Related papers: PT-symmetric quantum state discrimination
Experimental determination of an unknown quantum state usually requires several incompatible measurements. However, it is also possible to determine the full quantum state from a single, repeated measurement. For this purpose, the quantum…
The manifold of pure quantum states is a complex projective space endowed with the unitary-invariant geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given…
Parity-Time (PT) symmetric quantum mechanics is a complex extension of conventional Hermitian quantum mechanics in which physical observables possess a real eigenvalue spectrum. However, an experimental demonstration of the true quantum…
It is known that unambiguous discrimination among non-orthogonal but linearly independent quantum states is possible with a certain probability of success. Here, we consider a variant of that problem. Instead of discriminating among all of…
We consider two different optimized measurement strategies for the discrimination of nonorthogonal quantum states. The first is conclusive discrimination with a minimum probability of inferring an erroneous result, and the second is…
We discuss a possibility to build a programmable quantum measurement device (a "quantum multimeter"). That is, a device that would be able to perform various desired generalized, positive operator value measure (POVM) measurements depending…
We consider the task of deciding whether an unknown qubit state falls in a prescribed neighborhood of a reference state. We assume that several copies of the unknown state are given and apply a unitary operation pairwise on them combined…
We investigate the extent to which we can establish whether or not two quantum systems have been prepared in the same state. We investigate the possibility of universal unambiguous state comparison. We show that it is impossible to…
Distinguishing physical processes is one of the fundamental problems in quantum physics. Although distinguishability of quantum preparations and quantum channels have been studied considerably, distinguishability of quantum measurements…
Quantum state filtering is a variant of the unambiguous state discrimination problem: the states are grouped in sets and we want to determine to which particular set a given input state belongs.The simplest case, when the N given states are…
The ability to uniquely identify a quantum state is integral to quantum science, but for non-orthogonal states, quantum mechanics precludes deterministic, error-free discrimination. However, using the non-deterministic protocol of…
During the recent developments of quantum theory it has been clarified that the observable quantities (like energy or position) may be represented by operators (with real spectra) which are manifestly non-Hermitian. The mathematical…
I explore the possibility that a quantum system S may be described completely by the combination of its standard quantum state $|\psi\rangle$ and a (hidden) quantum state $|\phi\rangle$ (that lives in the same Hilbert space), such that the…
The theory of generalised measurements is used to examine the problem of discriminating unambiguously between non-orthogonal pure quantum states. Measurements of this type never give erroneous results, although, in general, there will be a…
Despite their inextricable quantum mechanical nature, events at a high energy particle collider experiment typically have very few unambiguous quantum signatures, due the type of data and the manner in which they are collected. We present a…
The standard approach to quantum measurement discrimination is to perform the given unknown measurement on a probe state, possibly entangled with an auxiliary system, and make a decision based on the measurement outcome obtained. In this…
The physical condition that the expectation values of physical observables are real quantities is used to give a precise formulation of PT-symmetric quantum mechanics. A mathematically rigorous proof is given to establish the physical…
We consider quantum state tomography with measurement procedures of the following type: First, we subject the quantum state we aim to identify to a know time evolution for a desired period of time. Afterwards we perform a measurement with a…
A discrimination problem consists of $N$ linearly independent pure quantum states $\Phi=\{\ket{\phi_i}\}$ and the corresponding occurrence probabilities $\eta=\{\eta_i\}$. To any such problem we associate, up to a permutation over the…
A diagonalizable non-Hermitian Hamiltonian having a real spectrum may be used to define a unitary quantum system, if one modifies the inner product of the Hilbert space properly. We give a comprehensive and essentially self-contained review…