393 research outputs found
Converse bounds for private communication over quantum channels
This paper establishes several converse bounds on the private transmission
capabilities of a quantum channel. The main conceptual development builds
firmly on the notion of a private state, which is a powerful, uniquely quantum
method for simplifying the tripartite picture of privacy involving local
operations and public classical communication to a bipartite picture of quantum
privacy involving local operations and classical communication. This approach
has previously led to some of the strongest upper bounds on secret key rates,
including the squashed entanglement and the relative entropy of entanglement.
Here we use this approach along with a "privacy test" to establish a general
meta-converse bound for private communication, which has a number of
applications. The meta-converse allows for proving that any quantum channel's
relative entropy of entanglement is a strong converse rate for private
communication. For covariant channels, the meta-converse also leads to
second-order expansions of relative entropy of entanglement bounds for private
communication rates. For such channels, the bounds also apply to the private
communication setting in which the sender and receiver are assisted by
unlimited public classical communication, and as such, they are relevant for
establishing various converse bounds for quantum key distribution protocols
conducted over these channels. We find precise characterizations for several
channels of interest and apply the methods to establish several converse bounds
on the private transmission capabilities of all phase-insensitive bosonic
channels.Comment: v3: 53 pages, 3 figures, final version accepted for publication in
IEEE Transactions on Information Theor
Discrimination of quantum states under locality constraints in the many-copy setting
We study the discrimination of a pair of orthogonal quantum states in the
many-copy setting. This is not a problem when arbitrary quantum measurements
are allowed, as then the states can be distinguished perfectly even with one
copy. However, it becomes highly nontrivial when we consider states of a
multipartite system and locality constraints are imposed. We hence focus on the
restricted families of measurements such as local operation and classical
communication (LOCC), separable operations (SEP), and the
positive-partial-transpose operations (PPT) in this paper.
We first study asymptotic discrimination of an arbitrary multipartite
entangled pure state against its orthogonal complement using LOCC/SEP/PPT
measurements. We prove that the incurred optimal average error probability
always decays exponentially in the number of copies, by proving upper and lower
bounds on the exponent. In the special case of discriminating a maximally
entangled state against its orthogonal complement, we determine the explicit
expression for the optimal average error probability and the optimal trade-off
between the type-I and type-II errors, thus establishing the associated
Chernoff, Stein, Hoeffding, and the strong converse exponents. Our technique is
based on the idea of using PPT operations to approximate LOCC.
Then, we show an infinite separation between SEP and PPT operations by
providing a pair of states constructed from an unextendible product basis
(UPB): they can be distinguished perfectly by PPT measurements, while the
optimal error probability using SEP measurements admits an exponential lower
bound. On the technical side, we prove this result by providing a quantitative
version of the well-known statement that the tensor product of UPBs is UPB.Comment: Comments are welcom
Device-independent Certification of One-shot Distillable Entanglement
Entanglement sources that produce many entangled states act as a main
component in applications exploiting quantum physics such as quantum
communication and cryptography. Realistic sources are inherently noisy, cannot
run for an infinitely long time, and do not necessarily behave in an
independent and identically distributed manner. An important question then
arises -- how can one test, or certify, that a realistic source produces high
amounts of entanglement? Crucially, a meaningful and operational solution
should allow us to certify the entanglement which is available for further
applications after performing the test itself (in contrast to assuming the
availability of an additional source which can produce more entangled states,
identical to those which were tested). To answer the above question and lower
bound the amount of entanglement produced by an uncharacterised source, we
present a protocol that can be run by interacting classically with
uncharacterised (but not entangled to one another) measurement devices used to
measure the states produced by the source. A successful run of the protocol
implies that the remaining quantum state has high amounts of one-shot
distillable entanglement. That is, one can distill many maximally entangled
states out of the single remaining state. Importantly, our protocol can
tolerate noise and, thus, certify entanglement produced by realistic sources.
