Searcharxiv⌕ Search

arXiv subjects

M. Baig

Publications and source records attributed to M. Baig.

At least 19 recordsLinked to original sources
arXiv2005

Cold atoms in non-Abelian gauge potentials: From the Hofstadter "moth" to lattice gauge theory

We demonstrate how to create artificial external non-Abelian gauge potentials acting on cold atoms in optical lattices. The method employs $n$ internal states of atoms and laser assisted state sensitive tunneling. Thus, dynamics are communicated by unitary $n\times n$-matrices. By experimental control of the tunneling parameters, the system can be made truly non-Abelian. We show that single particle dynamics in the case of intense U(2) vector potentials lead to a generalized Hofstadter butterfly spectrum which shows a complex ``moth''-like structure. We discuss the possibility to employ non-Abelian interferometry (Aharonov-Bohm effect) and address methods to realize matter dynamics in specific classes of lattice gauge fields.

cond-mat.other↗
arXiv2004

Secrecy content of two-qubit states

We analyze the set of two-qubit states from which a secret key can be extracted by single-copy measurements plus classical processing of the outcomes. We introduce a key distillation protocol and give the corresponding necessary and sufficient condition for positive key extraction. Our results imply that the critical error rate derived by Chau, Phys. Rev. A {\bf 66}, 060302 (2002), for a secure key distribution using the six-state scheme is tight. Remarkably, an optimal eavesdropping attack against this protocol does not require any coherent quantum operation.

quant-ph↗
arXiv2004

Multiple copy 2-state discrimination with individual measurements

We address the problem of non-orthogonal two-state discrimination when multiple copies of the unknown state are available. We give the optimal strategy when only fixed individual measurements are allowed and show that its error probability saturates the collective (lower) bound asymptotically. We also give the optimal strategy when adaptivity of individual von Neumann measurements is allowed (which requires classical communication), and show that the corresponding error probability is exactly equal to the collective one for any number of copies. We show that this strategy can be regarded as Bayesian updating.

quant-ph↗
arXiv2004

Quantum reverse-engineering and reference frame alignment without non-local correlations

Estimation of unknown qubit elementary gates and alignment of reference frames are formally the same problem. Using quantum states made out of $N$ qubits, we show that the theoretical precision limit for both problems, which behaves as $1/N^{2}$, can be asymptotically attained with a covariant protocol that exploits the quantum correlation of internal degrees of freedom instead of the more fragile entanglement between distant parties. This cuts by half the number of qubits needed to achieve the precision of the dense covariant coding protocol.

quant-ph↗
arXiv2004

Entanglement assisted alignment of reference frames using a dense covariant coding

We present a procedure inspired by dense coding, which enables a highly efficient transmission of information of a continuous nature. The procedure requires the sender and the recipient to share a maximally entangled state. We deal with the concrete problem of aligning reference frames or trihedra by means of a quantum system. We find the optimal covariant measurement and compute the corresponding average error, which has a remarkably simple close form. The connection of this procedure with that of estimating unitary transformations on qubits is briefly discussed.

quant-ph↗
arXiv2004

Fixed boundary conditions analysis of the 3d Gonihedric Ising model with $κ=0$

The Gonihedric Ising model is a particular case of the class of models defined by Savvidy and Wegner intended as discrete versions of string theories on cubic lattices. In this paper we perform a high statistics analysis of the phase transition exhibited by the 3d Gonihedric Ising model with $k=0$ in the light of a set of recently stated scaling laws applicable to first order phase transitions with fixed boundary conditions. Even though qualitative evidence was presented in a previous paper to support the existence of a first order phase transition at $k=0$, only now are we capable of pinpointing the transition inverse temperature at $β_c = 0.54757(63)$ and of checking the scaling of standard observables.

cond-mat.stat-mech↗
arXiv2003

Optimal reconstruction of a pure qubit state with local measurements

We analyse the reconstruction of an unknown pure qubit state. We derive the optimal guess that can be inferred from any set of measurements on N identical copies of the system with the fidelity as a figure of merit. We study in detail the estimation process with individual von Neumann measurements and demonstrate that they are very competitive as compared to (complicated) collective measurements. We compute the expressions of the fidelity for large $N$ and show that individual measurement schemes can perform optimally in the asymptotic regime.

quant-ph↗
arXiv2003

Collective vs local measurements in qubit mixed state estimation

We discuss the problem of estimating a general (mixed) qubit state. We give the optimal guess that can be inferred from any given set of measurements. For collective measurements and for a large number $N$ of copies, we show that the error in the estimation goes as 1/N. For local measurements we focus on the simpler case of states lying on the equatorial plane of the Bloch sphere. We show that standard tomographic techniques lead to an error proportional to $1/N^{1/4}$, while with our optimal data processing it is proportional to $1/N^{3/4}$.

