645 research outputs found
Broadband channel capacities
We study the communication capacities of bosonic broadband channels in the
presence of different sources of noise. In particular we analyze lossy channels
in presence of white noise and thermal bath. In this context, we provide a
numerical solution for the entanglement assisted capacity and upper and lower
bounds for the classical and quantum capacities.Comment: 11 pages, 7 figures, 3 table
Quantum channels with a finite memory
In this paper we study quantum communication channels with correlated noise
effects, i.e., quantum channels with memory. We derive a model for correlated
noise channels that includes a channel memory state. We examine the case where
the memory is finite, and derive bounds on the classical and quantum
capacities. For the entanglement-assisted and unassisted classical capacities
it is shown that these bounds are attainable for certain classes of channel.
Also, we show that the structure of any finite memory state is unimportant in
the asymptotic limit, and specifically, for a perfect finite-memory channel
where no nformation is lost to the environment, achieving the upper bound
implies that the channel is asymptotically noiseless.Comment: 7 Pages, RevTex, Jrnl versio
On the Interpretation of Energy as the Rate of Quantum Computation
Over the last few decades, developments in the physical limits of computing
and quantum computing have increasingly taught us that it can be helpful to
think about physics itself in computational terms. For example, work over the
last decade has shown that the energy of a quantum system limits the rate at
which it can perform significant computational operations, and suggests that we
might validly interpret energy as in fact being the speed at which a physical
system is "computing," in some appropriate sense of the word. In this paper, we
explore the precise nature of this connection. Elementary results in quantum
theory show that the Hamiltonian energy of any quantum system corresponds
exactly to the angular velocity of state-vector rotation (defined in a certain
natural way) in Hilbert space, and also to the rate at which the state-vector's
components (in any basis) sweep out area in the complex plane. The total angle
traversed (or area swept out) corresponds to the action of the Hamiltonian
operator along the trajectory, and we can also consider it to be a measure of
the "amount of computational effort exerted" by the system, or effort for
short. For any specific quantum or classical computational operation, we can
(at least in principle) calculate its difficulty, defined as the minimum effort
required to perform that operation on a worst-case input state, and this in
turn determines the minimum time required for quantum systems to carry out that
operation on worst-case input states of a given energy. As examples, we
calculate the difficulty of some basic 1-bit and n-bit quantum and classical
operations in an simple unconstrained scenario.Comment: Revised to address reviewer comments. Corrects an error relating to
time-ordering, adds some additional references and discussion, shortened in a
few places. Figures now incorporated into tex
Achievable rates for the Gaussian quantum channel
We study the properties of quantum stabilizer codes that embed a
finite-dimensional protected code space in an infinite-dimensional Hilbert
space. The stabilizer group of such a code is associated with a symplectically
integral lattice in the phase space of 2N canonical variables. From the
existence of symplectically integral lattices with suitable properties, we
infer a lower bound on the quantum capacity of the Gaussian quantum channel
that matches the one-shot coherent information optimized over Gaussian input
states.Comment: 12 pages, 4 eps figures, REVTe
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
Perfect state distinguishability and computational speedups with postselected closed timelike curves
Bennett and Schumacher's postselected quantum teleportation is a model of
closed timelike curves (CTCs) that leads to results physically different from
Deutsch's model. We show that even a single qubit passing through a
postselected CTC (P-CTC) is sufficient to do any postselected quantum
measurement, and we discuss an important difference between "Deutschian" CTCs
(D-CTCs) and P-CTCs in which the future existence of a P-CTC might affect the
present outcome of an experiment. Then, based on a suggestion of Bennett and
Smith, we explicitly show how a party assisted by P-CTCs can distinguish a set
of linearly independent quantum states, and we prove that it is not possible
for such a party to distinguish a set of linearly dependent states. The power
of P-CTCs is thus weaker than that of D-CTCs because the Holevo bound still
applies to circuits using them regardless of their ability to conspire in
violating the uncertainty principle. We then discuss how different notions of a
quantum mixture that are indistinguishable in linear quantum mechanics lead to
dramatically differing conclusions in a nonlinear quantum mechanics involving
P-CTCs. Finally, we give explicit circuit constructions that can efficiently
factor integers, efficiently solve any decision problem in the intersection of
NP and coNP, and probabilistically solve any decision problem in NP. These
circuits accomplish these tasks with just one qubit traveling back in time, and
they exploit the ability of postselected closed timelike curves to create
grandfather paradoxes for invalid answers.Comment: 15 pages, 4 figures; Foundations of Physics (2011
Universal quantum interfaces
To observe or control a quantum system, one must interact with it via an
interface. This letter exhibits simple universal quantum interfaces--quantum
input/output ports consisting of a single two-state system or quantum bit that
interacts with the system to be observed or controlled. It is shown that under
very general conditions the ability to observe and control the quantum bit on
its own implies the ability to observe and control the system itself. The
interface can also be used as a quantum communication channel, and multiple
quantum systems can be connected by interfaces to become an efficient universal
quantum computer. Experimental realizations are proposed, and implications for
controllability, observability, and quantum information processing are
explored.Comment: 4 pages, 3 figures, RevTe
Secure quantum key distribution using squeezed states
We prove the security of a quantum key distribution scheme based on
transmission of squeezed quantum states of a harmonic oscillator. Our proof
employs quantum error-correcting codes that encode a finite-dimensional quantum
system in the infinite-dimensional Hilbert space of an oscillator, and protect
against errors that shift the canonical variables p and q. If the noise in the
quantum channel is weak, squeezing signal states by 2.51 dB (a squeeze factor
e^r=1.34) is sufficient in principle to ensure the security of a protocol that
is suitably enhanced by classical error correction and privacy amplification.
Secure key distribution can be achieved over distances comparable to the
attenuation length of the quantum channel.Comment: 19 pages, 3 figures, RevTeX and epsf, new section on channel losse
Probabilistic instantaneous quantum computation
The principle of teleportation can be used to perform a quantum computation
even before its quantum input is defined. The basic idea is to perform the
quantum computation at some earlier time with qubits which are part of an
entangled state. At a later time a generalized Bell state measurement is
performed jointly on the then defined actual input qubits and the rest of the
entangled state. This projects the output state onto the correct one with a
certain exponentially small probability. The sufficient conditions are found
under which the scheme is of benefit.Comment: 4 pages, 1 figur
Quantum state merging and negative information
We consider a quantum state shared between many distant locations, and define
a quantum information processing primitive, state merging, that optimally
merges the state into one location. As announced in [Horodecki, Oppenheim,
Winter, Nature 436, 673 (2005)], the optimal entanglement cost of this task is
the conditional entropy if classical communication is free. Since this quantity
can be negative, and the state merging rate measures partial quantum
information, we find that quantum information can be negative. The classical
communication rate also has a minimum rate: a certain quantum mutual
information. State merging enabled one to solve a number of open problems:
distributed quantum data compression, quantum coding with side information at
the decoder and sender, multi-party entanglement of assistance, and the
capacity of the quantum multiple access channel. It also provides an
operational proof of strong subadditivity. Here, we give precise definitions
and prove these results rigorously.Comment: 23 pages, 3 figure
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