arXiv subjects

Gustavo Rigolin

Publications and source records attributed to Gustavo Rigolin.

48 records · Page 3Linked to original sources

arXiv2009

Complete State Reconstruction of a Two-Mode Gaussian State via Local Operations and Classical Communication

We propose a strictly local quantum tomography protocol for a bipartite system. We show that the joint density matrix of an arbitrary two-mode Gaussian state, entangled or not, is obtained via local operations and classical communication only. In contrast to previous proposals, simultaneous homodyne measurements (HM) on both modes are replaced by local homodyne detections and a set of local projective measurements.

quant-ph↗

arXiv2008

Quantification of Continuous Variable Entanglement with only Two Types of Simple Measurements

Here we propose an experimental set-up in which it is possible to measure the entanglement of a two-mode Gaussian state, be it pure or mixed, using only simple linear optical devices. After a proper unitary manipulation of the two-mode Gaussian state only number and purity measurements of just one of the modes suffice to give us a complete and exact knowledge of the state's entanglement.

quant-ph↗

arXiv2008

Minimal set of local measurements and classical communication for two-mode Gaussian state entanglement quantification

We develop the minimal requirements for the complete entanglement quantification of an arbitrary two-mode bipartite Gaussian state via local measurements and a classical communication channel. The minimal set of measurements is presented as a reconstruction protocol of local covariance matrices and no previous knowledge of the state is required but its Gaussian character. The protocol becomes very simple mostly when dealing with Gaussian states transformed to its standard form, since photocounting/intensity measurements define the whole set of entangled states. In addition, conditioned on some prior information, the protocol is also useful for a complete global state reconstruction.

quant-ph↗

arXiv2008

Symmetry breaking effects upon bipartite and multipartite entanglement in the XY model

We analyze the bipartite and multipartite entanglement for the ground state of the one-dimensional XY model in a transverse magnetic field in the thermodynamical limit. We explicitly take into account the spontaneous symmetry breaking in order to explore the relation between entanglement and quantum phase transitions. As a result we show that while both bipartite and multipartite entanglement can be enhanced by spontaneous symmetry breaking deep into the ferromagnetic phase, only the latter is affected by it in the vicinity of the critical point. This result adds to the evidence that multipartite, and not bipartite, entanglement is the fundamental indicator of long range correlations in quantum phase transitions.

quant-ph↗

arXiv2007

Generalized Quantum Telecloning

We present a generalized telecloning (GTC) protocol where the quantum channel is non-optimally entangled and we study how the fidelity of the telecloned states depends on the entanglement of the channel. We show that one can increase the fidelity of the telecloned states, achieving the optimal value in some situations, by properly choosing the measurement basis at Alice's, albeit turning the protocol to a probabilistic one. We also show how one can convert the GTC protocol to the teleportation protocol via proper unitary operations.

quant-ph↗

arXiv2007

Multipartite Entanglement Signature of Quantum Phase Transitions

We derive a general relation between the non-analyticities of the ground state energy and those of a subclass of the multipartite generalized global entanglement (GGE) measure defined by T. R. de Oliveira et al. [Phys. Rev. A 73, 010305(R) (2006)] for many-particle systems. We show that GGE signals both a critical point location and the order of a quantum phase transition (QPT). We also show that GGE allows us to study the relation between multipartite entanglement and QPTs, suggesting that multipartite but not bipartite entanglement is favored at the critical point. Finally, using GGE we were able, at a second order QPT, to define a diverging entanglement length (EL) in terms of the usual correlation length. We exemplify this with the XY spin-1/2 chain and show that the EL is half the correlation length.

cond-mat.str-el↗

arXiv2006

Quantum channels in random spin chains

We study the entanglement between pairs of qubits in a random antiferromagnetic spin-1/2 chain at zero temperature. We show that some very distant pairs of qubits are highly entangled, being almost pure Bell states. Furthermore, the probability to obtain such spin pairs is proportional to the chain disorder strenght and inversely proportional to the square of their separation.

quant-ph↗

arXiv2006

Operational Classification and Quantification of Multipartite Entangled States

We formalize and extend an operational multipartite entanglement measure introduced by T. R. Oliveira, G. Rigolin, and M. C. de Oliveira, Phys. Rev. A 73, 010305(R) (2006), through the generalization of global entanglement (GE) [D. A. Meyer and N. R. Wallach, J. Math. Phys. 43, 4273 (2002)]. Contrarily to GE the main feature of this measure lies in the fact that we study the mean linear entropy of all possible partitions of a multipartite system. This allows the construction of an operational multipartite entanglement measure which is able to distinguish among different multipartite entangled states that GE failed to discriminate. Furthermore, it is also maximum at the critical point of the Ising chain in a transverse magnetic field, being thus able to detect a quantum phase transition.

quant-ph↗

arXiv2006

Generalized Quantum State Sharing

We present two quantum state sharing protocols where the channels are not maximally entangled states. By properly choosing the measurement basis it is possible to achieve unity fidelity transfer of the state if the parties collaborate. We also show that contrary to the protocols where we have maximally entangled channels these protocols are probabilistic. We then compare the efficiency of both protocols and sketch the generalization of the protocols to N parties.

quant-ph↗

arXiv2006

Generalized Teleportation Protocol

A generalized teleportation protocol (GTP) for N qubits is presented, where the teleportation channels are non-maximally entangled and all the free parameters of the protocol are considered: Alice's measurement basis, her sets of acceptable results, and Bob's unitary operations. The full range of Fidelity (F) of the teleported state and the Probability of Success (P_{suc}) to obtain a given fidelity are achieved by changing these free parameters. A channel efficiency bound is found, where one can determine how to divide it between F and P_{suc}. A one qubit formulation is presented and then expanded to N qubits. A proposed experimental setup that implements the GTP is given using linear optics.

quant-ph↗

arXiv2006

Genuine Multipartite Entanglement in Quantum Phase Transitions

We demonstrate that the Global Entanglement (GE) measure defined by Meyer and Wallach, J. Math. Phys. 43, 4273 (2002), is maximal at the critical point for the Ising chain in a transverse magnetic field. Our analysis is based on the equivalence of GE to the averaged linear entropy, allowing the understanding of multipartite entanglement (ME) features through a generalization of GE for bipartite blocks of qubits. Moreover, in contrast to GE, the proposed ME measure can distinguish three paradigmatic entangled states: $GHZ_{N}$, $W_{N}$, and $EPR^{\otimes N/2}$. As such the generalized measure can detect genuine ME and is maximal at the critical point.

quant-ph↗

arXiv2005

Introduction to Quantum Cryptography

We show in details the four quantum key distribution protocols which initiated the important field of quantum cryptography, using an accessible language for undergraduate students. We begin presenting the BB84 protocol, which uses polarization states of photons in order to transmit cryptographic keys. Thereupon we show the E91 protocol, whose security is based on the use of singlet states to generate a random sequence of bits. We end the paper with the BBM92 and the B92 protocol. These last two protocols can be seen as simplified versions of the first two.

physics.ed-ph↗