arXiv subjects

Gustavo Rigolin

Publications and source records attributed to Gustavo Rigolin.

At least 37 records · Page 2Linked to original sources

arXiv2016

Entanglement, identical particles and the uncertainty principle

A new uncertainty relation (UR) is obtained for a system of N identical pure entangled particles if we use symmetrized observables when deriving the inequality. This new expression can be written in a form where we identify a term which explicitly shows the quantum correlations among the particles that constitute the system. For the particular cases of two and three particles, making use of the Schwarz inequality, we obtain new lower bounds for the UR that are different from the standard one.

quant-ph↗

arXiv2016

Probabilistic quantum teleportation in the presence of noise

We extend the research program initiated in [Phys. Rev. A 92, 012338 (2015)], where we restricted our attention to noisy deterministic teleportation protocols, to noisy probabilistic (conditional) protocols. Our main goal now is to study how we can increase the fidelity of the teleported state in the presence of noise by working with probabilistic protocols. We work with several scenarios involving the most common types of noise in realistic implementations of quantum communication tasks and find many cases where adding more noise to the probabilistic protocol increases considerably the fidelity of the teleported state, without decreasing the probability of a successful run of the protocol. Also, there are cases where the entanglement of the channel connecting Alice and Bob leading to the greatest fidelity is not maximal. Moreover, there exist cases where the optimal fidelity for the probabilistic protocols are greater than the maximal fidelity (2/3) achievable by using only classical resources, while the optimal ones for the deterministic protocols under the same conditions lie below this limit. This result clearly illustrates that in some cases we can only get a truly quantum teleportation if we use probabilistic instead of deterministic protocols.

quant-ph↗

arXiv2015

A Simple Derivation of Schroedinger Uncertainty Relation

We show how the Schroedinger Uncertainty Relation for a pair of observables can be deduced using the Cauchy-Schwarz inequality plus successive applications of the commutation relation involving the two observables. Our derivation differs from the original one in the sense that we do not need the expansion of the product of these two observables in a sum of symmetrical and anti-symmetrical operators.

physics.ed-ph↗

arXiv2015

Fighting noise with noise in realistic quantum teleportation

We investigate how the efficiency of the quantum teleportation protocol is affected when the qubits involved in the protocol are subjected to noise or decoherence. We study all types of noise usually encountered in real world implementations of quantum communication protocols, namely, the bit flip, phase flip (phase damping), depolarizing, and amplitude damping noise. Several realistic scenarios are studied in which a part or all of the qubits employed in the execution of the quantum teleportation protocol are subjected to the same or different types of noise. We find noise scenarios not yet known in which more noise or less entanglement lead to more efficiency. Furthermore, we show that if noise is unavoidable it is better to subject the qubits to different noise channels in order to obtain an increase in the efficiency of the protocol.

quant-ph↗

arXiv2015

Optimal continuous variable quantum teleportation protocol for realistic settings

We show the optimal setup that allows Alice to teleport coherent states to Bob giving the greatest fidelity (efficiency) when one takes into account two realistic assumptions. The first one says that in any actual implementation of the continuous variable teleportation protocol (CVTP) Alice and Bob necessarily share non-maximally entangled states (two-mode finitely squeezed states). The second one assumes that Alice's pool of possible coherent states to be teleported to Bob does not cover the whole complex plane. The optimal strategy is achieved by tuning three parameters in the original CVTP, namely, the beam splitter transmittance and the displacements in position and momentum implemented on the teleported state. These slight changes in the protocol are currently easy to be implemented and, as we show, give considerable gain in perfomance for a variety of possible pool of input states with Alice.

quant-ph↗

arXiv2014

Degenerate Adiabatic Perturbation Theory: Foundations and Applications

We present details and expand on the framework leading to the recently introduced degenerate adiabatic perturbation theory [Phys. Rev. Lett. 104, 170406 (2010)], and on the formulation of the degenerate adiabatic theorem, along with its necessary and sufficient conditions given in [Phys. Rev. A 85, 062111 (2012)]. We start with the adiabatic approximation for degenerate Hamiltonians that paves the way to a clear and rigorous statement of the associated degenerate adiabatic theorem, where the non-abelian geometric phase (Wilczek-Zee phase) plays a central role to its quantitative formulation. We then describe the degenerate adiabatic perturbation theory, whose zeroth order term is the degenerate adiabatic approximation, in its full generality. The parameter in the perturbative power series expansion of the time-dependent wave function is directly associated to the inverse of the time it takes to drive the system from its initial to its final state. With the aid of the degenerate adiabatic perturbation theory we obtain rigorous necessary and sufficient conditions for the validity of the adiabatic theorem of quantum mechanics. Finally, to illustrate the power and wide scope of the methodology, we apply the framework to a degenerate Hamiltonian, whose closed form time-dependent wave function is derived exactly, and also to other non-exactly-solvable Hamiltonians whose solutions are numerically computed.

