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Asher Peres

Overview

Asher Peres (1934–2005) was an Israeli physicist renowned for his foundational work in quantum mechanics and quantum information theory. He made numerous contributions to the understanding of quantum nonlocality, contextuality, and entanglement, and authored the influential textbook Quantum Theory: Concepts and Methods.

Peres was known for his physical intuition, mathematical elegance, and the clarity of his expositions. His work on Kochen–Specker proofs and the Peres–Mermin square remains central to the study of quantum contextuality.

Key Contributions

The Peres 33-Ray KS Set (3D)

In 1991, Peres published a 33-ray Kochen–Specker set in 3 dimensions—at the time, the smallest known. This work demonstrated that finite KS proofs could be remarkably compact.

The Peres–Mermin Square

Peres and David Mermin (independently) developed the "magic square" proof of quantum contextuality for two-qubit systems. The 3×3 array of observables:

Col 1 Col 2 Col 3
Row 1 \(X \otimes I\) \(I \otimes X\) \(X \otimes X\)
Row 2 \(I \otimes Z\) \(Z \otimes I\) \(Z \otimes Z\)
Row 3 \(X \otimes Z\) \(Z \otimes X\) \(Y \otimes Y\)

Each row and column consists of commuting observables whose product is \(+I\) (except one row/column with product \(-I\)). No noncontextual value assignment satisfies all constraints simultaneously.

This elegant proof became a paradigm for demonstrating contextuality without explicit ray constructions.

Collaboration with Kernaghan

In 1995, Peres collaborated with Michael Kernaghan on a 40-vector KS set in 8 dimensions (three qubits). This construction connected KS proofs to multi-qubit quantum systems and GHZ-type phenomena.

PPT Criterion for Entanglement

Beyond contextuality, Peres is famous for the Peres–Horodecki criterion (PPT criterion): a bipartite state is entangled if its partial transpose has negative eigenvalues. This became a fundamental tool in quantum information theory.

Quantum Teleportation

Peres was a co-author of the original 1993 quantum teleportation paper, one of the foundational results of quantum information science.

Quantum Theory: Concepts and Methods

Peres' 1993 textbook is a classic in quantum foundations, known for:

  • Rigorous yet accessible treatment of quantum mechanics
  • Emphasis on operational and information-theoretic perspectives
  • Coverage of Bell inequalities, contextuality, and quantum information

The book remains widely used and cited.

Philosophy and Approach

Peres was known for his operationalist philosophy: "Quantum phenomena do not occur in a Hilbert space, they occur in a laboratory." He emphasized:

  • Clear operational definitions of quantum concepts
  • Skepticism of overly metaphysical interpretations
  • Focus on what can be measured and observed

His famous aphorism captures this perspective:

"Unperformed experiments have no results."

Key Works

  • A. Peres, "Two simple proofs of the Kochen–Specker theorem," J. Phys. A: Math. Gen. 24, L175 (1991)

  • A. Peres, Quantum Theory: Concepts and Methods, Kluwer Academic Publishers (1993)

  • M. Kernaghan and A. Peres, "Kochen–Specker theorem for eight-dimensional space," Phys. Lett. A 198, 1 (1995)

  • A. Peres, "Separability criterion for density matrices," Phys. Rev. Lett. 77, 1413 (1996)

  • C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, "Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels," Phys. Rev. Lett. 70, 1895 (1993)