23 research outputs found
Limitations on Protecting Information Against Quantum Adversaries
The aim of this thesis is to understand the fundamental limitations on secret key distillation in various settings of quantum key distribution. We first consider quantum steering, which is a resource for one-sided device-independent quantum key distribution. We introduce a conditional mutual information based quantifier for quantum steering, which we call intrinsic steerability. Next, we consider quantum non-locality, which is a resource for device-independent quantum key distribution. In this context, we introduce a quantifier, intrinsic non-locality, which is a monotone in the resource theory of Bell non-locality. Both these quantities are inspired by intrinsic information and squashed entanglement and are based on conditional mutual information. The idea behind these quantifiers is to suppress the correlations that can be explained by a local hidden variable or by an inaccessible quantum system, thus quantifying the remaining intrinsic correlations. We then prove various properties of these two monotones, which includes the following: monotonicity under free operations, additivity under tensor product of objects, convexity, and faithfulness, among others.
Next, we prove that intrinsic steerability is an upper bound on the secret-key-agreement capacity of an assemblage, and intrinsic non-locality is an upper bound on the secret-key-agreement capacity of a quantum probability distribution. Thus we prove that these quantities are upper bounds on the achievable key rates in one-sided device-independent and device-independent quantum key distribution protocols. We also calculate these bounds for certain honest devices. The study of these upper bounds is instrumental in understanding the limitations of protocols that can be designed for various settings. These upper bounds inform us that, even if one considers the best possible protocol, there is no possibility of exceeding the upper bounds on key rates without a quantum repeater. The upper bounds introduced in this thesis are an important step for initiating this line of research in one-sided device-independent and in device-independent quantum key distribution
Upper bounds on secret key agreement over lossy thermal bosonic channels
Upper bounds on the secret-key-agreement capacity of a quantum channel serve
as a way to assess the performance of practical quantum-key-distribution
protocols conducted over that channel. In particular, if a protocol employs a
quantum repeater, achieving secret-key rates exceeding these upper bounds is a
witness to having a working quantum repeater. In this paper, we extend a recent
advance [Liuzzo-Scorpo et al., arXiv:1705.03017] in the theory of the
teleportation simulation of single-mode phase-insensitive Gaussian channels
such that it now applies to the relative entropy of entanglement measure. As a
consequence of this extension, we find tighter upper bounds on the
non-asymptotic secret-key-agreement capacity of the lossy thermal bosonic
channel than were previously known. The lossy thermal bosonic channel serves as
a more realistic model of communication than the pure-loss bosonic channel,
because it can model the effects of eavesdropper tampering and imperfect
detectors. An implication of our result is that the previously known upper
bounds on the secret-key-agreement capacity of the thermal channel are too
pessimistic for the practical finite-size regime in which the channel is used a
finite number of times, and so it should now be somewhat easier to witness a
working quantum repeater when using secret-key-agreement capacity upper bounds
as a benchmark.Comment: 16 pages, 1 figure, minor change
Entanglement distribution in two-dimensional square grid network
We study entanglement generation in a quantum network where repeater nodes
can perform -qubit Greenberger-Horne-Zeilinger(GHZ) swaps, i.e., projective
measurements, to fuse imperfect-Fidelity entangled-state fragments. We show
that the distance-independent entanglement distribution rate found previously
for this protocol, assuming perfectly-entangled states at the link level, does
not survive. This is true also in two modified protocols we study: one that
incorporates link-level distillation and another that spatially
constrains the repeater nodes involved in the swaps. We obtain analytical
formulas for a GHZ swap of multiple Werner states, which might be of
independent interest. Whether the distance-independent entanglement rate might
re-emerge with a spatio-temporally-optimized scheduling of GHZ swaps and
multi-site block-distillation codes remains open.Comment: 25 pages, 12 figure
Fundamental limits on key rates in device-independent quantum key distribution
In this paper, we introduce intrinsic non-locality as a quantifier for Bell
non-locality, and we prove that it satisfies certain desirable properties such