quant-ph↗

arXiv2014

Entangling Power of Disordered Quantum Walks

We investigate how the introduction of different types of disorder affects the generation of entanglement between the internal (spin) and external (position) degrees of freedom in one-dimensional quantum random walks (QRW). Disorder is modeled by adding another random feature to QRW, i.e., the quantum coin that drives the system's evolution is randomly chosen at each position and/or at each time step, giving rise to either dynamic, fluctuating, or static disorder. The first one is position-independent, with every lattice site having the same coin at a given time, the second has time and position dependent randomness, while the third one is time-independent. We show for several levels of disorder that dynamic disorder is the most powerful entanglement generator, followed closely by fluctuating disorder. Static disorder is the less efficient entangler, being almost always less efficient than the ordered case. Also, dynamic and fluctuating disorder lead to maximally entangled states asymptotically in time for any initial condition while static disorder has no asymptotic limit and, similarly to the ordered case, has a long time behavior highly sensitive to the initial conditions.

quant-ph↗

arXiv2013

Dynamically Disordered Quantum Walk as a Maximal Entanglement Generator

We show that the entanglement between the internal (spin) and external (position) degrees of freedom of a qubit in a random (dynamically disordered) one-dimensional discrete time quantum random walk (QRW) achieves its maximal possible value asymptotically in the number of steps, outperforming the entanglement attained by using ordered QRW. The disorder is modeled by introducing an extra random aspect to QRW, a classical coin that randomly dictates which quantum coin drives the system's time evolution. We also show that maximal entanglement is achieved independently of the initial state of the walker, study the number of steps the system must move to be within a small fixed neighborhood of its asymptotic limit, and propose two experiments where these ideas can be tested.

quant-ph↗

arXiv2013

Improving the efficiency of single and multiple teleportation protocols based on the direct use of partially entangled states

We push the limits of the direct use of partially pure entangled states to perform quantum teleportation by presenting several protocols in many different scenarios that achieve the optimal efficiency possible. We review and put in a single formalism the three major strategies known to date that allow one to use partially entangled states for direct quantum teleportation (no distillation strategies permitted) and compare their efficiencies in real world implementations. We show how one can improve the efficiency of many direct teleportation protocols by combining these techniques. We then develop new teleportation protocols employing multipartite partially entangled states. The three techniques are also used here in order to achieve the highest efficiency possible. Finally, we prove the upper bound for the optimal success rate for protocols based on partially entangled Bell states and show that some of the protocols here developed achieve such a bound.

quant-ph↗

arXiv2012

Interplay between quantum phase transitions and the behavior of quantum correlations at finite temperatures

We review the main results and ideas showing that quantum correlations at finite temperatures (T), in particular quantum discord, are useful tools in characterizing quantum phase transitions that only occur, in principle, at the unattainable absolute zero temperature. We first review some interesting results about the behavior of thermal quantum discord for small spin-1/2 chains and show that they already give us important hints of the infinite chain behavior. We then study in detail and in the thermodynamic limit (infinite chains) the thermal quantum correlations for the XXZ and XY models, where one can clearly appreciate that the behavior of thermal quantum discord at finite T is a useful tool to spotlight the critical point of a quantum phase transition.

quant-ph↗

arXiv2012

The Adiabatic Theorem for Quantum Systems with Spectral Degeneracy

By stating the adiabatic theorem of quantum mechanics in a clear and rigorous way, we establish a necessary condition and a sufficient condition for its validity, where the latter is obtained employing our recently developed adiabatic perturbation theory. Also, we simplify further the sufficient condition into a useful and simple practical test at the expenses of its mathematical rigor. We present results for the most general case of quantum systems, i.e., those with degenerate energy spectra. These conditions are of upmost importance to assess the validity of practical implementations of non-Abelian braiding and adiabatic quantum computation. To illustrate the degenerate adiabatic approximation, and the necessary and sufficient conditions for its validity, we analyze in depth an exactly solvable time-dependent degenerate problem.

quant-ph↗

arXiv2011

Spotlighting quantum critical points via quantum correlations at finite temperatures

