Gelo Noel Tabia

Post-Quantum Security of the CBC, CFB, OFB, CTR, and XTS Modes of Operation

We examine the IND-qCPA security of the wide-spread block cipher modes of operation CBC, CFB, OFB, CTR, and XTS i.e., security against quantum adversaries doing queries in superposition. We show that OFB and CTR are secure assuming that the underlying block cipher is a standard secure PRF a pseudorandom function secure under classical queries. We give counterexamples that show that CBC, CFB, and XTS are not secure under the same assumption. And we give proofs that CBC and CFB mode are secure if we assume a quantum secure PRF secure under queries in superposition.

Experimental scheme for qubit and qutrit symmetric informationally complete positive operator-valued measurements using multiport devices

It is crucial for various quantum information processing tasks that the state of a quantum system can be determined reliably and efficiently from general quantum measurements. One important class of measurements for this purpose is symmetric informationally complete positive operator-valued measurements (SIC-POVMs). SIC-POVMs have the advantage of providing an unbiased estimator for the quantum state with the minimal number of outcomes needed for full tomography. By virtue of Naimarks dilation theorem, any POVM can always be realized with a suitable coupling between the system and an auxiliary system and by performing a projective measurement on the joint system. In practice, finding the appropriate coupling is rather non-trivial. Here we propose an experimental design for directly implementing SIC-POVMs using multiport devices and path-encoded qubits and qutrits, the utility of which has recently been demonstrated by several experimental groups around the world. Furthermore, we describe how these multiports can be attained in practice with an integrated photonic system composed of nested linear optical elements.

Exploring the geometry of qutrit state space using symmetric informationally complete probabilities

We examine the geometric structure of qutrit state space by identifying the outcome probabilities of symmetric informationally complete (SIC) measurements with quantum states. We categorize the infinitely many qutrit SICs into eight SIC families corresponding to independent orbits of the extended Clifford group. Every SIC can be uniquely identified from a set of geometric invariants that we use to establish several properties of the convex body of qutrits, which include a simple formula describing its extreme points, an expression for the rotation between the probability vectors for distinct qutrit SICs, and a polar equation for its boundary states.

Universality in an information-theoretic motivated nonlinear Schrodinger equation

Using perturbative methods, we analyse a nonlinear generalization of Schrodingers equation that had previously been obtained through information-theoretic arguments. We obtain analytical expressions for the leading correction, in terms of the nonlinearity scale, to the energy eigenvalues of the linear Schrodinger equation in the presence of an external potential and observe some generic features. In one space dimension these are (i) for nodeless ground states, the energy shifts are subleading in the nonlinearity parameter compared to the shifts for the excited states; (ii) the shifts for the excited states are due predominantly to contribution from the nodes of the unperturbed wavefunctions, and (iii) the energy shifts for excited states are positive for small values of a regulating parameter and negative at large values, vanishing at a universal critical value that is not manifest in the equation. Some of these features hold true for higher dimensional problems. We also study two exactly solved nonlinear Schrodinger equations so as to contrast our observations. Finally, we comment on the possible significance of our results if the nonlinearity is physically realized.Using perturbative methods, we analyse a nonlinear generalisation of Schrodingers equation that had previously been obtained through information-theoretic arguments. We obtain analytical expressions for the leading correction, in terms of the nonlinearity scale, to the energy eigenvalues of the linear Schrodinger equation in the presence of an external potential and observe some generic features. In one space dimension these are: (i) For nodeless ground states, the energy shifts are subleading in the nonlinearity parameter compared to the shifts for the excited states, (ii) the shifts for the excited states are due predominantly to contribution from the nodes of the unperturbed wavefunctions and (iii) the energy shifts for excited states are positive for small values of a regulating parameter and negative at large values, vanishing at a universal critical value that is not manifest in the equation. Some of these features hold true for higher dimensional problems. We also study two exactly solved nonlinear Schrodinger equations so as to contrast our observations. Finally, we comment on the possible significance of our results if the nonlinearity is physically realised.

Symmetric construction of reference-frame-free qudits

Department of Physics, National University of Singapore, Singapore 117542, Singapore(Dated: 15 August 2008)By exploiting a symmetric scheme for coupling N spin-1/2 constituents (the physical qubits) tostates with total angular momentum N/2 − 1, we construct rotationally invariant logical qudits ofdimension d = N − 1. One can encode all qudit states, and realize all qudit measurements, bythis construction. The rotational invariance of all relevant objects enables one to transmit quantuminformation without having aligned reference frames between the parties that exchange the qudits.We illustrate the method by explicit constructions of reference-frame-free qubits and qutrits and,for the qubit case, comment on possible experimental implementations.

Recursive multiport schemes for implementing quantum algorithms with photonic integrated circuits

We present recursive multiport schemes for implementing quantum Fourier transforms and the inversion step in Grovers algorithm on an integrated linear optics device. In particular, each scheme shows how to execute a quantum operation on

Quantum Collision-Resistance of Non-uniformly Distributed Functions

2d

Efficient quantum key distribution with trines of reference-frame-free qubits

modes using a pair of circuits for the same operation on

Geometry of Quantum States from Symmetric Informationally Complete Probabilities

d

On Quantum Indifferentiability.

modes. The circuits operate on path-encoded qudits and realize