# Quantum detection and estimation theory

@article{Helstrom1969QuantumDA, title={Quantum detection and estimation theory}, author={Carl W. Helstrom}, journal={Journal of Statistical Physics}, year={1969}, volume={1}, pages={231-252} }

A review. Quantum detection theory is a reformulation, in quantum-mechanical terms, of statistical decision theory as applied to the detection of signals in random noise. Density operators take the place of the probability density functions of conventional statistics. The optimum procedure for choosing between two hypotheses, and an approximate procedure valid at small signal-to-noise ratios and called threshold detection, are presented. Quantum estimation theory seeks best estimators of…

## 2,014 Citations

### Quantum detection of signals in the presence of noise

- Computer ScienceSPIE LASE
- 2003

A discrete approximation to the coherent-state representation of signal-plus-noise density operators is developed, and solutions to optimum receiver performance in terms of quantum "measurement states" whose performance is optimized via generalized rotations in Hilbert space are presented.

### Quantum theory of the homodyne-direct receiver

- Physics
- 1997

Abstract A quantum-communication-theoretical approach to the homodyne-direct receiver is presented and used to obtain the quantum detection operators and average probability of error for any binary…

### Optimizations of quantum measurement processes for signal detection and information transmission in quantum systems

- Physics, Computer Science
- 1996

It is found that the optimum detection process minimizing the average probability of error is minimized and in which the mutual information is maximized are obtained.

### Quantum Detection of Binary and Ternary Signals in the Presence of Thermal Noise Fields

- Computer Science
- 2002

A discrete approximation to the coherent-state representation of signal-plusnoise density operators is developed, and solutions to optimum receiver performance in terms of quantum measurement states whose performance is optimized via generalized rotations in Hilbert space are presented.

### Towards Quantum ɛ—Entropy and Validity of Quantum Information

- Physics
- 1993

The Bayesian method in quantum signal processing was initiated by C W Helstrom and developed in quantum detection [1], estimation [2, 3] and hypothesis testing [4] theory. The aim of this theory was…

### Information and noise in quantum measurement

- Physics
- 2000

Even though measurement results obtained in the real world are generally both noisy and continuous, quantum measurement theory tends to emphasize the ideal limit of perfect precision and quantized…

### Physical Interpretation of Optimum Quantum Detection Operators

- Physics
- 1997

In this paper, it will be clarified why quantum detection theory may predict superior performance in comparison with semi-classical detection theory. The reason is based on the fact that in the…

### Fundamental Quantum Limits to Waveform Detection

- Physics
- 2012

Ever since the inception of gravitational-wave detectors, limits imposed by quantum mechanics to the detection of time-varying signals have been a subject of intense research and debate. Drawing…

### Relationship between optimum quantum detection operators for pure and mixed-state signals

- Computer Science
- 2003

The extent to which the optimum detection operators for pure-state signals can be applied to mixed- state signals is examined.

### On the detectabillity limit of coherent optical signals in thermal radiation

- Physics
- 1970

The problem of detecting a completely known coherent optical signal in a thermal background radiation is considered. The problem is a quantum mechanical analog of detection of a known signal in…

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