We extend the program initiated in [T. Werlang et al., Phys. Rev. Lett. 105, 095702 (2010)] in several directions. Firstly, we investigate how useful quantum correlations, such as entanglement and quantum discord, are in the detection of critical points of quantum phase transitions when the system is at finite temperatures. For that purpose we study several thermalized spin models in the thermodynamic limit, namely, the XXZ model, the XY model, and the Ising model, all of which with an external magnetic field. We compare the ability of quantum discord, entanglement, and some thermodynamic quantities to spotlight the quantum critical points for several different temperatures. Secondly, for some models we go beyond nearest-neighbors and also study the behavior of entanglement and quantum discord for second nearest-neighbors around the critical point at finite temperature. Finally, we furnish a more quantitative description of how good all these quantities are in spotlighting critical points of quantum phase transitions at finite T, bridging the gap between experimental data and those theoretical descriptions solely based on the unattainable absolute zero assumption.

quant-ph↗

arXiv2010

Quantum correlations in spin chains at finite temperatures and quantum phase transitions

We compute the quantum correlation (quantum discord (QD)) and the entanglement (EoF) between nearest neighbor qubits (spin-1/2) in an infinite chain described by the Heisenberg model (XXZ Hamiltonian) at finite temperatures. The chain is in the thermodynamic limit and thermalized with a reservoir at temperature T (canonical ensemble). We show that QD, in contrast to EoF and other thermodynamic quantities, spotlight the critical points associated to quantum phase transitions (QPT) for this model even at finite T. This remarkable property of QD may have important implications for experimental characterization of QPTs when one is unable to reach temperatures below which a QPT can be seen.

quant-ph↗

arXiv2010

Adiabatic Perturbation Theory and Geometric Phases for Degenerate Systems

We introduce an adiabatic perturbation theory for quantum systems with degenerate energy spectra. This perturbative series enables one to rigorously establish conditions for the validity of the adiabatic theorem of quantum mechanics for degenerate systems. The same formalism can be used to find non-adiabatic corrections to the non-Abelian Wilczek-Zee geometric phase. These corrections are relevant to assess the validity of the practical implementation of the concept of fractional exchange statistics. We illustrate the formalism by exactly solving a time-dependent problem and comparing its solution to the perturbative one.

quant-ph↗

arXiv2010

Thermal and Magnetic Quantum Discord in Heisenberg models

We investigate how the quantum correlations (quantum discord) of a two-qubit one dimensional XYZ Heisenberg chain in thermal equilibrium depends on the temperature (T) of the bath and also on an external magnetic field B. We show that the behavior of the thermal quantum discord (QD) differs in many unexpected ways from the thermal entanglement. For example, we show situations where QD increases with T when entanglement decreases, cases where QD increases with T even in regions with zero entanglement, and that QD signals a quantum phase transition even at finite T. We also show that by properly tuning B or the interaction between the qubits we get non-zero QD for any T and we present a new effect not seen for entanglement, the regrowth of thermal QD.

quant-ph↗

arXiv2009

Unity fidelity multiple teleportation using partially entangled states

We show that the recent multiple teleportation protocol (MTP) presented in Ref. [Phys. Rev. Lett. 100, 110503 (2008)] is not restricted to the Knill-Laflamme-Milburn (KLM) scheme. Rather, we show that MTP is quite general and can be implemented using whatever teleportation scheme at hand. We also present two new MTP's which are more efficient than the original proposal, requiring just half the number of teleportations of the original scheme to achieve at least the same probability of success. One of the protocols, however, employs less entanglement than all the previous ones yielding, surprisingly, the greatest probability of success.

quant-ph↗

arXiv2009

Quantum cryptography using partially entangled states

We show that non-maximally entangled states can be used to build a quantum key distribution (QKD) scheme whose security and key rate transmission is nearly equivalent to those of standard QKD protocols. These aspects can be controlled by using the new free parameter in the present scheme, namely, the degree of partial entanglement. Furthermore, we discuss how to build a controlled QKD scheme, also based on partially entangled states, where a third party can decide whether or not Alice and Bob are allowed to share a key.

quant-ph↗

arXiv2009

Beyond the Quantum Adiabatic Approximation: Adiabatic Perturbation Theory

We introduce a perturbative approach to solving the time dependent Schroedinger equation, named adiabatic perturbation theory (APT), whose zeroth order term is the quantum adiabatic approximation. The small parameter in the power series expansion of the time-dependent wave function is the inverse of the time it takes to drive the system's Hamiltonian from the initial to its final form. We review other standard perturbative and non-perturbative ways of going beyond the adiabatic approximation, extending and finding exact relations among them, and also compare the efficiency of those methods against the APT. Most importantly, we determine APT corrections to the Berry phase by use of the Aharonov-Anandan geometric phase. We then solve several time dependent problems allowing us to illustrate that the APT is the only perturbative method that gives the right corrections to the adiabatic approximation. Finally, we propose an experiment to measure the APT corrections to the Berry phase and show, for a particular spin-1/2 problem, that to first order in APT the geometric phase should be two and a half times the (adiabatic) Berry phase.

quant-ph↗