37 research outputs found
Testing local-realism and macro-realism under generalized dichotomic measurements
Generalised quantum measurements with two outcomes are fully characterised by
two real parameters, dubbed as sharpness parameter and biasedness parameter and
they can be linked with different aspects of the experimental setup. It is
known that precision of measurements, characterised by the sharpness parameter
of the measurements, reduces the possibility of probing quantum features like
violation of local-realism (LR) or macro-realism (MR). Here we investigate the
effect of biasedness together with sharpness of measurement and find a
trade-off between those two parameters in the context of probing violation of
LR and MR. Interestingly we also find the above mentioned trade-off is more
robust in the later case.Comment: 10 pages, 3 figure
Role of fine-grained uncertainty in determining the limit of preparation contextuality
The optimal success probability of a communication game sets fundamental
limitations on an operational theory. Quantum advantage of parity oblivious
random access code (PORAC), a communication game, over classical resources
reveals the preparation contextuality of quantum theory [Phys. Rev. Lett. 102,
010401 (2009)]. Optimal quantum advantage in the N-dit PORAC game for finite
dimensions is an open problem. Here, we show that the degree of uncertainty
allowed in an operational theory determines the amount of preparation
contextuality. We connect the upper bound of fine-grained uncertainty relation
to the success probability of PORAC game played with the quantum resource.
Subsequently, we find the optimal success probability for the 2-dit PORAC game
using MUBs for the decoding strategy. Finally, we also derive an upper bound on
quantum advantage for the N-dit PORAC game.Comment: Close to the published versio
Sharing of Nonlocality of a single member of an Entangled Pair Is Not Possible by More Than Two Unbiased Observers on the other wing
We address the recently posed question as to whether the nonlocality of a
single member of an entangled pair of spin particles can be shared among
multiple observers on the other wing who act sequentially and independently of
each other [1]. We first show that the optimality condition for the trade-off
between information gain and disturbance in the context of weak or non-ideal
measurements emerges naturally when one employs a one-parameter class of
positive operator valued measures (POVMs). Using this formalism we then prove
analytically that it is impossible to obtain violation of the
Clauser-Horne-Shimony-Holt (CHSH) inequality by more than two Bobs in one of
the two wings using unbiased input settings with an Alice in the other wing
Probing hierarchy of temporal correlation requires either generalised measurement or nonunitary evolution
Temporal steering and violation of the Leggett-Garg inequality are two
different ways of probing the violation of macro-realistic assumptions in
quantum mechanics. It is shown here that under unitary evolution and projective
measurements the two types of temporal correlations lead to similar results.
However, their inequivalence may be exhibited if either one of them is relaxed,
i.e., by employing either generalized measurements, or noisy evolution, as we
show here using relevant examples.Comment: 8 pages, 3 figure
Protecting temporal correlations of two-qubit states using quantum channels with memory
Quantum temporal correlations exhibited by violations of Leggett-Garg
Inequality (LGI) and Temporal Steering Inequality (TSI) are in general found to
be non-increasing under decoherence channels when probed on two-qubit pure
entangled states. We study the action of decoherence channels, such as
amplitude damping, phase-damping and depolarising channels when partial memory
is introduced in a way such that two consecutive uses of the channels are
time-correlated. We show that temporal correlations demonstrated by violations
of the above temporal inequalities can be protected against decoherence using
the effect of memory.Comment: 12 pages, 8 figure
Inhibition of spreading in quantum random walks due to quenched Poisson-distributed disorder
We consider a quantum particle (walker) on a line who coherently chooses to
jump to the left or right depending on the result of toss of a quantum coin.
The lengths of the jumps are considered to be independent and identically
distributed quenched Poisson random variables. We find that the spread of the
walker is significantly inhibited, whereby it resides in the near-origin
region, with respect to the case when there is no disorder. The scaling
exponent of the quenched-averaged dispersion of the walker is sub-ballistic but
super-diffusive. We also show that the features are universal to a class of
sub- and super-Poissonian distributed quenched randomized jumps.Comment: 7 pages, 3 figures; v2: further distributions considered, close to
published versio
Constructive Feedback of Non-Markovianity on Resources in Random Quantum States
We explore the impact of non-Markovian channels on the quantum correlations
(QCs) of Haar uniformly generated random two-qubit input states with different
ranks -- either one of the qubits (single-sided) or both the qubits
independently (double-sided) are passed through noisy channels. Under dephasing
and depolarizing channels with varying non-Markovian strength, entanglement and
quantum discord of the output states collapse and revive with the increase of
noise. We find that in case of the depolarizing double-sided channel, both the
QCs of random states show a higher number of revivals on average than that of
the single-sided ones with a fixed non-Markovianity strength, irrespective of
the rank of the states -- we call such a counter-intuitive event as a
constructive feedback of non-Markovianity. Consequently, the average noise at
which QCs of random states show first revival decreases with the increase of
the strength of non-Markovian noise, thereby indicating the role of
non-Markovian channels on the regenerations of QCs even in presence of a high
amount of noise. However, we observe that non-Markovianity does not play any
role to increase the robustness in random quantum states which can be measured
by the mean value of critical noise at which quantum correlations first
collapse. Moreover, we observe that the tendency of a state to show
regeneration increases with the increase of average QCs of the random input
states along with non-Markovianity.Comment: V2: results unchanged, some figures are update
Necessary and sufficient state condition for two-qubit steering using two measurement settings per party and monogamy of steering
We consider the Cavalcanti-Foster-Fuwa-Wiseman inequality~\cite{achsh} which
is a necessary and sufficient steerability condition for two-qubit states with
two measurement settings on each side. We derive the criterion which an
arbitrary two-qubit state must satisfy in order to violate this inequality, and
obtain its maximum attainable violation in quantum mechanics. The derived
condition on the state parameters enables us to establish a tight monogamy
relation for two-qubit steering.Comment: 4 page
Wigner's form of the Leggett-Garg inequality, No-Signalling in Time, and Unsharp Measurements
Wigner's form of the local realist inequality is used to derive its temporal
version for an oscillating two-level system involving two-time joint
probabilities. Such an inequality may be regarded as a novel form of the
Leggett-Garg inequality (LGI) constituting a necessary condition for
macrorealism. The robustness of its quantum mechanical (QM) violation against
unsharpness of measurement is investigated by using a suitable model of unsharp
measurements. It is found that there exists a range of values of the sharpness
parameter (characterizing precision of the relevant measurements) for which the
usual LGI is satisfied by QM, but Wigner's form of the LGI (WLGI) is violated.
This implies that for such unsharp measurements, the QM violation of
macrorealism cannot be tested using the usual LGI, but can be tested using
WLGI. In showing this, we take into account the general form of the usual LGI
involving an arbitrary number of pairs of two-time correlation functions.
Another recently proposed necessary condition for macrorealism, called
`no-signalling in time', is also probed, showing that its QM violation persists
for arbitrarily unsharp measurements
Steering a single system sequentially by multiple observers
Quantum mechanics puts a restriction on the number of observers who can
simultaneously steer another observer's system, known as the monogamy of
steering. In this work we find the limit of the number of observers (Bobs) who
can steer another party's (Alice's) system invoking a scenario where half of an
entangled pair is shared between a single Alice in one wing and several Bobs on
the other wing, who act sequentially and independently of each other. When all
the observers measure two dichotomic observables, we find that two Bobs can
steer Alice's system going beyond the monogamy restriction. We further show
that three Bobs can steer Alice's system considering a three-settings linear
steering inequality, and then conjecture that at most Bobs can demonstrate
steering of Alice's system when steering is probed through an -settings
linear steering inequality.Comment: 6 page