17 research outputs found
Private quantum decoupling and secure disposal of information
Given a bipartite system, correlations between its subsystems can be
understood as information that each one carries about the other. In order to
give a model-independent description of secure information disposal, we propose
the paradigm of private quantum decoupling, corresponding to locally reducing
correlations in a given bipartite quantum state without transferring them to
the environment. In this framework, the concept of private local randomness
naturally arises as a resource, and total correlations get divided into
eliminable and ineliminable ones. We prove upper and lower bounds on the amount
of ineliminable correlations present in an arbitrary bipartite state, and show
that, in tripartite pure states, ineliminable correlations satisfy a monogamy
constraint, making apparent their quantum nature. A relation with entanglement
theory is provided by showing that ineliminable correlations constitute an
entanglement parameter. In the limit of infinitely many copies of the initial
state provided, we compute the regularized ineliminable correlations to be
measured by the coherent information, which is thus equipped with a new
operational interpretation. In particular, our results imply that two
subsystems can be privately decoupled if their joint state is separable.Comment: Child of 0807.3594 v2: minor changes v3: presentation improved, one
figure added v4: extended version with a lot of discussions and examples v5:
published versio
Continuity of quantum channel capacities
We prove that a broad array of capacities of a quantum channel are
continuous. That is, two channels that are close with respect to the diamond
norm have correspondingly similar communication capabilities. We first show
that the classical capacity, quantum capacity, and private classical capacity
are continuous, with the variation on arguments epsilon apart bounded by a
simple function of epsilon and the channel's output dimension. Our main tool is
an upper bound of the variation of output entropies of many copies of two
nearby channels given the same initial state; the bound is linear in the number
of copies. Our second proof is concerned with the quantum capacities in the
presence of free backward or two-way public classical communication. These
capacities are proved continuous on the interior of the set of non-zero
capacity channels by considering mutual simulation between similar channels.Comment: 12 pages, Revised according to referee's suggestion
Gaussian bosonic synergy: quantum communication via realistic channels of zero quantum capacity
As with classical information, error-correcting codes enable reliable
transmission of quantum information through noisy or lossy channels. In
contrast to the classical theory, imperfect quantum channels exhibit a strong
kind of synergy: there exist pairs of discrete memoryless quantum channels,
each of zero quantum capacity, which acquire positive quantum capacity when
used together. Here we show that this "superactivation" phenomenon also occurs
in the more realistic setting of optical channels with attenuation and Gaussian
noise. This paves the way for its experimental realization and application in
real-world communications systems.Comment: 5 pages, 4 figures, one appendi
Quantum capacity under adversarial quantum noise: arbitrarily varying quantum channels
We investigate entanglement transmission over an unknown channel in the
presence of a third party (called the adversary), which is enabled to choose
the channel from a given set of memoryless but non-stationary channels without
informing the legitimate sender and receiver about the particular choice that
he made. This channel model is called arbitrarily varying quantum channel
(AVQC). We derive a quantum version of Ahlswede's dichotomy for classical
arbitrarily varying channels. This includes a regularized formula for the
common randomness-assisted capacity for entanglement transmission of an AVQC.
Quite surprisingly and in contrast to the classical analog of the problem
involving the maximal and average error probability, we find that the capacity
for entanglement transmission of an AVQC always equals its strong subspace
transmission capacity. These results are accompanied by different notions of
symmetrizability (zero-capacity conditions) as well as by conditions for an
AVQC to have a capacity described by a single-letter formula. In he final part
of the paper the capacity of the erasure-AVQC is computed and some light shed
on the connection between AVQCs and zero-error capacities. Additionally, we
show by entirely elementary and operational arguments motivated by the theory
of AVQCs that the quantum, classical, and entanglement-assisted zero-error
capacities of quantum channels are generically zero and are discontinuous at
every positivity point.Comment: 49 pages, no figures, final version of our papers arXiv:1010.0418v2
and arXiv:1010.0418. Published "Online First" in Communications in
Mathematical Physics, 201
Faithful Squashed Entanglement
Squashed entanglement is a measure for the entanglement of bipartite quantum
states. In this paper we present a lower bound for squashed entanglement in
terms of a distance to the set of separable states. This implies that squashed
entanglement is faithful, that is, strictly positive if and only if the state
is entangled. We derive the bound on squashed entanglement from a bound on
quantum conditional mutual information, which is used to define squashed
entanglement and corresponds to the amount by which strong subadditivity of von
Neumann entropy fails to be saturated. Our result therefore sheds light on the
structure of states that almost satisfy strong subadditivity with equality. The
proof is based on two recent results from quantum information theory: the
operational interpretation of the quantum mutual information as the optimal
rate for state redistribution and the interpretation of the regularised
relative entropy of entanglement as an error exponent in hypothesis testing.
The distance to the set of separable states is measured by the one-way LOCC
norm, an operationally-motivated norm giving the optimal probability of
distinguishing two bipartite quantum states, each shared by two parties, using
any protocol formed by local quantum operations and one-directional classical
communication between the parties. A similar result for the Frobenius or
Euclidean norm follows immediately. The result has two applications in
complexity theory. The first is a quasipolynomial-time algorithm solving the
weak membership problem for the set of separable states in one-way LOCC or
Euclidean norm. The second concerns quantum Merlin-Arthur games. Here we show
that multiple provers are not more powerful than a single prover when the
verifier is restricted to one-way LOCC operations thereby providing a new
characterisation of the complexity class QMA.Comment: 24 pages, 1 figure, 1 table. Due to an error in the published
version, claims have been weakened from the LOCC norm to the one-way LOCC
nor
Sequential, successive, and simultaneous decoders for entanglement-assisted classical communication
Bennett et al. showed that allowing shared entanglement between a sender and
receiver before communication begins dramatically simplifies the theory of
quantum channels, and these results suggest that it would be worthwhile to
study other scenarios for entanglement-assisted classical communication. In
this vein, the present paper makes several contributions to the theory of
entanglement-assisted classical communication. First, we rephrase the
Giovannetti-Lloyd-Maccone sequential decoding argument as a more general
"packing lemma" and show that it gives an alternate way of achieving the
entanglement-assisted classical capacity. Next, we show that a similar
sequential decoder can achieve the Hsieh-Devetak-Winter region for
entanglement-assisted classical communication over a multiple access channel.
Third, we prove the existence of a quantum simultaneous decoder for
entanglement-assisted classical communication over a multiple access channel
with two senders. This result implies a solution of the quantum simultaneous
decoding conjecture for unassisted classical communication over quantum
multiple access channels with two senders, but the three-sender case still
remains open (Sen recently and independently solved this unassisted two-sender
case with a different technique). We then leverage this result to recover the
known regions for unassisted and assisted quantum communication over a quantum
multiple access channel, though our proof exploits a coherent quantum
simultaneous decoder. Finally, we determine an achievable rate region for
communication over an entanglement-assisted bosonic multiple access channel and
compare it with the Yen-Shapiro outer bound for unassisted communication over
the same channel.Comment: 33 pages, 2 figures; v2 contains a proof of the quantum simultaneous
decoding conjecture for two-sender quantum multiple access channels; v3 shows
how to recover the known unassisted and assisted quantum communication
regions with a coherent quantum simultaneous decode