Related papers: Towards a resolution of the spin alignment problem
We consider the problem of designing an optimal quantum detector that distinguishes unambiguously between a collection of mixed quantum states. Using arguments of duality in vector space optimization, we derive necessary and sufficient…
A measurement strategy is developed for a new kind of hypothesis testing. It assigns, with minimum probability of error, the state of a quantum system to one or the other of two complementary subsets of a set of N given non-orthogonal…
The existence of a maximally entangled pure state is a cornerstone result of entanglement theory that has paramount consequences in quantum information theory. A natural generalization of this property is to consider whether a notion of…
We present a formula that determines the optimal number of qubits per message that allows asymptotically faithful compression of the quantum information carried by an ensemble of mixed states. The set of mixed states determines a…
We consider the problem of optimally approximating an unavailable quantum state $\rho $ by the convex mixing of states drawn from a set of available states $\{ \nu_i\}$. The problem is recast to look for the least distinguishable state from…
This paper is concerned with a shape optimization problem governed by a non-smooth PDE, i.e., the nonlinearity in the state equation is not necessarily differentiable. We follow the functional variational approach of [40] where the set of…
The heart of the measurement puzzle, namely the problem of definite outcomes, remains unresolved. This paper shows that Josef Jauch's 1968 reduced density operator approach is the solution, even though many question it: The entangled…
A complete set of generalized spin-squeezing inequalities is derived for an ensemble of particles with an arbitrary spin. Our conditions are formulated with the first and second moments of the collective angular momentum coordinates. A…
Given two arbitrary pure states $ |\phi>$ and $ |\psi>$ of qubits or higher level states, we provide arguments in favor of states of the form $ \frac{1}{\sqrt{2}}(|\psi> |\phi> + i |\phi> |\psi>) $ instead of symmetric or anti-symmetric…
We consider the image of some classes of bipartite quantum states under a tensor product of random quantum channels. Depending on natural assumptions that we make on the states, the eigenvalues of their outputs have new properties which we…
The quantum guesswork quantifies the minimum number of queries needed to guess the state of a quantum ensemble if one is allowed to query only one state at a time. Previous approaches to the computation of the guesswork were based on…
This paper is about minimum cost constrained selection of inputs and outputs for generic arbitrary pole placement. The input-output set is constrained in the sense that the set of states that each input can influence and the set of states…
The work is organized in two main topics. At first we will outline the relation between spin squeezing, quantum metrology and entanglement detection, with a particular focus on the last. We will derive spin squeezing criteria for the…
Optimisation problems in science and engineering typically involve finding the ground state (i.e. the minimum energy configuration) of a cost function with respect to many variables. If the variables are corrupted by noise then this…
We extend the notion of estimation entropy of autonomous dynamical systems proposed by Liberzon and Mitra [1] to nonlinear dynamical systems with uncertain inputs with bounded variation. We call this new notion the {$\epsilon$}-estimation…
The optimal state determination (or tomography) is studied for a composite system of two qubits when measurements can be performed on one of the qubits and interactions of the two qubits can be implemented. The goal is to minimize the…
Relaxation and rounding approaches became a standard and extremely versatile tool for constrained submodular function maximization. One of the most common rounding techniques in this context are contention resolution schemes. Such schemes…
The concept of entangled quantum states is considered in the context of systems of identical particles, based on the requirement that in order to represent physical states both for the overall system and the sub-systems which may be…
Predictive inference requires balancing statistical accuracy against informational complexity, yet the choice of complexity measure is usually imposed rather than derived. We treat econometric objects as predictive rules, mappings from…
We propose a new spin squeezing criterion for arbitrary multi-qubit states that is invariant under local unitary operations. We find that, for arbitrary pure two-qubit states, spin squeezing is equivalent to entanglement, and multi-qubit…