scholarly journals Discrimination of POVMs with rank-one effects

2020 ◽  
Vol 19 (12) ◽  
Author(s):  
Aleksandra Krawiec ◽  
Łukasz Pawela ◽  
Zbigniew Puchała
Keyword(s):  
Positive Operator ◽  
Adaptive Scheme ◽  
Explicit Algorithm ◽  
Positive Operator Valued Measures ◽  
Parallel Scheme ◽  
Rank One ◽  
Multiple Shot ◽  
Insight Into

AbstractThe main goal of this work is to provide an insight into the problem of discrimination of positive operator-valued measures with rank-one effects. It is our intention to study multiple-shot discrimination of such measurements, that is the case when we are able to use to unknown measurement a given number of times. Furthermore, we are interested in comparing two possible discrimination schemes: the parallel and adaptive ones. To this end, we construct a pair of symmetric informationally complete positive operator-valued measures which can be perfectly discriminated in a two-shot adaptive scheme but cannot be distinguished in the parallel scheme. On top of this, we provide an explicit algorithm which allows us to find this adaptive scheme.

Two new constructions of approximately symmetric informationally complete positive operator-valued measures

2019 ◽  
Vol 17 (03) ◽  
pp. 1950021
Author(s):  
Gang Wang ◽  
Min-Yao Niu ◽  
Fang-Wei Fu
Keyword(s):  
Positive Operator ◽  
Special Functions ◽  
Basic Research ◽  
Quantum Information Theory ◽  
Character Sums ◽  
Positive Operator Valued Measures ◽  
Inner Products ◽  
Rank One ◽  
State Tomography ◽  
Positive Operator Valued Measure

A symmetric informationally complete positive operator-valued measure (SIC-POVM) is a POVM in [Formula: see text] consisting of [Formula: see text] positive operators of rank one such that all of whose Hermite inner products are equal. SIC-POVMs are important in quantum information theory, which have many applications in quantum state tomography, quantum cryptography and basic research in quantum mechanics. However, it is very difficult to construct SIC-POVMs. Therefore, many scholars have focused on approximately symmetric informationally complete positive operator-valued measures (ASIC-POVMs) for which the Hermite inner products are close to equal. In this paper, two new constructions of ASIC-POVMs are provided by using character sums and some special functions over finite fields.

Optimal quantum measurements for spin-1 and spin-3/2 particles

2001 ◽  
Vol 1 (3) ◽  
pp. 52-61
Author(s):  
P Aravind
Keyword(s):  
Positive Operator ◽  
Pure State ◽  
Quantum Measurements ◽  
Positive Operator Valued Measures ◽  
Unknown State

Positive operator valued measures (POVMs) are presented that allow an unknown pure state of a spin-1 particle to be determined with optimal fidelity when 2 to 5 copies of that state are available. Optimal POVMs are also presented for a spin-3/2 particle when 2 or 3 copies of the unknown state are available. Although these POVMs are optimal they are not always minimal, indicating that there is room for improvement.

scholarly journals Quantum metrology with full and fast quantum control

Quantum ◽  
2017 ◽  
Vol 1 ◽  
pp. 27 ◽  
Author(s):  
Pavel Sekatski ◽  
Michalis Skotiniotis ◽  
Janek Kołodyński ◽  
Wolfgang Dür
Keyword(s):  
Quantum Control ◽  
Frequency Estimation ◽  
Fixed Number ◽  
Constant Factor ◽  
Quantum Limit ◽  
Single Shot ◽  
Standard Quantum Limit ◽  
Parallel Scheme ◽  
Rank One ◽  
Fast Control

We establish general limits on how precise a parameter, e.g. frequency or the strength of a magnetic field, can be estimated with the aid of full and fast quantum control. We consider uncorrelated noisy evolutions of N qubits and show that fast control allows to fully restore the Heisenberg scaling (~1/N^2) for all rank-one Pauli noise except dephasing. For all other types of noise the asymptotic quantum enhancement is unavoidably limited to a constant-factor improvement over the standard quantum limit (~1/N) even when allowing for the full power of fast control. The latter holds both in the single-shot and infinitely-many repetitions scenarios. However, even in this case allowing for fast quantum control helps to increase the improvement factor. Furthermore, for frequency estimation with finite resource we show how a parallel scheme utilizing any fixed number of entangled qubits but no fast quantum control can be outperformed by a simple, easily implementable, sequential scheme which only requires entanglement between one sensing and one auxiliary qubit.

scholarly journals Operational link between mutually unbiased bases and symmetric informationally complete positive operator-valued measures

2013 ◽  
Vol 88 (3) ◽  
Author(s):  
Roberto Beneduci ◽  
Thomas J. Bullock ◽  
Paul Busch ◽  
Claudio Carmeli ◽  
Teiko Heinosaari ◽  
...  
Keyword(s):  
Positive Operator ◽  
Mutually Unbiased Bases ◽  
Positive Operator Valued Measures

scholarly journals Probing qubit by qubit: Properties of the POVM and the information/disturbance tradeoff

2014 ◽  
Vol 12 (02) ◽  
pp. 1461012 ◽  
Author(s):  
Carlo Sparaciari ◽  
Matteo G. A. Paris
Keyword(s):  
Positive Operator ◽  
Projective Measurement ◽  
Matrix Elements ◽  
Positive Operator Valued Measures ◽  
Unitary Coupling ◽  
Probe System ◽  
Initial Preparation ◽  
Free Parameters

We address the class of positive operator-valued measures (POVMs) for qubit systems that are obtained by coupling the signal qubit with a probe qubit and then performing a projective measurement on the sole probe system. These POVMs, which represent the simplest class of qubit POVMs, depends on 3 + 3 + 2 = 8 free parameters describing the initial preparation of the probe qubit, the Cartan representative of the unitary coupling, and the projective measurement at the output, respectively. We analyze in some detail the properties of the POVM matrix elements, and investigate their values for given ranges of the free parameters. We also analyze in detail the tradeoff between information and disturbance for different ranges of the free parameters, showing, among other things, that (i) typical values of the tradeoff are close to optimality and (ii) even using a maximally mixed probe one may achieve optimal tradeoff.

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