17,903 research outputs found
Scalable Generation and Characterization of a Four-Photon Twelve-Qubit Hyperentangled State
An experimentally feasible scheme for generating a 12-qubit hyperentangled
state via four photons, entangled in polarization, frequency and spatial mode,
is proposed. We study the nature of quantum non-locality of this hyperentangled
state by evaluating its violation degree to a Bell-type inequality, and find
that the result agrees well with quantum mechanics prediction while extremely
contradicts to the local realism constraint.Comment: 14 pages, 6 Postscript figure
Quantum Circuit Design for Solving Linear Systems of Equations
Recently, it is shown that quantum computers can be used for obtaining
certain information about the solution of a linear system Ax=b exponentially
faster than what is possible with classical computation. Here we first review
some key aspects of the algorithm from the standpoint of finding its efficient
quantum circuit implementation using only elementary quantum operations, which
is important for determining the potential usefulness of the algorithm in
practical settings. Then we present a small-scale quantum circuit that solves a
2x2 linear system. The quantum circuit uses only 4 qubits, implying a tempting
possibility for experimental realization. Furthermore, the circuit is
numerically simulated and its performance under different circuit parameter
settings is demonstrated.Comment: 7 pages, 3 figures. The errors are corrected. For the general case,
discussions are added to account for recent results. The 4x4 example is
replaced by a 2x2 one due to recent experimental efforts. The 2x2 example was
devised at the time of writing v1 but not included in v1 for brevit
Locking classical information
It is known that the maximum classical mutual information that can be
achieved between measurements on a pair of quantum systems can drastically
underestimate the quantum mutual information between those systems. In this
article, we quantify this distinction between classical and quantum information
by demonstrating that after removing a logarithmic-sized quantum system from
one half of a pair of perfectly correlated bitstrings, even the most sensitive
pair of measurements might only yield outcomes essentially independent of each
other. This effect is a form of information locking but the definition we use
is strictly stronger than those used previously. Moreover, we find that this
property is generic, in the sense that it occurs when removing a random
subsystem. As such, the effect might be relevant to statistical mechanics or
black hole physics. Previous work on information locking had always assumed a
uniform message. In this article, we assume only a min-entropy bound on the
message and also explore the effect of entanglement. We find that classical
information is strongly locked almost until it can be completely decoded. As a
cryptographic application of these results, we exhibit a quantum key
distribution protocol that is "secure" if the eavesdropper's information about
the secret key is measured using the accessible information but in which
leakage of even a logarithmic number of key bits compromises the secrecy of all
the others.Comment: 32 pages, 2 figure
A very brief introduction to quantum computing and quantum information theory for mathematicians
This is a very brief introduction to quantum computing and quantum
information theory, primarily aimed at geometers. Beyond basic definitions and
examples, I emphasize aspects of interest to geometers, especially connections
with asymptotic representation theory. Proofs of most statements can be found
in standard references
Entanglement dynamics and quasi-periodicity in discrete quantum walks
We study the entanglement dynamics of discrete time quantum walks acting on
bounded finite sized graphs. We demonstrate that, depending on system
parameters, the dynamics may be monotonic, oscillatory but highly regular, or
quasi-periodic. While the dynamics of the system are not chaotic since the
system comprises linear evolution, the dynamics often exhibit some features
similar to chaos such as high sensitivity to the system's parameters,
irregularity and infinite periodicity. Our observations are of interest for
entanglement generation, which is one primary use for the quantum walk
formalism. Furthermore, we show that the systems we model can easily be mapped
to optical beamsplitter networks, rendering experimental observation of
quasi-periodic dynamics within reach.Comment: 9 pages, 8 figure
Matrix realignment and partial transpose approach to entangling power of quantum evolutions
Based on the matrix realignment and partial transpose, we develop an approach
to entangling power and operator entanglement of quantum unitary operators. We
demonstrate efficiency of the approach by studying several unitary operators on
qudits, and indicate that these two matrix rearrangements are not only powerful
for studying separability problem of quantum states, but also useful in
studying entangling capabilities of quantum operators.Comment: Four pages and no figure
Three-Way Entanglement and Three-Qubit Phase Gate Based on a Coherent Six-Level Atomic System
We analyze the nonlinear optical response of a six-level atomic system under
a configuration of electromagnetically induced transparency. The giant
fifth-order nonlinearity generated in such a system with a relatively large
cross-phase modulation effect can produce efficient three-way entanglement and
may be used for realizing a three-qubit quantum phase gate. We demonstrate that
such phase gate can be transferred to a Toffoli gate, facilitating practical
applications in quantum information and computation.Comment: 10 pages, 2 figure
Hybrid solid state qubits: the powerful role of electron spins
We review progress on the use of electron spins to store and process quantum
information, with particular focus on the ability of the electron spin to
interact with multiple quantum degrees of freedom. We examine the benefits of
hybrid quantum bits (qubits) in the solid state that are based on coupling
electron spins to nuclear spin, electron charge, optical photons, and
superconducting qubits. These benefits include the coherent storage of qubits
for times exceeding seconds, fast qubit manipulation, single qubit measurement,
and scalable methods for entangling spatially separated matter-based qubits. In
this way, the key strengths of different physical qubit implementations are
brought together, laying the foundation for practical solid-state quantum
technologies.Comment: 54 pages, 7 figure
Geometric interpretation for A-fidelity and its relation with Bures fidelity
A geometric interpretation for the A-fidelity between two states of a qubit
system is presented, which leads to an upper bound of the Bures fidelity. The
metrics defined based on the A-fidelity are studied by numerical method. An
alternative generalization of the A-fidelity, which has the same geometric
picture, to a -state quantum system is also discussed.Comment: 4 pages, 1 figure. Phys. Rev.
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