2,429 research outputs found
A triangle of dualities: reversibly decomposable quantum channels, source-channel duality, and time reversal
Two quantum information processing protocols are said to be dual under
resource reversal if the resources consumed (generated) in one protocol are
generated (consumed) in the other. Previously known examples include the
duality between entanglement concentration and dilution, and the duality
between coherent versions of teleportation and super-dense coding. A quantum
feedback channel is an isometry from a system belonging to Alice to a system
shared between Alice and Bob. We show that such a resource may be reversibly
decomposed into a perfect quantum channel and pure entanglement, generalizing
both of the above examples. The dual protocols responsible for this
decomposition are the ``feedback father'' (FF) protocol and the ``fully quantum
reverse Shannon'' (FQRS) protocol. Moreover, the ``fully quantum Slepian-Wolf''
protocol (FQSW), a generalization of the recently discovered ``quantum state
merging'', is related to FF by source-channel duality, and to FQRS by time
reversal duality, thus forming a triangle of dualities. The source-channel
duality is identified as the origin of the previously poorly understood
``mother-father'' duality. Due to a symmetry breaking, the dualities extend
only partially to classical information theory.Comment: 5 pages, 5 figure
Distillation of local purity from quantum states
Recently Horodecki et al. [Phys. Rev. Lett. 90, 100402 (2003)] introduced an
important quantum information processing paradigm, in which two parties sharing
many copies of the same bipartite quantum state distill local pure states, by
means of local unitary operations assisted by a one-way (two-way) completely
dephasing channel. Local pure states are a valuable resource from a
thermodynamical point of view, since they allow thermal energy to be converted
into work by local quantum heat engines. We give a simple
information-theoretical characterization of the one-way distillable local
purity, which turns out to be closely related to a previously known operational
measure of classical correlations, the one-way distillable common randomness.Comment: 8 page
On the quantum, classical and total amount of correlations in a quantum state
We give an operational definition of the quantum, classical and total amount
of correlations in a bipartite quantum state. We argue that these quantities
can be defined via the amount of work (noise) that is required to erase
(destroy) the correlations: for the total correlation, we have to erase
completely, for the quantum correlation one has to erase until a separable
state is obtained, and the classical correlation is the maximal correlation
left after erasing the quantum correlations.
In particular, we show that the total amount of correlations is equal to the
quantum mutual information, thus providing it with a direct operational
interpretation for the first time. As a byproduct, we obtain a direct,
operational and elementary proof of strong subadditivity of quantum entropy.Comment: 12 pages ReVTeX4, 2 eps figures. v2 has some arguments clarified and
references update
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
The quantum dynamic capacity formula of a quantum channel
The dynamic capacity theorem characterizes the reliable communication rates
of a quantum channel when combined with the noiseless resources of classical
communication, quantum communication, and entanglement. In prior work, we
proved the converse part of this theorem by making contact with many previous
results in the quantum Shannon theory literature. In this work, we prove the
theorem with an "ab initio" approach, using only the most basic tools in the
quantum information theorist's toolkit: the Alicki-Fannes' inequality, the
chain rule for quantum mutual information, elementary properties of quantum
entropy, and the quantum data processing inequality. The result is a simplified
proof of the theorem that should be more accessible to those unfamiliar with
the quantum Shannon theory literature. We also demonstrate that the "quantum
dynamic capacity formula" characterizes the Pareto optimal trade-off surface
for the full dynamic capacity region. Additivity of this formula simplifies the
computation of the trade-off surface, and we prove that its additivity holds
for the quantum Hadamard channels and the quantum erasure channel. We then
determine exact expressions for and plot the dynamic capacity region of the
quantum dephasing channel, an example from the Hadamard class, and the quantum
erasure channel.Comment: 24 pages, 3 figures; v2 has improved structure and minor corrections;
v3 has correction regarding the optimizatio
Entanglement measures and approximate quantum error correction
It is shown that, if the loss of entanglement along a quantum channel is
sufficiently small, then approximate quantum error correction is possible,
thereby generalizing what happens for coherent information. Explicit bounds are
obtained for the entanglement of formation and the distillable entanglement,
and their validity naturally extends to other bipartite entanglement measures
in between. Robustness of derived criteria is analyzed and their tightness
compared. Finally, as a byproduct, we prove a bound quantifying how large the
gap between entanglement of formation and distillable entanglement can be for
any given finite dimensional bipartite system, thus providing a sufficient
condition for distillability in terms of entanglement of formation.Comment: 7 pages, two-columned revtex4, no figures. v1: Deeply revised and
extended version: different entanglement measures are separately considered,
references are added, and some remarks are stressed. v2: Added a sufficient
condition for distillability in terms of entanglement of formation; published
versio
Classical information deficit and monotonicity on local operations
We investigate classical information deficit: a candidate for measure of
classical correlations emerging from thermodynamical approach initiated in
[Phys. Rev. Lett 89, 180402]. It is defined as a difference between amount of
information that can be concentrated by use of LOCC and the information
contained in subsystems. We show nonintuitive fact, that one way version of
this quantity can increase under local operation, hence it does not possess
property required for a good measure of classical correlations. Recently it was
shown by Igor Devetak, that regularised version of this quantity is monotonic
under LO. In this context, our result implies that regularization plays a role
of "monotoniser".Comment: 6 pages, revte
Quantum information can be negative
Given an unknown quantum state distributed over two systems, we determine how
much quantum communication is needed to transfer the full state to one system.
This communication measures the "partial information" one system needs
conditioned on it's prior information. It turns out to be given by an extremely
simple formula, the conditional entropy. In the classical case, partial
information must always be positive, but we find that in the quantum world this
physical quantity can be negative. If the partial information is positive, its
sender needs to communicate this number of quantum bits to the receiver; if it
is negative, the sender and receiver instead gain the corresponding potential
for future quantum communication. We introduce a primitive "quantum state
merging" which optimally transfers partial information. We show how it enables
a systematic understanding of quantum network theory, and discuss several
important applications including distributed compression, multiple access
channels and multipartite assisted entanglement distillation (localizable
entanglement). Negative channel capacities also receive a natural
interpretation
Strong Secrecy for Multiple Access Channels
We show strongly secret achievable rate regions for two different wiretap
multiple-access channel coding problems. In the first problem, each encoder has
a private message and both together have a common message to transmit. The
encoders have entropy-limited access to common randomness. If no common
randomness is available, then the achievable region derived here does not allow
for the secret transmission of a common message. The second coding problem
assumes that the encoders do not have a common message nor access to common
randomness. However, they may have a conferencing link over which they may
iteratively exchange rate-limited information. This can be used to form a
common message and common randomness to reduce the second coding problem to the
first one. We give the example of a channel where the achievable region equals
zero without conferencing or common randomness and where conferencing
establishes the possibility of secret message transmission. Both coding
problems describe practically relevant networks which need to be secured
against eavesdropping attacks.Comment: 55 page
A dynamical model for quantum memory channels
A dynamical model for quantum channel is introduced which allows one to pass
continuously from the memoryless case to the case in which memory effects are
present. The quantum and classical communication rates of the model are defined
and explicit expression are provided in some limiting case. In this context we
introduce noise attenuation strategies where part of the signals are sacrificed
to modify the channel environment. The case of qubit channel with phase damping
noise is analyzed in details.Comment: 11 pages, 4 figures; minor correction adde
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