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Unknown quantum states: the quantum de Finetti representation
 J. Math. Phys
"... We present an elementary proof of the quantum de Finetti representation theorem, a quantum analogue 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 advanc ..."
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We present an elementary proof of the quantum de Finetti representation theorem, a quantum analogue 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 probability theory, where probabilities are taken to be degrees of belief instead of objective states of nature. The quantum de Finetti theorem, in a closely analogous fashion, deals with exchangeable densityoperator assignments and provides an operational definition of the concept of an “unknown quantum state ” in quantumstate tomography. This result is especially important for informationbased interpretations of quantum mechanics, where quantum states, like probabilities, are taken to be states of knowledge rather than states of nature. We further demonstrate that the theorem fails for real Hilbert spaces and discuss the significance of this point. I.
Is quantum mechanics an island in theoryspace
 Proceedings of the Växjö Conference “Quantum Theory: Reconsideration of Foundations
, 2004
"... This recreational paper investigates what happens if we change quantum mechanics in several ways. The main results are as follows. First, if we replace the 2norm by some other pnorm, then there are no nontrivial normpreserving linear maps. Second, if we relax the demand that norm be preserved, we ..."
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Cited by 11 (5 self)
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This recreational paper investigates what happens if we change quantum mechanics in several ways. The main results are as follows. First, if we replace the 2norm by some other pnorm, then there are no nontrivial normpreserving linear maps. Second, if we relax the demand that norm be preserved, we end up with a
Programmable Quantum Networks with Pure States
, 2008
"... Modern classical computing devices, except of simplest calculators, have von Neumann architecture, i.e., a part of the memory is used for the program and a part for the data. It is likely, that analogues of such architecture are also desirable for the future applications in quantum computing, commun ..."
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Cited by 4 (0 self)
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Modern classical computing devices, except of simplest calculators, have von Neumann architecture, i.e., a part of the memory is used for the program and a part for the data. It is likely, that analogues of such architecture are also desirable for the future applications in quantum computing, communications and control. It is also interesting for the modern theoretical research in the quantum information science and raises challenging questions about an experimental assessment of such a programmable models. Together with some progress in the given direction, such ideas encounter specific problems arising from the very essence of quantum laws. Currently are known two different ways to overcome such problems, sometime denoted as a stochastic and deterministic approach. The presented paper is devoted to the second one, that is also may be called the programmable quantum networks with pure states. In the paper are discussed basic principles and theoretical models that can be used for the design of such nanodevices, e.g., the conditional quantum dynamics, the NielsenChuang “noprogramming theorem, ” the idea of deterministic and stochastic quantum gates arrays. Both programmable quantum networks with finite registers and hybrid models with continuous quantum variables are considered. As a basic model for the universal programmable quantum network with pure states and finite program register is chosen a “ControlShift” quantum processor architecture with three buses introduced in earlier works. It is shown also, that quantum cellular automata approach to the construction of an universal programmable quantum computer often may be considered as the particular case of such design. 1
Black Holes, Qubits and Octonions
, 2008
"... We review the recently established relationships between black hole entropy in string theory and the quantum entanglement of qubits and qutrits in quantum information theory. The first example is provided by the measure of the tripartite entanglement of three qubits (Alice, Bob and Charlie), known a ..."
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Cited by 4 (0 self)
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We review the recently established relationships between black hole entropy in string theory and the quantum entanglement of qubits and qutrits in quantum information theory. The first example is provided by the measure of the tripartite entanglement of three qubits (Alice, Bob and Charlie), known as the 3tangle, and the entropy of the 8charge ST U black hole of N = 2 supergravity, both of which are given by the [SL(2)] 3 invariant hyperdeterminant, a quantity first introduced by Cayley in 1845. Moreover the classification of threequbit entanglements is related to the classification of N = 2 supersymmetric ST U black holes. There are further relationships between the attractor mechanism and local distillation protocols and between supersymmetry and the suppression of bit flip errors. At the microscopic level, the black holes are described by intersecting D3branes whose wrapping around the six compact dimensions T 6 provides the stringtheoretic interpretation of the charges and we associate the threequbit basis vectors, ABC〉 (A, B, C = 0 or 1), with the corresponding 8 wrapping cycles. The black hole/qubit correspondence extends to the 56 charge N = 8 black holes and the tripartite entanglement of seven qubits where the measure is provided by Cartan’s E7 ⊃ [SL(2)] 7 invariant. The qubits are naturally described by the seven vertices ABCDEF G of the Fano plane, which provides the multiplication table of the seven imaginary octonions,
Primitive Nonclassical Structures of the Nqubit Pauli Group
, 2013
"... Several types of nonclassical structures within the Nqubit Pauli group that can be seen as fundamental resources for quantum information processing are presented and discussed. Identity Products (IDs), structures fundamentally related to entanglement, are defined and explored. The KochenSpecker ..."
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Several types of nonclassical structures within the Nqubit Pauli group that can be seen as fundamental resources for quantum information processing are presented and discussed. Identity Products (IDs), structures fundamentally related to entanglement, are defined and explored. The KochenSpecker theorem is proved by particular sets of IDs that we call KS sets. We also present a new theorem that we call the Nqubit KochenSpecker theorem, which is proved by particular sets of IDs that we call NKS sets, and whose utility is that it leads to efficient constructions for KS sets. We define the criticality, or irreducibility, of these structures, and its connection to entanglement. All representative critical IDs for up to N = 4 qubits are presented, and numerous families of critical IDs for arbitrarily large values of N are discussed. The critical IDs for a given N are a finite set of geometric objects that appear to fully characterize the nonclassicality of the Nqubit Pauli group. Methods for constructing critical KS sets and NKS sets from IDs are given, and experimental tests of entanglement, contextuality, and nonlocality are discussed. Possible applications and connections to other work are also discussed