With the above properties, the protocol acts as the first "operational
device-independent entanglement certification protocol" and allows one to test
and benchmark uncharacterised entanglement sources which may be otherwise
incomparable
Entanglement cost and quantum channel simulation
This paper proposes a revised definition for the entanglement cost of a
quantum channel . In particular, it is defined here to be the
smallest rate at which entanglement is required, in addition to free classical
communication, in order to simulate calls to , such that the
most general discriminator cannot distinguish the calls to
from the simulation. The most general discriminator is one who tests the
channels in a sequential manner, one after the other, and this discriminator is
known as a quantum tester [Chiribella et al., Phys. Rev. Lett., 101, 060401
(2008)] or one who is implementing a quantum co-strategy [Gutoski et al., Symp.
Th. Comp., 565 (2007)]. As such, the proposed revised definition of
entanglement cost of a quantum channel leads to a rate that cannot be smaller
than the previous notion of a channel's entanglement cost [Berta et al., IEEE
Trans. Inf. Theory, 59, 6779 (2013)], in which the discriminator is limited to
distinguishing parallel uses of the channel from the simulation. Under this
revised notion, I prove that the entanglement cost of certain
teleportation-simulable channels is equal to the entanglement cost of their
underlying resource states. Then I find single-letter formulas for the
entanglement cost of some fundamental channel models, including dephasing,
erasure, three-dimensional Werner--Holevo channels, epolarizing channels
(complements of depolarizing channels), as well as single-mode pure-loss and
pure-amplifier bosonic Gaussian channels. These examples demonstrate that the
resource theory of entanglement for quantum channels is not reversible.
Finally, I discuss how to generalize the basic notions to arbitrary resource
theories.Comment: 28 pages, 7 figure
Converse bounds for private communication over quantum channels
© 1963-2012 IEEE. This paper establishes several converse bounds on the private transmission capabilities of a quantum channel. The main conceptual development builds firmly on the notion of a private state, which is a powerful, uniquely quantum method for simplifying the tripartite picture of privacy involving local operations and public classical communication to a bipartite picture of quantum privacy involving local operations and classical communication. This approach has previously led to some of the strongest upper bounds on secret key rates, including the squashed entanglement and the relative entropy of entanglement. Here, we use this approach along with a 'privacy test' to establish a general meta-converse bound for private communication, which has a number of applications. The meta-converse allows for proving that any quantum channel's relative entropy of entanglement is a strong converse rate for private communication. For covariant channels, the meta-converse also leads to second-order expansions of relative entropy of entanglement bounds for private communication rates. For such channels, the bounds also apply to the private communication setting in which the sender and the receiver are assisted by unlimited public classical communication, and as such, they are relevant for establishing various converse bounds for quantum key distribution protocols conducted over these channels. We find precise characterizations for several channels of interest and apply the methods to establish converse bounds on the private transmission capabilities of all phase-insensitive bosonic channels
Benchmarking one-shot distillation in general quantum resource theories
We study the one-shot distillation of general quantum resources, providing a
unified quantitative description of the maximal fidelity achievable in this
task, and revealing similarities shared by broad classes of resources. We
establish fundamental quantitative and qualitative limitations on resource
distillation applicable to all convex resource theories. We show that every
convex quantum resource theory admits a meaningful notion of a pure maximally
resourceful state which maximizes several monotones of operational relevance
and finds use in distillation. We endow the generalized robustness measure with
an operational meaning as an exact quantifier of performance in distilling such
maximal states in many classes of resources including bi- and multipartite
entanglement, multi-level coherence, as well as the whole family of affine
resource theories, which encompasses important examples such as asymmetry,
coherence, and thermodynamics.Comment: 8+5 pages, 1 figure. v3: fixed (inconsequential) error in Lemma 1
Bell nonlocality
Bell's 1964 theorem, which states that the predictions of quantum theory
cannot be accounted for by any local theory, represents one of the most
profound developments in the foundations of physics. In the last two decades,
Bell's theorem has been a central theme of research from a variety of
perspectives, mainly motivated by quantum information science, where the
nonlocality of quantum theory underpins many of the advantages afforded by a
quantum processing of information. The focus of this review is to a large
extent oriented by these later developments. We review the main concepts and
tools which have been developed to describe and study the nonlocality of
quantum theory, and which have raised this topic to the status of a full
sub-field of quantum information science.Comment: 65 pages, 7 figures. Final versio
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