75 research outputs found
Measurement incompatibility and Schr\"odinger-EPR steering in a class of probabilistic theories
Steering is one of the most counter intuitive non classical features of
bipartite quantum system, first noticed by Schr\"odinger at the early days of
quantum theory. On the other hand measurement incompatibility is another non
classical feature of quantum theory, initially pointed out by N. Bohr. Recently
the authors of Refs.
[\href{http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.160402}{Phys.
Rev. Lett. {\bf 113}, 160402 (2014)}] and
[\href{http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.160403}{Phys.
Rev. Lett. {\bf 113}, 160403 (2014)}] have investigated the relation between
these two distinct non classical features. They have shown that a set of
measurements is not jointly measurable (i.e. incompatible) if and only if they
can be used for demonstrating Schr\"odinger-Einstein-Podolsky-Rosen steering.
The concept of steering has been generalized for more general abstract tensor
product theories rather than just Hilbert space quantum mechanics. In this
article we discuss that the notion of measurement incompatibility can be
extended for general probability theories. Further we show that the connection
between steering and measurement incompatibility holds in a border class of
tensor product theories rather than just quantum theory.Comment: Accepted in Journal of Mathematical Physics (close to accepted
version). arXiv admin note: text overlap with arXiv:1402.6562,
arXiv:1406.6976, arXiv:1311.1462, arXiv:0707.0620 by other author
Several foundational and information theoretic implications of Bell's theorem
In 1935, Albert Einstein and two colleagues, Boris Podolsky and Nathan Rosen
(EPR) developed a thought experiment to demonstrate what they felt was a lack
of completeness in quantum mechanics. EPR also postulated the existence of more
fundamental theory where physical reality of any system would be completely
describe by the variables/states of that fundamental theory. This variable is
commonly called hidden variable and the theory is called hidden variable theory
(HVT). In 1964, John Bell proposed an empirically verifiable criterion to test
for the existence of these HVTs. He derived an inequality, which must be
satisfied by any theory that fulfill the conditions of locality and reality} He
also showed that quantum mechanics, as it violates this inequality, is
incompatible with any local-realistic theory. Later it has been shown that
Bell's inequality can be derived from different set of assumptions and it also
find applications in useful information theoretic protocols. In this review we
will discuss various foundational as well as information theoretic implications
of Bell's inequality. We will also discuss about some restricted nonlocal
feature of quantum nonlocality and elaborate the role of Uncertainty principle
and Complementarity principle in explaining this feature.Comment: 27 pages; This article is a modified version of the tutorial lecture
delivered by G. Kar at IPQI, February 17-28, 2014, Institute of Physics,
Bhubaneswar, Indi
Biased Non-Causal Game
The standard formulation of quantum theory assumes that events are ordered is
a background global causal structure. Recently in
Ref.[], the authors have developed a new formalism,
namely, the \emph{process matrix} formalism, which is locally in agreement with
quantum physics but assumes no global causal order. They have further shown
that there exist \emph{non-causal} correlations originating from
\emph{inseparable} process matrices that violate a \emph{causal inequality}
(CI) derived under the assumption that events are ordered with respect to some
global causal relation. This CI can be understood as a guessing game, where two
separate parties, say Alice and Bob, generate random bits (say input bit) in
their respective local laboratories. Bob generates another random bit (say
decision bit) which determines their goal: whether Alice has to guess Bob's bit
or vice-verse. Here we study this causal game but with biased bits and derive a
biased causal inequality (BCI). We then study the possibility of violation of
this BCI by inseparable process matrices. Interestingly, we show that there
exist \emph{inseparable} qubit process matrices that can be used to violate the
BCI for an arbitrary bias in the decision bit. In such scenario, we also derive
the maximal violation of the BCI under local operations involving traceless
binary observables. However, for biased input bits, we find that there is a
threshold bias beyond which no valid qubit process matrix can be used to
violate the causal inequality under \emph{measurement-repreparation} type
operation.Comment: Revised manuscript; comments are welcom
Lack of measurement independence can simulate quantum correlation even when signaling cannot
In Bell scenario, any nonlocal correlation, shared between two spatially
separated parties, can be modeled deterministically either by allowing
communications between the two parties or by restricting their free will in
choosing the measurement settings. Recently, Bell scenario has been generalized
into `semi-quantum' scenario where external quantum inputs are provided to the
parties. We show that in `semi-quantum' scenario, entangled states produce
correlations whose deterministic explanation is possible only if measurement
independence is reduced. Thus in simulating quantum correlation `semi-quantum'
scenario reveals a qualitative distinction between signaling and measurement
dependence which is absent in Bell scenario. We further show that such
distinction is not observed in `steering game' scenario, a special case of
`semi-quantum' scenario.Comment: 5 pages (double column); accepted in Phys. Rev.
