22 research outputs found
Quantum Entropy and Special Relativity
We consider a single free spin-1/2 particle. The reduced density matrix for its spin is not covariant under Lorentz transformations. The spin entropy is not a relativistic scalar and has no invariant meaning
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
Entanglement, discord and the power of quantum computation
We show that the ability to create entanglement is necessary for execution of
bipartite quantum gates even when they are applied to unentangled states and
create no entanglement. Starting with a simple example we demonstrate that to
execute such a gate bi-locally the local operations and classical
communications (LOCC) should be supplemented by shared entanglement. Our
results point to the changes in quantum discord, which is a measure of
quantumness of correlations even in the absence of entanglement, as the
indicator of failure of a LOCC implementation of the gates.Comment: Published version. More results are adde
Entropy, holography and the second law
The geometric entropy in quantum field theory is not a Lorentz scalar and has
no invariant meaning, while the black hole entropy is invariant.
Renormalization of entropy and energy for reduced density matrices may lead to
the negative free energy even if no boundary conditions are imposed. Presence
of particles outside the horizon of a uniformly accelerated observer prevents
the description in terms of a single Unruh temperature.Comment: 4 pages, RevTex 4, 1 eps figur
Non-linear operations in quantum information theory
Quantum information theory is used to analize various non-linear operations
on quantum states. The universal disentanglement machine is shown to be
impossible, and partial (negative) results are obtained in the state-dependent
case. The efficiency of the transformation of non-orthogonal states into
orthogonal ones is discussed.Comment: 11 pages, LaTeX, 3 figures on separate page
Entanglement from longitudinal and scalar photons
The covariant quantization of the electromagnetic field in the Lorentz gauge
gives rise to longitudinal and scalar photons in addition to the usual
transverse photons. It is shown here that the exchange of longitudinal and
scalar photons can produce entanglement between two distant atoms or harmonic
oscillators. The form of the entangled states produced in this way is very
different from that obtained in the Coulomb gauge, where the longitudinal and
scalar photons do not exist. A generalized gauge transformation is used to show
that all physically observable effects are the same in the two gauges, despite
the differences in the form of the entangled states. An approach of this kind
may be useful for a covariant description of the dynamics of quantum
information processing.Comment: 12 pages, 1 figur
Realization of Optimal Disentanglement by Teleportation via Separable Channel
We discuss here the best disentanglement processes of states of two two-level
systems which belong to (i) the universal set, (ii) the set in which the states
of one party lie on a single great circle of the Bloch sphere, and (iii) the
set in which the states of one party commute with each other, by teleporting
the states of one party (on which the disentangling machine is acting) through
three particular type of separable channels, each of which is a mixture of Bell
states. In the general scenario, by teleporting one party's state of an
arbitrary entangled state of two two-level parties through some mixture of Bell
states, we have shown that this entangled state can be made separable by using
a physically realizable map , acting on one party's states, if
, where
(for ), and .Comment: 20 pages Late
Nonquantum Gravity
One of the great challenges for 21st century physics is to quantize gravity
and generate a theory that will unify gravity with the other three fundamental
forces of nature. This paper takes the (heretical) point of view that gravity
may be an inherently classical, i.e., nonquantum, phenomenon and investigates
the experimental consequences of such a model. At present there is no
experimental evidence of the quantum nature of gravity and the liklihood of
definitive tests in the future is not at all certain. If gravity is, indeed, a
nonquantum phenomenon, then it is suggested that evidence will most likely
appear at mesoscopic scales.Comment: essentially the same as the version that appears in Foundations of
Physics, 39, 331 (2009