Specifically, for discriminating the 'double tri
Quantum Correlations in Large-Dimensional States of High Symmetry
In this article, we investigate how quantum correlations behave for the
so-called Werner and pseudo-pure families of states. The latter refers to
states formed by mixing any pure state with the totally mixed state. We derive
closed expressions for the Quantum Discord (QD) and the Relative Entropy of
Quantumness (REQ) for these families of states. For Werner states, the
classical correlations are seen to vanish in high dimensions while the amount
of quantum correlations remain bounded and become independent of whether or not
the the state is entangled. For pseudo-pure states, nearly the opposite effect
is observed with both the quantum and classical correlations growing without
bound as the dimension increases and only as the system becomes more entangled.
Finally, we verify that pseudo-pure states satisfy the conjecture of
[\textit{Phys. Rev. A} \textbf{84}, 052110 (2011)] which says that the
Geometric Measure of Discord (GD) always upper bounds the squared Negativity of
the state
Entanglement and coherence in quantum state merging
Understanding the resource consumption in distributed scenarios is one of the
main goals of quantum information theory. A prominent example for such a
scenario is the task of quantum state merging where two parties aim to merge
their parts of a tripartite quantum state. In standard quantum state merging,
entanglement is considered as an expensive resource, while local quantum
operations can be performed at no additional cost. However, recent developments
show that some local operations could be more expensive than others: it is
reasonable to distinguish between local incoherent operations and local
operations which can create coherence. This idea leads us to the task of
incoherent quantum state merging, where one of the parties has free access to
local incoherent operations only. In this case the resources of the process are
quantified by pairs of entanglement and coherence. Here, we develop tools for
studying this process, and apply them to several relevant scenarios. While
quantum state merging can lead to a gain of entanglement, our results imply
that no merging procedure can gain entanglement and coherence at the same time.
We also provide a general lower bound on the entanglement-coherence sum, and
show that the bound is tight for all pure states. Our results also lead to an
incoherent version of Schumacher compression: in this case the compression rate
is equal to the von Neumann entropy of the diagonal elements of the
corresponding quantum state.Comment: 9 pages, 1 figure. Lemma 5 in Appendix D of the previous version was
not correct. This did not affect the results of the main tex
A Hierarchy of Multipartite Correlations Based on Concentratable Entanglement
Multipartite entanglement is one of the hallmarks of quantum mechanics and is
central to quantum information processing. In this work we show that
Concentratable Entanglement (CE), an operationally motivated entanglement
measure, induces a hierarchy upon pure states from which different entanglement
structures can be certified. In particular, we find that nearly all genuine
multipartite entangled states can be verified through CE. In the process we
find the exact maximal value of CE and corresponding states for up to 18 qubits
and show that these correspond to extremal quantum error correcting codes. The
latter allows us to unravel a deep connection between CE and coding theory.
Finally, our results also offer an alternative proof, on up to 31 qubits, that
absolutely maximally entangled states do not exist
Tripartite to Bipartite Entanglement Transformations and Polynomial Identity Testing
We consider the problem of deciding if a given three-party entangled pure
state can be converted, with a non-zero success probability, into a given
two-party pure state through local quantum operations and classical
communication. We show that this question is equivalent to the well-known
computational problem of deciding if a multivariate polynomial is identically
zero. Efficient randomized algorithms developed to study the latter can thus be
applied to the question of tripartite to bipartite entanglement
transformations
Inferring Quantum Network Topology using Local Measurements
Statistical correlations that can be generated across the nodes in a quantum
network depend crucially on its topology. However, this topological information
might not be known a priori, or it may need to be verified. In this paper, we
propose an efficient protocol for distinguishing and inferring the topology of
a quantum network. We leverage entropic quantities -- namely, the von Neumann
entropy and the measured mutual information -- as well as measurement
covariance to uniquely characterize the topology. We show that the entropic
quantities are sufficient to distinguish two networks that prepare GHZ states.
Moreover, if qubit measurements are available, both entropic quantities and
covariance can be used to infer the network topology. We show that the protocol
can be entirely robust to noise and can be implemented via quantum variational
optimization. Numerical experiments on both classical simulators and quantum
hardware show that covariance is generally more reliable for accurately and
efficiently inferring the topology, whereas entropy-based methods are often
better at identifying the absence of entanglement in the low-shot regime
The Parametric Symmetry and Numbers of the Entangled Class of 2 \times M \times N System
We present in the work two intriguing results in the entanglement
classification of pure and true tripartite entangled state of under stochastic local operation and classical communication. (i) the
internal symmetric properties of the nonlocal parameters in the continuous
entangled class; (ii) the analytic expression for the total numbers of the true
and pure entangled class states. These properties help
people to know more of the nature of the entangled system.Comment: 12 pages, 5 figure
Characterising two-sided quantum correlations beyond entanglement via metric-adjusted f-correlations
We introduce an infinite family of quantifiers of quantum correlations beyond
entanglement which vanish on both classical-quantum and quantum-classical
states and are in one-to-one correspondence with the metric-adjusted skew
informations. The `quantum correlations' are defined as the maximum
metric-adjusted correlations between pairs of local observables with the
same fixed equispaced spectrum. We show that these quantifiers are entanglement
monotones when restricted to pure states of qubit-qudit systems. We also
evaluate the quantum correlations in closed form for two-qubit systems and
discuss their behaviour under local commutativity preserving channels. We
finally provide a physical interpretation for the quantifier corresponding to
the average of the Wigner-Yanase-Dyson skew informations.Comment: 20 pages, 1 figure. Published versio
Entanglement distribution and quantum discord
Establishing entanglement between distant parties is one of the most
important problems of quantum technology, since long-distance entanglement is
an essential part of such fundamental tasks as quantum cryptography or quantum
teleportation. In this lecture we review basic properties of entanglement and
quantum discord, and discuss recent results on entanglement distribution and
the role of quantum discord therein. We also review entanglement distribution
with separable states, and discuss important problems which still remain open.
One such open problem is a possible advantage of indirect entanglement
distribution, when compared to direct distribution protocols.Comment: 7 pages, 2 figures, contribution to "Lectures on general quantum
correlations and their applications", edited by Felipe Fanchini, Diogo
Soares-Pinto, and Gerardo Adess
Assisted distillation of quantum coherence
We introduce and study the task of assisted coherence distillation. This task arises naturally in bipartite systems where both parties work together to generate the maximal possible coherence on one of the subsystems. Only incoherent operations are allowed on the target system, while general local quantum operations are permitted on the other; this is an operational paradigm that we call local quantum-incoherent operations and classical communication. We show that the asymptotic rate of assisted coherence distillation for pure states is equal to the coherence of assistance, an analog of the entanglement of assistance, whose properties we characterize. Our findings imply a novel interpretation of the von Neumann entropy: it quantifies the maximum amount of extra quantum coherence a system can gain when receiving assistance from a collaborative party. Our results are generalized to coherence localization in a multipartite setting and possible applications are discussed
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