quant-ph↗
arXiv2002

Optimal scheme for estimating a pure qubit state via local measurements

We present the optimal scheme for estimating a pure qubit state by means of local measurements on N identical copies. We give explicit examples for low N. For large N, we show that the fidelity saturates the collective measurement bound up to order 1/N. When the signal state lays on a meridian of the Bloch sphere, we show that this can be achieved without classical communication.

quant-ph↗
arXiv2002

Minimal measurements of the gate fidelity of a qudit map

We obtain a simple formula for the average gate fidelity of a linear map acting on qudits. It is given in terms of minimal sets of pure state preparations alone, which may be interesting from the experimental point of view. These preparations can be seen as the outcomes of certain minimal positive operator valued measures. The connection of our results with these generalized measurements is briefly discussed.

quant-ph↗
arXiv2002

Scaling laws for the 2d 8-state Potts model with Fixed Boundary Conditions

We study the effects of frozen boundaries in a Monte Carlo simulation near a first order phase transition. Recent theoretical analysis of the dynamics of first order phase transitions has enabled to state the scaling laws governing the critical regime of the transition. We check these new scaling laws performing a Monte Carlo simulation of the 2d, 8-state spin Potts model. In particular, our results support a pseudo-critical beta finite-size scaling of the form beta(infinity) + a/L + b/L^2, instead of beta(infinity) + c/L^d + d/L^{2d}. Moreover, our value for the latent heat is 0.294(11), which does not coincide with the latent heat analytically derived for the same model if periodic boundary conditions are assumed, which is 0.486358...

hep-lat↗
arXiv2001

Communicating a direction using spin states

The communication of directions using quantum states is a useful laboratory test for some basic facts of quantum information. For a system of spin-1/2 particles there are different quantum states that can encode directions. This information can later be decoded by means of a generalized measurement. In this talk we present the optimal strategies under different assumptions.

quant-ph↗
arXiv2001

Aligning Reference Frames Using Quantum States

We analyze the problem of sending, in a single transmission, the information required to specify an orthogonal trihedron or reference frame through a quantum channel made out of N elementary spins. We analytically obtain the optimal strategy, i.e., the best encoding state and the best measurement. For large N, we show that the average error goes to zero linearly in 1/N. Finally, we discus the construction of finite optimal measurements.

quant-ph↗
arXiv2001

Communication of Spin Directions with Product States and Finite Measurements

Total spin eigenstates can be used to intrinsically encode a direction, which can later be decoded by means of a quantum measurement. We study the optimal strategy that can be adopted if, as is likely in practical applications, only product states of $N$-spins are available. We obtain the asymptotic behaviour of the average fidelity which provides a proof that the optimal states must be entangled. We also give a prescription for constructing finite measurements for general encoding eigenstates.

quant-ph↗
arXiv2000

Optimal encoding and decoding of a spin direction

For a system of N spins 1/2 there are quantum states that can encode a direction in an intrinsic way. Information on this direction can later be decoded by means of a quantum measurement. We present here the optimal encoding and decoding procedure using the fidelity as a figure of merit. We compute the maximal fidelity and prove that it is directly related to the largest zeroes of the Legendre and Jacobi polynomials. We show that this maximal fidelity approaches unity quadratically in 1/N. We also discuss this result in terms of the dimension of the encoding Hilbert space.

quant-ph↗
arXiv2000

Optimal strategies for sending information through a quantum channel

Quantum states can be used to encode the information contained in a direction, i.e., in a unit vector. We present the best encoding procedure when the quantum state is made up of $N$ spins (qubits). We find that the quality of this optimal procedure, which we quantify in terms of the fidelity, depends solely on the dimension of the encoding space. We also investigate the use of spatial rotations on a quantum state, which provide a natural and less demanding encoding. In this case we prove that the fidelity is directly related to the largest zeros of the Legendre and Jacobi polynomials. We also discuss our results in terms of the information gain.

quant-ph↗
arXiv1998

Numerical simulation of random paths with a curvature dependent action

We study an ensemble of closed random paths, embedded in R^3, with a curvature dependent action. Previous analytical results indicate that there is no crumpling transition for any finite value of the curvature coupling. Nevertheless, in a high statistics numerical simulation, we observe two different regimes for the specific heat separated by a rather smooth structure. The analysis of this fact warns us about the difficulties in the interpretation of numerical results obtained in cases where theoretical results are absent and a high statistics simulation is unreachable. This may be the case of random surfaces.

hep-lat↗