Wigner-Yanase skew information and entanglement generation in quantum measurement
The first step of quantum measurement procedure is known as
\emph{premeasurement}, during when correlation between measuring system and
measurement apparatus is established. One compelling non-classical correlation
is entanglement, a useful resource for various quantum information theoretic
protocols. Quantifying the amount of entanglement in the premeasurement state,
therefore, seeks importance from practical ground and this is the central issue
of the present paper. Interestingly, for a two-label quantum system we obtain
that the amount of entanglement, measured in term of \emph{negativity},
generated in premeasurement process is actually quantified by two factors:
\emph{skew information} between system's initial state and the measurement
direction, which quantifies the amount of information on the values of
observables not commuting with the conserved quantity of the system, and
\emph{mixedness parameter} of the system's initial state.Comment: 6 pages, 3 figure
Study of nonlocal correlations in macroscopic measurement scenario
Nonlocality is one of the main characteristic features of quantum systems
involving more than one spatially separated subsystems. It is manifested
theoretically as well as experimentally through violation of some local
realistic inequality. On the other hand, classical behavior of all physical
phenomena in the macroscopic limit gives a general intuition that any physical
theory for describing microscopic phenomena should resemble classical physics
in the macroscopic regime-- the so-called macro-realism. In the 2-2-2 scenario
(two parties, each performing two measurements, each measurement with two
outcomes), contemplating all the no-signaling correlations, we characterize
which of them would exhibit classical (local-realistic) behavior in the
macroscopic limit. Interestingly, we find correlations which at single copy
level violate the Bell-Clauser-Horne-Shimony-Holt inequality by an amount less
than optimal quantum violation (i.e. the Cirel'son bound ), but in
the macroscopic limit gives rise to a value which is higher than .
Such correlations are therefore not considered as physical. Our study thus
provides a sufficient criterion to identify some of unphysical correlations.Comment: Accepted in Physical Review A, Close to accepted versio
Implications of Coupling in Quantum Thermodynamic Machines
We study coupled quantum systems as the working media of thermodynamic
machines. Under a suitable phase-space transformation, the coupled systems can
be expressed as a composition of independent subsystems. We find that for the
coupled systems, the figures of merit, that is the efficiency for engine and
the coefficient of performance for refrigerator, are bounded (both from above
and from below) by the corresponding figures of merit of the independent
subsystems. We also show that the optimum work extractable from a coupled
system is upper bounded by the optimum work obtained from the uncoupled system,
thereby showing that the quantum correlations do not help in optimal work
extraction. Further, we study two explicit examples, coupled spin- systems
and coupled quantum oscillators with analogous interactions. Interestingly, for
particular kind of interactions, the efficiency of the coupled oscillators
outperforms that of the coupled spin- systems when they work as heat
engines. However, for the same interaction, the coefficient of performance
behaves in a reverse manner, while the systems work as the refrigerator. Thus
the same coupling can cause opposite effects in the figures of merit of heat
engine and refrigerator.Comment: 19 pages, 8 figure
Genuinely entangled subspace with all-encompassing distillable entanglement across every bipartition
In a multipartite scenario quantum entanglement manifests its most dramatic
form when the state is genuinely entangled. Such a state is more beneficial for
information theoretic applications if it contains distillable entanglement in
every bipartition. It is, therefore, of significant operational interest to
identify subspaces of multipartite quantum systems that contain such properties
apriori. In this letter, we introduce the notion of unextendible biseparable
bases (UBB) that provides an adequate method to construct genuinely entangled
subspaces (GES). We provide an explicit construction of two types of UBBs --
party symmetric and party asymmetric -- for every -{\it qudit} quantum
system, with local dimension d\ge 3. Further, we show that the GES resulting
from the symmetric construction is indeed a {\it bidistillable} subspace, i.e.,
all the states supported on it contain distillable entanglement across every
bipartition.Comment: Close to published versio
Uncertainty principle certifies genuine source of intrinsic randomness
The Born's rule introduces intrinsic randomness to the outcomes of a
measurement performed on a quantum mechanical system. But, if the system is
prepared in the eigenstate of an observable then the measurement outcome of
that observable is completely predictable and hence there is no intrinsic
randomness. On the other hand, if two incompatible observables are measured
(either sequentially on a particle or simultaneously on two identical copies of
the particle) then uncertainty principle guarantees intrinsic randomness in the
subsequent outcomes independent of the preparation state of the system. In this
article we show that this is true not only in quantum mechanics but for any
no-signaling probabilistic theory. Also the minimum amount of intrinsic
randomness that can be guaranteed for arbitrarily prepared state of the system
is quantified by the amount of (un)certainty.Comment: Accepted in Quantum Info. Proces
Exclusivity principle and unphysicality of Garg-Mermin correlation
The question concerning the physical realizability of a probability
distribution is of quite importance in Quantum foundations. Specker first
pointed out that this question cannot be answered from Kolmogorov's axioms
alone. Lately, this observation of Specker has motivated simple principles
(exclusivity principle/ local orthogonality principle) that can explain quantum
limit regarding the possible sets of experimental probabilities in various
nonlocality and contextuality experiments. We study Specker's observation in
the simplest scenario involving three inputs each with two outputs. Then using
only linear constraints imposed on joint probabilities by this principle, we
reveal unphysical nature of Garg-Mermin (GM) correlation. Interestingly, GM
correlation was proposed to falsify the following suggestion by Fine: if the
inequalities of Clauser and Horne (CH) holds, then there exists a deterministic
local hidden-variable model for a spin-1/2 correlation experiment of the
Einstein-Podolsky-Rosen type, even when more than two observables are involved
on each side. Our result establishes that, unlike in the CH scenario, the local
orthogonality principle at single copy level is not equivalent to the
no-signaling condition in the GM scenario.Comment: New references are adde
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