48,268 research outputs found
Finer Distribution of Quantum Correlations among Multiqubit Systems
We study the distribution of quantum correlations characterized by monogamy
relations in multipartite systems. By using the Hamming weight of the binary
vectors associated with the subsystems, we establish a class of monogamy
inequalities for multiqubit entanglement based on the th () power of concurrence, and a class of polygamy inequalities for multiqubit
entanglement in terms of the th () power of
concurrence and concurrence of assistance. Moveover, we give the monogamy and
polygamy inequalities for general quantum correlations. Application of these
results to quantum correlations like squared convex-roof extended negativity
(SCREN), entanglement of formation and Tsallis- entanglement gives rise to
either tighter inequalities than the existing ones for some classes of quantum
states or less restrictions on the quantum states. Detailed examples are
presented
Minimum Entangling Power is Close to Its Maximum
Given a quantum gate acting on a bipartite quantum system, its maximum
(average, minimum) entangling power is the maximum (average, minimum)
entanglement generation with respect to certain entanglement measure when the
inputs are restricted to be product states. In this paper, we mainly focus on
the 'weakest' one, i.e., the minimum entangling power, among all these
entangling powers. We show that, by choosing von Neumann entropy of reduced
density operator or Schmidt rank as entanglement measure, even the 'weakest'
entangling power is generically very close to its maximal possible entanglement
generation. In other words, maximum, average and minimum entangling powers are
generically close. We then study minimum entangling power with respect to other
Lipschitiz-continuous entanglement measures and generalize our results to
multipartite quantum systems.
As a straightforward application, a random quantum gate will almost surely be
an intrinsically fault-tolerant entangling device that will always transform
every low-entangled state to near-maximally entangled state.Comment: 26 pages, subsection III.A.2 revised, authors list updated, comments
are welcom
Entanglement Distribution and Entangling Power of Quantum Gates
Quantum gates, that play a fundamental role in quantum computation and other
quantum information processes, are unitary evolution operators that
act on a composite system changing its entanglement. In the present
contribution we study some aspects of these entanglement changes. By recourse
of a Monte Carlo procedure, we compute the so called "entangling power" for
several paradigmatic quantum gates and discuss results concerning the action of
the CNOT gate. We pay special attention to the distribution of entanglement
among the several parties involved
Entanglement as a signature of quantum chaos
We explore the dynamics of entanglement in classically chaotic systems by
considering a multiqubit system that behaves collectively as a spin system
obeying the dynamics of the quantum kicked top. In the classical limit, the
kicked top exhibits both regular and chaotic dynamics depending on the strength
of the chaoticity parameter in the Hamiltonian. We show that the
entanglement of the multiqubit system, considered for both bipartite and
pairwise entanglement, yields a signature of quantum chaos. Whereas bipartite
entanglement is enhanced in the chaotic region, pairwise entanglement is
suppressed. Furthermore, we define a time-averaged entangling power and show
that this entangling power changes markedly as moves the system from
being predominantly regular to being predominantly chaotic, thus sharply
identifying the edge of chaos. When this entangling power is averaged over
initial states, it yields a signature of global chaos. The qualitative behavior
of this global entangling power is similar to that of the classical Lyapunov
exponent.Comment: 8 pages, 8 figure
Multipartite entanglement, quantum-error-correcting codes, and entangling power of quantum evolutions
We investigate the average bipartite entanglement, over all possible
divisions of a multipartite system, as a useful measure of multipartite
entanglement. We expose a connection between such measures and
quantum-error-correcting codes by deriving a formula relating the weight
distribution of the code to the average entanglement of encoded states.
Multipartite entangling power of quantum evolutions is also investigated.Comment: 13 pages, 1 figur
Tighter weighted polygamy inequalities of multipartite entanglement in arbitrary-dimensional quantum systems
We investigate polygamy relations of multipartite entanglement in
arbitrary-dimensional quantum systems. By improving an inequality and using the
th () power of entanglement of assistance, we provide a
new class of weighted polygamy inequalities of multipartite entanglement in
arbitrary-dimensional quantum systems. We show that these new polygamy
relations are tighter than the ones given in [Phys. Rev. A 97, 042332 (2018)]
Entangling power and operator entanglement in qudit systems
We establish the entangling power of a unitary operator on a general
finite-dimensional bipartite quantum system with and without ancillas, and give
relations between the entangling power based on the von Neumann entropy and the
entangling power based on the linear entropy. Significantly, we demonstrate
that the entangling power of a general controlled unitary operator acting on
two equal-dimensional qudits is proportional to the corresponding operator
entanglement if linear entropy is adopted as the quantity representing the
degree of entanglement. We discuss the entangling power and operator
entanglement of three representative quantum gates on qudits: the SUM, double
SUM, and SWAP gates.Comment: 8 pages, 1 figure. Version 3: Figure was improved and the MS was a
bit shortene
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