How many measurements are needed to detect bound entangled states?

From a practical perspective it is advantageous to develop experimental methods that verify entanglement in quantum states with as few measurements as possible. In this paper we investigate the minimal number of measurements needed to detect bound entanglement in bipartite $(dtimes d)$-dimensional states, i.e. entangled states that are positive under partial transposition. In particular, we show that a class of entanglement witnesses composed of mutually unbiased bases (MUBs) can detect bound entanglement if the number of measurements is greater than $d/2+1$. This is a substantial improvement over other detection methods, requiring significantly fewer resources than either full quantum state tomography or measuring a complete set of $d+1$ MUBs. Our approach is based on a partial characterisation of the (non-)decomposability of entanglement witnesses. We show that non-decomposability is a universal property of MUBs, which holds regardless of the choice of complementary observables, and we find that both the number of measurements and the structure of the witness play an important role in the detection of bound entanglement.

Thermodynamic quantities in quantum speed limit for non-Markovian dynamics

Quantum speed limit (QSL) for open quantum systems in the non-Markovian regime is analyzed. We provide the lower bound for the time required to transform an initial state to a final state in terms of thermodynamic quantities such as the energy fluctuation, entropy production rate and dynamical activity. Such bound was already analyzed for Markovian evolution satisfying detailed balance condition. Here we generalize this approach to deal with arbitrary evolution governed by time-local generator. Our analysis is illustrated by three paradigmatic examples of qubit evolution: amplitude damping, pure dephasing, and the eternally non-Markovian evolution.

No causal order and topological phases

We consider a topological Hamiltonian and establish a correspondence between its eigenstates and the resource for a causal order game introduced in Ref. [1], known as process matrix. We show that quantum correlations generated in the quantum many-body energy eigenstates of the model can mimic the statistics that can be obtained by exploiting different quantum measurements on the process matrix of the game. This provides an interpretation of the expectation values of the observables computed for the quantum many-body states in terms of success probabilities of the game. As a result, we show that the ground state of the model can be related to the optimal strategy of the causal order game. Along with this, we show that a correspondence between the considered topological quantum Hamiltonian and the causal order game can also be made by relating the behavior of topological order parameters characterizing different phases of the model with the different regions of the causal order game.

Growth of genuine multipartite entanglement in random unitary circuits

We study the growth of genuine multipartite entanglement in random quantum circuit models, which include random unitary circuit models and the random Clifford circuit. We find that for the random Clifford circuit, the growth of multipartite entanglement remains slower in comparison to the random unitary case. However, the final saturation value of multipartite entanglement is almost the same in both cases. The behavior is then compared to the genuine multipartite entanglement obtained in random matrix product states with a moderately high bond dimension. We then relate the behavior of multipartite entanglement to other global properties of the system, viz. the delocalization of the many-body wavefunctions in Hilbert space. Along with this, we analyze the robustness of such highly entangled quantum states obtained through random unitary dynamics under weak measurements.

Recycling the resource: Sequential usage of shared state in quantum teleportation with weak measurements

Complete measurements, while providing maximal information gain, results in destruction of the shared entanglement. In the standard teleportation scheme, the senders measurement on the shared entangled state between the sender and the receiver has that consequence. We propose here a teleportation scheme involving weak measurements which can sustain entanglement upto a certain level so that the reusability of the shared resource state is possible. The measurements are chosen in such a way that it is weak enough to retain entanglement and hence can be reused for quantum tasks, yet adequately strong to ensure quantum advantage in the protocol. In this scenario, we report that at most six sender-receiver duos can reuse the state, when the initial shared state is entangled in a finite neighborhood of the maximally entangled state and for a suitable choice of weak measurements. However, we observe that the reusability number decreases with the decrease in the entanglement of the initial shared state. Among the weakening strategies studied, Bell measurement admixed with white noise performs better than any other low-rank weak measurements in this situation.

One-shot conclusive multiport quantum dense coding capacities

We introduce a probabilistic version of the one-shot quantum dense coding protocol in both two- and multiport scenarios, and refer to it as conclusive quantum dense coding. Specifically, we analyze the corresponding capacities of two-qubit, two-qutrit, and three-qubit shared states. We identify cases where Pauli and generalized Pauli operators are not sufficient as encoders to attain the optimal one-shot conclusive quantum dense coding capacities. We find that there is a rich connection between the capacities, and the bipartite and multipartite entanglements of the shared state.

Witnessing entanglement sequentially: Maximally entangled states are not special

We investigate sharing of bipartite entanglement in a scenario where half of an entangled pair is possessed and projectively measured by one observer, called Alice, while the other half is subjected to measurements performed sequentially, independently, and unsharply, by multiple observers, called Bobs. We find that there is a limit on the number of observers in this entanglement distribution scenario. In particular, for a two-qubit maximally entangled initial shared state, no more than twelve Bobs can detect entanglement with a single Alice for arbitrary -- possibly unequal -- sharpness parameters of the measurements by the Bobs. Moreover, the number of Bobs remains unaltered for a finite range of near-maximal pure initial entanglement, a feature that also occurs in the case of equal sharpness parameters at the Bobs. Furthermore, we show that for non-maximally entangled shared pure states, the number of Bobs reduces with the amount of initial entanglement, providing a coarse-grained but operational measure of entanglement.

Position and momentum cannot both be lazy: Quantum reciprocity relation with Lipschitz constants

We propose a trade-off between the Lipschitz constants of the position and momentum probability distributions for arbitrary quantum states. We refer to the trade-off as a quantum reciprocity relation. The Lipschitz constant of a function may be considered to quantify the extent of fluctuations of that function, and is, in general, independent of its spread. The spreads of the position and momentum distributions are used to obtain the celebrated Heisenberg quantum uncertainty relations. We find that the product of the Lipschitz constants of position and momentum probability distributions is bounded below by a number that is of the order of the inverse square of the Plancks constant.

Response of entanglement to annealed vis-`a-vis quenched disorder in quantum spin models

We investigate bipartite entanglement in random quantum $XY$ models at equilibrium. Depending on the intrinsic time scales associated with equilibration of the random parameters and measurements associated with observation of the system, we consider two distinct kinds of disorder, namely annealed and quenched disorders. We conduct a comparative study of the effects of disorder on nearest-neighbor entanglement, when the nature of randomness changes from being annealed to quenched. We find that entanglement properties of the annealed and quenched disordered systems are drastically different from each other. This is realized by identifying the regions of parameter space in which the nearest-neighbor state is entangled, and the regions where a disorder-induced enhancement of entanglement $-$ order-from-disorder $-$ is obtained. We also analyze the response of the quantum phase transition point of the ordered system with the infusion of disorder.

Benford analysis of quantum critical phenomena: First digit provides high finite-size scaling exponent while first two and further are not much better

Benfords law is an empirical edict stating that the lower digits appear more often than higher ones as the first few significant digits in statistics of natural phenomena and mathematical tables. A marked proportion of such analyses is restricted to the first significant digit. We employ violation of Benfords law, up to the first four significant digits, for investigating magnetization and correlation data of paradigmatic quantum many-body systems to detect cooperative phenomena, focusing on the finite-size scaling exponents thereof. We find that for the transverse field quantum XY model, behavior of the very first significant digit of an observable, at an arbitrary point of the parameter space, is enough to capture the quantum phase transition in the model with a relatively high scaling exponent. A higher number of significant digits do not provide an appreciable further advantage, in particular, in terms of an increase in scaling exponents. Since the first significant digit of a physical quantity is relatively simple to obtain in experiments, the results have potential implications for laboratory observations in noisy environments.