arXiv subjects

Caslav Brukner

Publications and source records attributed to Caslav Brukner.

83 records · Page 5Linked to original sources

arXiv2002

Bell's theorem for general N-qubit states

We derive a single general Bell inequality which is a necessary and sufficient condition for the correlation function for N particles to be describable in a local and realistic picture, for the case in which measurements on each particle can be chosen between two arbitrary dichotomic observables. We also derive a necessary and sufficient condition for an arbitrary N-qubit mixed state to violate this inequality. This condition is a generalization and reformulation of the Horodeccy family condition for two qubits.

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arXiv2002

Do all pure entangled states violate Bell's inequalities for correlation functions?

Any pure entangled state of two particles violates a Bell inequality for two-particle correlation functions (Gisin's theorem). We show that there exist pure entangled N>2 qubit states that do not violate any Bell inequality for N particle correlation functions for experiments involving two dichotomic observables per local measuring station. We also find that Mermin-Ardehali-Belinskii-Klyshko inequalities may not always be optimal for refutation of local realistic description.

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arXiv2002

Quantum communication complexity protocol with two entangled qutrits

We formulate a two-party communication complexity problem and present its quantum solution that exploits the entanglement between two qutrits. We prove that for a broad class of protocols the entangled state can enhance the efficiency of solving the problem in the quantum protocol over any classical one if and only if the state violates Bell's inequality for two qutrits.

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arXiv2002

Young's experiment and the finiteness of information

Young's experiment is the quintessential quantum experiment. It is argued here that quantum interference is a consequence of the finiteness of information. The observer has the choice whether that information manifests itself as path information or in the interference pattern or in both partially to the extent defined by the finiteness of information.

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arXiv2002

Mutually unbiased binary observable sets on N qubits

The Pauli operators (tensor products of Pauli matrices) provide a complete basis of operators on the Hilbert space of N qubits. We prove that the set of 4^N-1 Pauli operators may be partitioned into 2^N+1 distinct subsets, each consisting of 2^N-1 internally commuting observables. Furthermore, each such partitioning defines a unique choice of 2^N+1 mutually unbiased basis sets in the N-qubit Hilbert space. Examples for 2 and 3 qubit systems are discussed with emphasis on the nature and amount of entanglement that occurs within these basis sets.

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arXiv2002

Conceptual Inadequacy of the Shannon Information in Quantum Measurements

In a classical measurement the Shannon information is a natural measure of our ignorance about properties of a system. There, observation removes that ignorance in revealing properties of the system which can be considered to preexist prior to and independent of observation. Because of the completely different root of a quantum measurement as compared to a classical measurement conceptual difficulties arise when we try to define the information gain in a quantum measurement using the notion of Shannon information. The reason is that, in contrast to classical measurement, quantum measurement, with very few exceptions, cannot be claimed to reveal a property of the individual quantum system existing before the measurement is performed.

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arXiv2001

The essence of entanglement

Entanglement, according to Erwin Schroedinger the essence of quantum mechanics, is at the heart of the Einstein-Podolsky-Rosen paradox and of the so called quantum-nonlocality - the fact that a local realistic explanation of quantum mechanics is not possible as quantitatively expressed by violation of Bell's inequalities. Even as entanglement gains increasing importance in most quantum information processing protocols, its conceptual foundation is still widely debated. Among the open questions are: What is the conceptual meaning of quantum entanglement? What are the most general constraints imposed by local realism? Which general quantum states violate these constraints? Developing Schroedinger's ideas in an information-theoretic context we suggest that a natural understanding of quantum entanglement results when one accepts (1) that the amount of information per elementary system is finite and (2) that the information in a composite system resides more in the correlations than in properties of individuals. The quantitative formulation of these ideas leads to a rather natural criterion of quantum entanglement. Independently, extending Bell's original ideas, we obtain a single general Bell inequality that summarizes all possible constraints imposed by local realism on the correlations for a multi-particle system. Violation of the general Bell inequality results in an independent general criterion for quantum entanglement. Most importantly, the two criteria agree in essence, though the two approaches are conceptually very different. This concurrence strongly supports the information-theoretic interpretation of quantum entanglement and of quantum physics in general.

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arXiv2001

Hidden-variable theorems for real experiments

It has recently been questioned whether the Kochen-Specker theorem is relevant to real experiments, which by necessity only have finite precision. We give an affirmative answer to this question by showing how to derive hidden-variable theorems that apply to real experiments, so that non-contextual hidden variables can indeed be experimentally disproved. The essential point is that for the derivation of hidden-variable theorems one does not have to know which observables are really measured by the apparatus. Predictions can be derived for observables that are defined in an entirely operational way.

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arXiv2000

Feasible Entanglement Purification for Quantum Communication

The distribution of entangled states between distant locations will be essential for the future large scale realization of quantum communication schemes such as quantum cryptography and quantum teleportation. Because of the unavoidable noise in the quantum communication channel, the entanglement between two particles is more and more degraded the further they propagate. Entanglement purification is thus essential to distill highly entangled states from less entangled ones. Existing general purification protocols are based on the quantum controlled-NOT (CNOT) or similar quantum logic operations, which are very difficult to implement experimentally. Present realizations of CNOT gates are much too imperfect to be useful for long-distance quantum communication. Here we present a feasible scheme for the entanglement purification of general mixed entangled states, which does not require any CNOT operations, but only simple linear optical elements. Since the perfection of such elements is very high, the local operations necessary for purification can be performed with the required precision. Our procedure is within the reach of current technology and should significantly simplify the implementation of long-distance quantum communication.

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arXiv2000

Quantum Measurement and Shannon Information, A Reply to M. J. W. Hall

Motivated by Hall's recent comment in quant-ph/0007116 we point out in some detail the essence of our reasoning why we believe that Shannon's information is not an adequate choice when defining the information gain in quantum measurements as opposed to classical observations.

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arXiv2000

Operationally Invariant Information in Quantum Measurements

A new measure of information in quantum mechanics is proposed which takes into account that for quantum systems the only feature known before an experiment is performed are the probabilities for various events to occur. The sum of the individual measures of information for mutually complementary observations is invariant under the choice of the particular set of complementary observations and conserved if there is no information exchange with an environment. That operational quantum information invariant results in N bits of information for a system consisting of N qubits.

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