Related papers: Quantifier elimination theory and maps which prese…
In the Schroedinger formulation of non-Hermitian quantum theories a positive-definite metric operator $\eta\equiv e^{-Q}$ must be introduced in order to ensure their probabilistic interpretation. This operator also gives an equivalent…
Quantum information theory is used to analize various non-linear operations on quantum states. The universal disentanglement machine is shown to be impossible, and partial (negative) results are obtained in the state-dependent case. The…
The example of nonpositive trace-class Hermitian operator for which Robertson-Schroedinger uncertainty relation is fulfilled is presented. The partial scaling criterion of separability of multimode continuous variable system is discussed in…
Medium-scale quantum devices that integrate about hundreds of physical qubits are likely to be developed in the near future. However, such devices will lack the resources for realizing quantum fault tolerance. Therefore, the main challenge…
In quantum computing, the computation is achieved by linear operators in or between Hilbert spaces. In this work, we explore a new computation scheme, in which the linear operators in quantum computing are replaced by (higher) functors…
We propose an operational quasiprobability function for qudits, enabling a comparison between quantum and hidden-variable theories. We show that the quasiprobability function becomes positive semidefinite if consecutive measurement results…
Quantifier elimination over the reals is a central problem in computational real algebraic geometry, polynomial system solving and symbolic computation. Given a semi-algebraic formula (whose atoms are polynomial constraints) with…
The rather unintuitive nature of quantum theory has led numerous people to develop sets of (physically motivated) principles that can be used to derive quantum mechanics from the ground up, in order to better understand where the structure…
Quantum error mitigation is expected to play a crucial role in the practical applications of quantum machines for the foreseeable future. Thus it is important to put the numerous quantum error mitigation schemes proposed under a coherent…
We consider some important computational aspects of the long-step path-following algorithm developed in our previous work and show that a broad class of complicated optimization problems arising in quantum information theory can be solved…
The manipulation of quantum states through linear maps beyond quantum operations has many important applications in various areas of quantum information processing. Current methods simulate unphysical maps by sampling physical operations…
Quantum computing promises the possibility of studying the real-time dynamics of nonperturbative quantum field theories while avoiding the sign problem that obstructs conventional lattice approaches. Current and near-future quantum devices…
Motivated by quantum thermodynamics we first investigate the notion of strict positivity, that is, linear maps which map positive definite states to something positive definite again. We show that strict positivity is decided by the action…
We show that any quantum information theory based on anticommuting operators must be supplemented by a superselection rule deeply rooted in relativity to establish a reasonable notion of entanglement. While quantum information may be…
The elements of a deterministic quantum theory are developed, which reformulates and extends standard quantum theory. The proposed theory is `realistic' in the sense that in it, a general M-level quantum state is represented by a single…
A quasi-Hermitian operator is an operator that is similar to its adjoint in some sense, via a metric operator, i.e., a strictly positive self-adjoint operator. Whereas those metric operators are in general assumed to be bounded, we analyze…
In this thesis, we investigate whether quantum algorithms can be used in the field of machine learning for both long and near term quantum computers. We will first recall the fundamentals of machine learning and quantum computing and then…
The measured relative entropies of quantum states and channels find operational significance in quantum information theory as achievable error rates in hypothesis testing tasks. They are of interest in the near term, as they correspond to…
The interplay between supersymmetry and classical and quantum computation is discussed. First, it is shown that the problem of computing the Witten index of $\mathcal N \leq 2$ quantum mechanical systems is $\#P$-complete and therefore…
We give a direct tensor decomposition for any density matrix into Hermitian operators. Based upon the decomposition we study when the mixed states are separable and generalize the separability indicators to multi-partite states and show…