4,077 research outputs found
Robust polarization-based quantum key distribution over collective-noise channel
We present two polarization-based protocols for quantum key distribution. The
protocols encode key bits in noiseless subspaces or subsystems, and so can
function over a quantum channel subjected to an arbitrary degree of collective
noise, as occurs, for instance, due to rotation of polarizations in an optical
fiber. These protocols can be implemented using only entangled photon-pair
sources, single-photon rotations, and single-photon detectors. Thus, our
proposals offer practical and realistic alternatives to existing schemes for
quantum key distribution over optical fibers without resorting to
interferometry or two-way quantum communication, thereby circumventing,
respectively, the need for high precision timing and the threat of Trojan horse
attacks.Comment: Minor changes, added reference
Efficient discrete-time simulations of continuous-time quantum query algorithms
The continuous-time query model is a variant of the discrete query model in
which queries can be interleaved with known operations (called "driving
operations") continuously in time. Interesting algorithms have been discovered
in this model, such as an algorithm for evaluating nand trees more efficiently
than any classical algorithm. Subsequent work has shown that there also exists
an efficient algorithm for nand trees in the discrete query model; however,
there is no efficient conversion known for continuous-time query algorithms for
arbitrary problems.
We show that any quantum algorithm in the continuous-time query model whose
total query time is T can be simulated by a quantum algorithm in the discrete
query model that makes O[T log(T) / log(log(T))] queries. This is the first
upper bound that is independent of the driving operations (i.e., it holds even
if the norm of the driving Hamiltonian is very large). A corollary is that any
lower bound of T queries for a problem in the discrete-time query model
immediately carries over to a lower bound of \Omega[T log(log(T))/log (T)] in
the continuous-time query model.Comment: 12 pages, 6 fig
Improvement of stabilizer based entanglement distillation protocols by encoding operators
This paper presents a method for enumerating all encoding operators in the
Clifford group for a given stabilizer. Furthermore, we classify encoding
operators into the equivalence classes such that EDPs (Entanglement
Distillation Protocol) constructed from encoding operators in the same
equivalence class have the same performance. By this classification, for a
given parameter, the number of candidates for good EDPs is significantly
reduced. As a result, we find the best EDP among EDPs constructed from [[4,2]]
stabilizer codes. This EDP has a better performance than previously known EDPs
over wide range of fidelity.Comment: 22 pages, 2 figures, In version 2, we enumerate all encoding
operators in the Clifford group, and fix the wrong classification of encoding
operators in version
Developing the Deutsch-Hayden approach to quantum mechanics
The formalism of Deutsch and Hayden is a useful tool for describing quantum
mechanics explicitly as local and unitary, and therefore quantum information
theory as concerning a "flow" of information between systems. In this paper we
show that these physical descriptions of flow are unique, and develop the
approach further to include the measurement interaction and mixed states. We
then give an analysis of entanglement swapping in this approach, showing that
it does not in fact contain non-local effects or some form of superluminal
signalling.Comment: 14 pages. Added section on entanglement swappin
Counterfactual Quantum Cryptography
Quantum cryptography allows one to distribute a secret key between two remote
parties using the fundamental principles of quantum mechanics. The well-known
established paradigm for the quantum key distribution relies on the actual
transmission of signal particle through a quantum channel. This paper shows
that the task of a secret key distribution can be accomplished even though a
particle carrying secret information is not in fact transmitted through the
quantum channel. The proposed protocols can be implemented with current
technologies and provide practical security advantages by eliminating the
possibility that an eavesdropper can directly access the entire quantum system
of each signal particle.Comment: 19 pages, 1 figure; a little ambiguity in the version 1 removed;
abstract, text, references, and appendix revised; suggestions and comments
are highly appreciate
A Theory of Fault-Tolerant Quantum Computation
In order to use quantum error-correcting codes to actually improve the
performance of a quantum computer, it is necessary to be able to perform
operations fault-tolerantly on encoded states. I present a general theory of
fault-tolerant operations based on symmetries of the code stabilizer. This
allows a straightforward determination of which operations can be performed
fault-tolerantly on a given code. I demonstrate that fault-tolerant universal
computation is possible for any stabilizer code. I discuss a number of examples
in more detail, including the five-qubit code.Comment: 30 pages, REVTeX, universal swapping operation added to allow
universal computation on any stabilizer cod
Encoding a qubit in an oscillator
Quantum error-correcting codes are constructed that embed a
finite-dimensional code space in the infinite-dimensional Hilbert space of a
system described by continuous quantum variables. These codes exploit the
noncommutative geometry of phase space to protect against errors that shift the
values of the canonical variables q and p. In the setting of quantum optics,
fault-tolerant universal quantum computation can be executed on the protected
code subspace using linear optical operations, squeezing, homodyne detection,
and photon counting; however, nonlinear mode coupling is required for the
preparation of the encoded states. Finite-dimensional versions of these codes
can be constructed that protect encoded quantum information against shifts in
the amplitude or phase of a d-state system. Continuous-variable codes can be
invoked to establish lower bounds on the quantum capacity of Gaussian quantum
channels.Comment: 22 pages, 8 figures, REVTeX, title change (qudit -> qubit) requested
by Phys. Rev. A, minor correction
From qubits to black holes: entropy, entanglement and all that
Entropy plays a crucial role in characterization of information and
entanglement, but it is not a scalar quantity and for many systems it is
different for different relativistic observers. Loop quantum gravity predicts
the Bekenstein-Hawking term for black hole entropy and logarithmic correction
to it. The latter originates in the entanglement between the pieces of spin
networks that describe black hole horizon. Entanglement between gravity and
matter may restore the unitarity in the black hole evaporation process. If the
collapsing matter is assumed to be initially in a pure state, then entropy of
the Hawking radiation is exactly the created entanglement between matter and
gravity.Comment: Honorable Mention in the 2005 Gravity Research Foundation Essay
Competitio
Generation of Kerr non-Gaussian motional states of trapped ions
Non-Gaussian states represent a powerful resource for quantum information
protocols in the continuous variables regime. Cat states, in particular, have
been produced in the motional degree of freedom of trapped ions by controlled
displacements dependent on the ionic internal state. An alternative method
harnesses the Kerr nonlinearity naturally existent in this kind of system. We
present detailed calculations confirming its feasibility for typical
experimental conditions. Additionally, this method permits the generation of
complex non-Gaussian states with negative Wigner functions. Especially,
superpositions of many coherent states are achieved at a fraction of the time
necessary to produce the cat state.Comment: 6 pages, 5 figure
Unified derivations of measurement-based schemes for quantum computation
We present unified, systematic derivations of schemes in the two known
measurement-based models of quantum computation. The first model (introduced by
Raussendorf and Briegel [Phys. Rev. Lett., 86, 5188 (2001)]) uses a fixed
entangled state, adaptive measurements on single qubits, and feedforward of the
measurement results. The second model (proposed by Nielsen [Phys. Lett. A, 308,
96 (2003)] and further simplified by Leung [Int. J. Quant. Inf., 2, 33 (2004)])
uses adaptive two-qubit measurements that can be applied to arbitrary pairs of
qubits, and feedforward of the measurement results. The underlying principle of
our derivations is a variant of teleportation introduced by Zhou, Leung, and
Chuang [Phys. Rev. A, 62, 052316 (2000)]. Our derivations unify these two
measurement-based models of quantum computation and provide significantly
simpler schemes.Comment: 14 page
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