Unknown Quantum States: The Quantum de Finetti Representation

@article{Caves2001UnknownQS,
  title={Unknown Quantum States: The Quantum de Finetti Representation},
  author={Carlton M. Caves and Christopher A. Fuchs and R. Schack},
  journal={Journal of Mathematical Physics},
  year={2001},
  volume={43},
  pages={4537-4559}
}
We present an elementary proof of the quantum de Finetti representation theorem, a quantum analog of de Finetti’s classical theorem on exchangeable probability assignments. This contrasts with the original proof of Hudson and Moody [Z. Wahrschein. verw. Geb. 33, 343 (1976)], which relies on advanced mathematics and does not share the same potential for generalization. The classical de Finetti theorem provides an operational definition of the concept of an unknown probability in Bayesian… 

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References

SHOWING 1-10 OF 117 REFERENCES
Quantum gravity as a dissipative deterministic system
It is argued that the so-called holographic principle will obstruct attempts to produce physically realistic models for the unification of general relativity with quantum mechanics, unless
Quorum of observables for universal quantum estimation
Quantum tomography is the process of reconstructing the ensemble average of an arbitrary operator (observable or not, including the density matrix), which may not be directly accessible by feasible
Information-tradeoff relations for finite-strength quantum measurements
In this paper we describe a way to quantify the folkloric notion that quantum measurements bring a disturbance to the system being measured. We consider two observers who initially assign identical
Quantum State Reconstruction From Incomplete Data
Knowing and guessing, these are two essential epistemological pillars in the theory of quantum-mechanical measurement. As formulated quantum mechanics is a statistical theory. In general, a priori
Bell's theorem, quantum theory and conceptions of the universe
On a Theory of the Collapse of the Wave Function.- On the Measurement Problem of Quantum Mechanics.- A New Characteristic of a Quantum System Between Two Measurements - A "Weak Value".- Can the
Analogs of de Finetti's theorem and interpretative problems of quantum mechanics
It is argued that the characterization of the states of an infinite system of indistinguishable particles satisfying Bose-Einstein statistics which follows from the quantum-mechanical analog of de
Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels.
An unknown quantum state \ensuremath{\Vert}\ensuremath{\varphi}〉 can be disassembled into, then later reconstructed from, purely classical information and purely nonclassical Einstein-Podolsky-Rosen
Mathematical Foundations of Quantum Mechanics
Mathematical Foundations of Quantum Mechanics was a revolutionary book that caused a sea change in theoretical physics. Here, John von Neumann, one of the leading mathematicians of the twentieth
The empirical determination of quantum states
A common approach to quantum physics is enshrouded in a jargon which treats state vectors as attributes of physical systems and the concept of state preparation as a filtration scheme wherein a
Error Correcting Codes in Quantum Theory.
  • Steane
  • Physics
    Physical review letters
  • 1996
TLDR
It is shown that a pair of states which are, in a certain sense, “macroscopically different,” can form a superposition in which the interference phase between the two parts is measurable, providing a highly stabilized “Schrodinger cat” state.
...
...