1,590 research outputs found
Parsing a sequence of qubits
We develop a theoretical framework for frame synchronization, also known as
block synchronization, in the quantum domain which makes it possible to attach
classical and quantum metadata to quantum information over a noisy channel even
when the information source and sink are frame-wise asynchronous. This
eliminates the need of frame synchronization at the hardware level and allows
for parsing qubit sequences during quantum information processing. Our
framework exploits binary constant-weight codes that are self-synchronizing.
Possible applications may include asynchronous quantum communication such as a
self-synchronizing quantum network where one can hop into the channel at any
time, catch the next coming quantum information with a label indicating the
sender, and reply by routing her quantum information with control qubits for
quantum switches all without assuming prior frame synchronization between
users.Comment: 11 pages, 2 figures, 1 table. Final accepted version for publication
in the IEEE Transactions on Information Theor
Direct Characterization of Quantum Dynamics: General Theory
The characterization of the dynamics of quantum systems is a task of both
fundamental and practical importance. A general class of methods which have
been developed in quantum information theory to accomplish this task is known
as quantum process tomography (QPT). In an earlier paper [M. Mohseni and D. A.
Lidar, Phys. Rev. Lett. 97, 170501 (2006)] we presented a new algorithm for
Direct Characterization of Quantum Dynamics (DCQD) of two-level quantum
systems. Here we provide a generalization by developing a theory for direct and
complete characterization of the dynamics of arbitrary quantum systems. In
contrast to other QPT schemes, DCQD relies on quantum error-detection
techniques and does not require any quantum state tomography. We demonstrate
that for the full characterization of the dynamics of n d-level quantum systems
(with d a power of a prime), the minimal number of required experimental
configurations is reduced quadratically from d^{4n} in separable QPT schemes to
d^{2n} in DCQD.Comment: 17 pages, 6 figures, minor modifications are mad
PON Downstream Scheme Supporting Simultaneously Different ONU Categories
We propose a PON downstream scheme simultaneously supporting different categories of ONUs (e.g. different generations), whereby lower-category ONUs employ components with limited bandwidth. Our solution relies upon CDM utilizing Hadamard codes and the spectral properties of its code words. We propose a novel code allocation scheme and provide two optimization approaches by employing an optimized secondary spreading code and a power allocation scheme to improve the system performance
Quantum Error Correcting Codes and Fault-Tolerant Quantum Computation over Nice Rings
Quantum error correcting codes play an essential role in protecting quantum information from the noise and the decoherence. Most quantum codes have been constructed based on the Pauli basis indexed by a finite field. With a newly introduced algebraic class called a nice ring, it is possible to construct the quantum codes such that their alphabet sizes are not restricted to powers of a prime.
Subsystem codes are quantum error correcting schemes unifying stabilizer codes, decoherence free subspaces and noiseless subsystems. We show a generalization of subsystem codes over nice rings. Furthermore, we prove that free subsystem codes over a finite chain ring cannot outperform those over a finite field. We also generalize entanglement-assisted quantum error correcting codes to nice rings. With the help of the entanglement, any classical code can be used to derive the corresponding quantum codes, even if such codes are not self-orthogonal. We prove that an R-module with antisymmetric bicharacter can be decomposed as an orthogonal direct sum of hyperbolic pairs using symplectic geometry over rings. So, we can find hyperbolic pairs and commuting generators generating the check matrix of the entanglement-assisted quantum code.
Fault-tolerant quantum computation has been also studied over a finite field. Transversal operations are the simplest way to implement fault-tolerant quantum gates. We derive transversal Clifford operations for CSS codes over nice rings, including Fourier transforms, SUM gates, and phase gates. Since transversal operations alone cannot provide a computationally universal set of gates, we add fault-tolerant implementations of doubly-controlled Z gates for triorthogonal stabilizer codes over nice rings.
Finally, we investigate optimal key exchange protocols for unconditionally secure key distribution schemes. We prove how many rounds are needed for the key exchange between any pair of the group on star networks, linear-chain networks, and general networks
On Protected Realizations of Quantum Information
There are two complementary approaches to realizing quantum information so
that it is protected from a given set of error operators. Both involve encoding
information by means of subsystems. One is initialization-based error
protection, which involves a quantum operation that is applied before error
events occur. The other is operator quantum error correction, which uses a
recovery operation applied after the errors. Together, the two approaches make
it clear how quantum information can be stored at all stages of a process
involving alternating error and quantum operations. In particular, there is
always a subsystem that faithfully represents the desired quantum information.
We give a definition of faithful realization of quantum information and show
that it always involves subsystems. This justifies the "subsystems principle"
for realizing quantum information. In the presence of errors, one can make use
of noiseless, (initialization) protectable, or error-correcting subsystems. We
give an explicit algorithm for finding optimal noiseless subsystems. Finding
optimal protectable or error-correcting subsystems is in general difficult.
Verifying that a subsystem is error-correcting involves only linear algebra. We
discuss the verification problem for protectable subsystems and reduce it to a
simpler version of the problem of finding error-detecting codes.Comment: 17 page
Quantum information with continuous variables
Quantum information is a rapidly advancing area of interdisciplinary
research. It may lead to real-world applications for communication and
computation unavailable without the exploitation of quantum properties such as
nonorthogonality or entanglement. We review the progress in quantum information
based on continuous quantum variables, with emphasis on quantum optical
implementations in terms of the quadrature amplitudes of the electromagnetic
field.Comment: accepted for publication in Reviews of Modern Physic
Anyon computers with smaller groups
Anyons obtained from a finite gauge theory have a computational power that
depends on the symmetry group. The relationship between group structure and
computational power is discussed in this paper. In particular, it is shown that
anyons based on finite groups that are solvable but not nilpotent are capable
of universal quantum computation. This extends previously published results to
groups that are smaller, and therefore more practical. Additionally, a new
universal gate-set is built out of an operation called a probabilistic
projection, and a quasi-universal leakage correction scheme is discussed.Comment: 28 pages, REVTeX 4 (minor corrections in v2
Self-Synchronizing Pulse Position Modulation With Error Tolerance
Pulse position modulation (PPM) is a popular signal modulation technique which converts signals into M-ary data by means of the position of a pulse within a time interval. While PPM and its variations have great advantages in many contexts, this type of modulation is vulnerable to loss of synchronization, potentially causing a severe error floor or throughput penalty even when little or no noise is assumed. Another disadvantage is that this type of modulation typically offers no error correction mechanism on its own, making them sensitive to intersymbol interference and environmental noise. In this paper, we propose a coding theoretic variation of PPM that allows for significantly more efficient symbol and frame synchronization as well as strong error correction. The proposed scheme can be divided into a synchronization layer and a modulation layer. This makes our technique compatible with major existing techniques such as standard PPM, multipulse PPM, and expurgated PPM as well in that the scheme can be realized by adding a simple synchronization layer to one of these standard techniques. We also develop a generalization of expurgated PPM suited for the modulation layer of the proposed self-synchronizing modulation scheme. This generalized PPM can also be used as stand-alone error-correcting PPM with a larger number of available symbols
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