13 research outputs found
Discord and quantum computational resources
Discordant states appear in a large number of quantum phenomena and seem to
be a good indicator of divergence from classicality. While there is evidence
that they are essential for a quantum algorithm to have an advantage over a
classical one, their precise role is unclear. We examine the role of discord in
quantum algorithms using the paradigmatic framework of `restricted distributed
quantum gates' and show that manipulating discordant states using local
operations has an associated cost in terms of entanglement and communication
resources. Changing discord reduces the total correlations and reversible
operations on discordant states usually require non-local resources. Discord
alone is, however, not enough to determine the need for entanglement. A more
general type of similar quantities, which we call K-discord, is introduced as a
further constraint on the kinds of operations that can be performed without
entanglement resources.Comment: Closer to published versio
Vanishing quantum discord is not necessary for completely-positive maps
The description of the dynamics of a system that may be correlated with its
environment is only meaningful within the context of a specific framework.
Different frameworks rely upon different assumptions about the initial
system-environment state. We reexamine the connections between
complete-positivity and quantum discord within two different sets of
assumptions about the relevant family of initial states. We present an example
of a system-environment state with non-vanishing quantum discord that leads to
a completely-positive map. This invalidates an earlier claim on the necessity
of vanishing quantum discord for completely-positive maps. In our final remarks
we discuss the physical validity of each approach.Comment: close to published versio
Quantum discord and local demons
Quantum discord was proposed as a measure of the "quantumness" of
correlations. There are at least three different discord-like quantities, two
of which determine the difference between the efficiencies of a Szilard's
engine under different sets of restrictions. The three discord measures vanish
simulataneosly. We introduce an easy way to test for zero discord, relate it to
the Cerf-Adami conditional entropy and show that there is no relation between
the discord and the local disitnguishability.Comment: 7 pages, RevTeX. Some minor changes after comments from colleagues,
some references added. Similar to published versio
Entanglement, discord and the power of quantum computation
We show that the ability to create entanglement is necessary for execution of
bipartite quantum gates even when they are applied to unentangled states and
create no entanglement. Starting with a simple example we demonstrate that to
execute such a gate bi-locally the local operations and classical
communications (LOCC) should be supplemented by shared entanglement. Our
results point to the changes in quantum discord, which is a measure of
quantumness of correlations even in the absence of entanglement, as the
indicator of failure of a LOCC implementation of the gates.Comment: Published version. More results are adde
The classical-quantum boundary for correlations: discord and related measures
One of the best signatures of nonclassicality in a quantum system is the
existence of correlations that have no classical counterpart. Different methods
for quantifying the quantum and classical parts of correlations are amongst the
more actively-studied topics of quantum information theory over the past
decade. Entanglement is the most prominent of these correlations, but in many
cases unentangled states exhibit nonclassical behavior too. Thus distinguishing
quantum correlations other than entanglement provides a better division between
the quantum and classical worlds, especially when considering mixed states.
Here we review different notions of classical and quantum correlations
quantified by quantum discord and other related measures. In the first half, we
review the mathematical properties of the measures of quantum correlations,
relate them to each other, and discuss the classical-quantum division that is
common among them. In the second half, we show that the measures identify and
quantify the deviation from classicality in various
quantum-information-processing tasks, quantum thermodynamics, open-system
dynamics, and many-body physics. We show that in many cases quantum
correlations indicate an advantage of quantum methods over classical ones.Comment: Close to the published versio
Experimental Demonstration of Quantum Fully Homomorphic Encryption with Application in a Two-Party Secure Protocol
A fully homomorphic encryption system hides data from unauthorized parties while still allowing them to perform computations on the encrypted data. Aside from the straightforward benefit of allowing users to delegate computations to a more powerful server without revealing their inputs, a fully homomorphic cryptosystem can be used as a building block in the construction of a number of crypt
Experimental demonstration of quantum fully homomorphic encryption with application in a two-party secure protocol
A fully homomorphic encryption system hides data from unauthorized parties, while still allowing them to perform computations on the encrypted data. Aside from the straightforward benefit of allowing users to delegate computations to a more powerful server without revealing their inputs, a fully homomorphic cryptosystem can be used as a building block in the construction of a number of cryptographic functionalities. Designing such a scheme remained an open problem until 2009, decades after the idea was first conceived, and the past few years have seen the generalization of this functionality to the world of quantum machines. Quantum schemes prior to the one implemented here were able to replicate some features in particular use-cases often associated with homomorphic encryption but lacked other crucial properties, for example, relying on continual interaction to perform a computation or leaking information about the encrypted data. We present the first experimental realisation of a quantum fully homomorphic encryption scheme. We further present a toy two-party secure computation task enabled by our scheme. Finally, as part of our implementation, we also demonstrate a post-selective two-qubit linear optical controlled-phase gate with a much higher post-selection success probability (1/2) when compared to alternate implementations, e.g. with post-selective controlled-Z or controlled-X gates (1/9).</p