Related papers: Quantum Tomography under Prior Information
State of a $d$-dimensional quantum system can only be inferred by performing an informationally complete measurement with $m\geqslant d^2$ outcomes. However, an experimentally accessible measurement can be informationally incomplete. Here…
We consider measurements, described by a positive-operator-valued measure (POVM), whose outcome probabilities determine an arbitrary pure state of a D-dimensional quantum system. We call such a measurement a pure-state informationally…
Quantum state tomography seeks to reconstruct an unknown state from measurement statistics. A finite measurement (POVM) is \emph{pure-state informationally complete} (PSI-Complete) if the outcome probabilities determine any pure state up to…
It has been recently shown that an observable that identifies all pure states of a d-dimensional quantum system has minimally 4d-4 outcomes or slightly less (the exact number depending on the dimension d). However, no simple construction of…
What is the minimal number of elements in a rank-1 positive-operator-valued measure (POVM) which can uniquely determine any pure state in $d$-dimensional Hilbert space $\mathcal{H}_d$? The known result is that the number is no less than…
We consider the problem of quantum-state tomography under the assumption that the state is pure, and more generally that its rank is bounded by a given value. In this scenario, new notions of informationally complete POVMs emerge, which…
We study quantum process tomography given the prior information that the map is a unitary or close to a unitary process. We show that a unitary map on a $d$-level system is completely characterized by a minimal set of $d^2{+}d$ elements…
We analyze quantum state tomography in scenarios where measurements and states are both constrained. States are assumed to live in a semi-algebraic subset of state space and measurements are supposed to be rank-one POVMs, possibly with…
The amount of information that can be accessed via measurement of a quantum system prepared in different states is limited by the Kholevo bound. We present a simple proof of this theorem and its extension to sequential measurements based on…
We introduce informationally complete measurements whose outcomes are entanglement witnesses and so answer the question of how many witnesses need to be measured to decide whether an arbitrary state is entangled or not: as many as the…
Determining the state of a quantum system is a consuming procedure. For this reason, whenever one is interested only in some particular property of a state, it would be desirable to design a measurement setup that reveals this property with…
The number of outcomes is a defining property of a quantum measurement, in particular, if the measurement cannot be decomposed into simpler measurements with fewer outcomes. Importantly, the number of outcomes of a quantum measurement can…
We study informationally overcomplete measurements for quantum state estimation so as to clarify their tomographic significance as compared with minimal informationally complete measurements. We show that informationally overcomplete…
Every sufficiently rich set of measurements on a fixed quantum system defines a statistical norm on the states of that system via the optimal bias that can be achieved in distinguishing the states using measurements from that set (assuming…
We present a framework that formulates the quest for the most efficient quantum state tomography scheme as an optimization problem which can be solved numerically. This approach can be applied to a broad spectrum of relevant setups…
In quantum-state tomography on sources with quantum degrees of freedom of large Hilbert spaces, inference of quantum states of light for instance, a complete characterization of the quantum states for these sources is often not feasible…
We investigate quantum tomography in scenarios where prior information restricts the state space to a smooth manifold of lower dimensionality. By considering stability we provide a general framework that relates the topology of the manifold…
We present an analytical method to estimate pure quantum states using a minimum of three measurement bases in any finite-dimensional Hilbert space. This is optimal as two bases are insufficient to construct an informationally complete…
Quantum state tomography, the ability to deduce the state of a quantum system from measured data, is the gold standard for verification and benchmarking of quantum devices. It has been realized in systems with few components, but for larger…
One of the basic lessons of quantum theory is that one cannot obtain information on an unknown quantum state without disturbing it. Hence, by performing a certain measurement, we limit the other possible measurements that can be effectively…