as faithfulness, convexity, and monotonicity under local operations and shared
randomness. We then prove that intrinsic non-locality is an upper bound on the
secret-key-agreement capacity of any device-independent protocol conducted
using a device characterized by a correlation . We also prove that intrinsic
steerability is an upper bound on the secret-key-agreement capacity of any
semi-device-independent protocol conducted using a device characterized by an
assemblage . We also establish the faithfulness of intrinsic
steerability and intrinsic non-locality. Finally, we prove that intrinsic
non-locality is bounded from above by intrinsic steerability.Comment: 44 pages, 4 figures, final version accepted for publication in New
Journal of Physic
Relative entropy of steering: On its definition and properties
In Gallego and Aolita (2015 Phys. Rev. X 5 041008), the authors proposed a definition for the relative entropy of steering and showed that the resulting quantity is a convex steering monotone. Here we advocate for a different definition for relative entropy of steering, based on well grounded concerns coming from quantum Shannon theory. We prove that this modified relative entropy of steering is a convex steering monotone. Furthermore, we establish that it is uniformly continuous and faithful, in both cases giving quantitative bounds that should be useful in applications. We also consider a restricted relative entropy of steering which is relevant for the case in which the free operations in the resource theory of steering have a more restricted form (the restricted operations could be more relevant in practical scenarios). The restricted relative entropy of steering is convex, monotone with respect to these restricted operations, uniformly continuous, and faithful
Amortized entanglement of a quantum channel and approximately teleportationsimulable channels
This paper defines the amortized entanglement of a quantum channel as the largest difference in entanglement between the output and the input of the channel, where entanglement is quantified by an arbitrary entanglement measure. We prove that the amortized entanglement of a channel obeys several desirable properties, and we also consider special cases such as the amortized relative entropy of entanglement and the amortized Rains relative entropy. These latter quantities are shown to be single-letter upper bounds on the secret-key-agreement and PPT-assisted quantum capacities of a quantum channel, respectively. Of especial interest is a uniform continuity bound for these latter two special cases of amortized entanglement, in which the deviation between the amortized entanglement of two channels is bounded from above by a simple function of the diamond norm of their difference and the output dimension of the channels. We then define approximately teleportation- and positive-partial-transpose-simulable (PPT-simulable) channels as those that are close in diamond norm to a channel which is either exactly teleportationor PPT-simulable, respectively. These results then lead to single-letter upper bounds on the secret-key-agreement and PPT-assisted quantum capacities of channels that are approximately teleportation- or PPT-simulable, respectively. Finally, we generalize many of the concepts in the paper to the setting of general resource theories, defining the amortized resourcefulness of a channel and the notion of ν-freely-simulable channels, connecting these concepts in an operational way as well
Extendibility limits the performance of quantum processors
Resource theories in quantum information science are helpful for the study
and quantification of the performance of information-processing tasks that
involve quantum systems. These resource theories also find applications in
other areas of study; e.g., the resource theories of entanglement and coherence
have found use and implications in the study of quantum thermodynamics and
memory effects in quantum dynamics. In this paper, we introduce the resource
theory of unextendibility, which is associated to the inability of extending
quantum entanglement in a given quantum state to multiple parties. The free
states in this resource theory are the -extendible states, and the free
channels are -extendible channels, which preserve the class of
-extendible states. We make use of this resource theory to derive
non-asymptotic, upper bounds on the rate at which quantum communication or
entanglement preservation is possible by utilizing an arbitrary quantum channel
a finite number of times, along with the assistance of -extendible channels
at no cost. We then show that the bounds we obtain are significantly tighter
than previously known bounds for both the depolarizing and erasure channels.Comment: 39 pages, 6 figures, v2 includes pretty strong converse bounds for
antidegradable channels, as well as other improvement