83 research outputs found
Quantum Feedback Channels
In Shannon information theory the capacity of a memoryless communication
channel cannot be increased by the use of feedback. In quantum information
theory the no-cloning theorem means that noiseless copying and feedback of
quantum information cannot be achieved. In this paper, quantum feedback is
defined as the unlimited use of a noiseless quantum channel from receiver to
sender. Given such quantum feedback, it is shown to provide no increase in the
entanglement--assisted capacities of a memoryless quantum channel, in direct
analogy to the classical case. It is also shown that in various cases of
non-assisted capacities, feedback may increase the capacity of memoryless
quantum channels.Comment: 5 pages, requires IEEEtran.cls, expanded, proofs added, references
adde
A decoupling approach to the quantum capacity
We give a short proof that the coherent information is an achievable rate for
the transmission of quantum information through a noisy quantum channel. Our
method is to produce random codes by performing a unitarily covariant
projective measurement on a typical subspace of a tensor power state. We show
that, provided the rank of each measurement operator is sufficiently small, the
transmitted data will with high probability be decoupled from the channel's
environment. We also show that our construction leads to random codes whose
average input is close to a product state and outline a modification yielding
unitarily invariant ensembles of maximally entangled codes.Comment: 13 pages, published versio
Analysis of radiatively stable entanglement in a system of two dipole-interacting three-level atoms
We explore the possibilities of creating radiatively stable entangled states
of two three-level dipole-interacting atoms in a configuration by
means of laser biharmonic continuous driving or pulses. We propose three
schemes for generation of entangled states which involve only the lower states
of the system, not vulnerable to radiative decay. Two of them employ
coherent dynamics to achieve entanglement in the system, whereas the third one
uses optical pumping, i.e., an essentially incoherent process.Comment: Replaced with the final version; 14 pages, 6 figures; to appear in
Phys. Rev. A, vol. 61 (2000
Uncertainty, Monogamy, and Locking of Quantum Correlations
Squashed entanglement and entanglement of purification are quantum mechanical
correlation measures and defined as certain minimisations of entropic
quantities. We present the first non-trivial calculations of both quantities.
Our results lead to the conclusion that both measures can drop by an arbitrary
amount when only a single qubit of a local system is lost. This property is
known as "locking" and has previously been observed for other correlation
measures, such as the accessible information, entanglement cost and the
logarithmic negativity.
In the case of squashed entanglement, the results are obtained with the help
of an inequality that can be understood as a quantum channel analogue of
well-known entropic uncertainty relations. This inequality may prove a useful
tool in quantum information theory.
The regularised entanglement of purification is known to equal the
entanglement needed to prepare a many copies of quantum state by local
operations and a sublinear amount of communication. Here, monogamy of quantum
entanglement (i.e., the impossibility of a system being maximally entangled
with two others at the same time) leads to an exact calculation for all quantum
states that are supported either on the symmetric or on the antisymmetric
subspace of a dxd-dimensional system.Comment: 7 pages revtex4, no figures. v2 has improved presentation and a
couple of references adde
Teleportation and entanglement distillation in the presence of correlation among bipartite mixed states
The teleportation channel associated with an arbitrary bipartite state
denotes the map that represents the change suffered by a teleported state when
the bipartite state is used instead of the ideal maximally entangled state for
teleportation. This work presents and proves an explicit expression of the
teleportation channel for the teleportation using Weyl's projective unitary
representation of the space of 2n-tuples of numbers from Z/dZ for integers d>1,
n>0, which has been known for n=1. This formula allows any correlation among
the n bipartite mixed states, and an application shows the existence of
reliable schemes for distillation of entanglement from a sequence of mixed
states with correlation.Comment: 12 pages, 1 figur
Communicating over adversarial quantum channels using quantum list codes
We study quantum communication in the presence of adversarial noise. In this
setting, communicating with perfect fidelity requires using a quantum code of
bounded minimum distance, for which the best known rates are given by the
quantum Gilbert-Varshamov (QGV) bound. By asking only for arbitrarily high
fidelity and allowing the sender and reciever to use a secret key with length
logarithmic in the number of qubits sent, we achieve a dramatic improvement
over the QGV rates. In fact, we find protocols that achieve arbitrarily high
fidelity at noise levels for which perfect fidelity is impossible. To achieve
such communication rates, we introduce fully quantum list codes, which may be
of independent interest.Comment: 6 pages. Discussion expanded and more details provided in proofs. Far
less unclear than previous versio
Semidefinite programming converse bounds for quantum communication
We derive several efficiently computable converse bounds for quantum
communication over quantum channels in both the one-shot and asymptotic regime.
First, we derive one-shot semidefinite programming (SDP) converse bounds on the
amount of quantum information that can be transmitted over a single use of a
quantum channel, which improve the previous bound from [Tomamichel/Berta/Renes,
Nat. Commun. 7, 2016]. As applications, we study quantum communication over
depolarizing channels and amplitude damping channels with finite resources.
Second, we find an SDP strong converse bound for the quantum capacity of an
arbitrary quantum channel, which means the fidelity of any sequence of codes
with a rate exceeding this bound will vanish exponentially fast as the number
of channel uses increases. Furthermore, we prove that the SDP strong converse
bound improves the partial transposition bound introduced by Holevo and Werner.
Third, we prove that this SDP strong converse bound is equal to the so-called
max-Rains information, which is an analog to the Rains information introduced
in [Tomamichel/Wilde/Winter, IEEE Trans. Inf. Theory 63:715, 2017]. Our SDP
strong converse bound is weaker than the Rains information, but it is
efficiently computable for general quantum channels.Comment: 17 pages, extended version of arXiv:1601.06888. v3 is closed to the
published version, IEEE Transactions on Information Theory, 201
Quantum Entanglement Capacity with Classical Feedback
For any quantum discrete memoryless channel, we define a quantity called
quantum entanglement capacity with classical feedback (), and we show that
this quantity lies between two other well-studied quantities. These two
quantities - namely the quantum capacity assisted by two-way classical
communication () and the quantum capacity with classical feedback ()
- are widely conjectured to be different: there exists quantum discrete
memoryless channel for which . We then present a general scheme to
convert any quantum error-correcting codes into adaptive protocols for this
newly-defined quantity of the quantum depolarizing channel, and illustrate with
Cat (repetition) code and Shor code. We contrast the present notion with
entanglement purification protocols by showing that whilst the Leung-Shor
protocol can be applied directly, recurrence methods need to be supplemented
with other techniques but at the same time offer a way to improve the
aforementioned Cat code. For the quantum depolarizing channel, we prove a
formula that gives lower bounds on the quantum capacity with classical feedback
from any protocols. We then apply this formula to the protocols
that we discuss to obtain new lower bounds on the quantum capacity with
classical feedback of the quantum depolarizing channel
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