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The Entropy as a State Function01:14

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Consider an arbitrary process that moves between two specific states (A and B) in a cyclic manner. This process is reversible and broken down into smaller parts that each follow a Carnot cycle. A Carnot cycle has two isothermal (constant temperature) processes. During these processes, the ratio of the amount of heat transferred to their respective temperature remains constant. The other two processes in the Carnot cycle are also reversible but adiabatic, which means they occur without any heat...
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Entangled Pure State Transformations via Local Operations Assisted by Finitely Many Rounds of Classical

C Spee1, J I de Vicente2, D Sauerwein1

  • 1Institute for Theoretical Physics, University of Innsbruck, Technikerstraße 21a, A-6020 Innsbruck, Austria.

Physical Review Letters
|February 11, 2017
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Summary
This summary is machine-generated.

For multi-qubit systems (n>3), generic states are rarely reachable using local operations and classical communication (LOCC). Maximally entangled states are generally achievable with LOCC, though some transformations require probabilistic steps.

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Area of Science:

  • Quantum Information Science
  • Quantum Computing
  • Quantum Entanglement

Background:

  • Local Operations and Classical Communication (LOCC) are fundamental tools for manipulating quantum states.
  • Understanding the set of states reachable via LOCC is crucial for quantum information processing.
  • Previous work has focused on bipartite systems, with multipartite scenarios presenting unique challenges.

Purpose of the Study:

  • To characterize generic pure n-qubit states and general pure states of arbitrary dimensions and subsystems.
  • To determine the set of states reachable via a finite number of Local Operations and Classical Communication rounds (LOCC_N).
  • To investigate the role of deterministic versus probabilistic steps in multipartite LOCC protocols.

Main Methods:

  • Analysis of generic pure n-qubit states for n>3.
  • Characterization of state transformations under LOCC_N.
  • Identification of states transformable through deterministic LOCC_N protocols.
  • Comparison of bipartite and multipartite LOCC capabilities.

Main Results:

  • For n>3 qubits, the set of generic states reachable by LOCC_N is of measure zero.
  • The set of maximally entangled states is generically of full measure under LOCC_N.
  • A class of states requiring only deterministic LOCC_N steps was identified.
  • Certain state transformations necessitate probabilistic steps in multipartite LOCC, distinguishing them from bipartite scenarios.

Conclusions:

  • Generic multipartite quantum states are highly fragile and rarely accessible via standard LOCC protocols.
  • Maximally entangled states represent a robust and generally achievable resource in multipartite quantum information tasks.
  • The inherent probabilistic nature of some multipartite transformations highlights fundamental differences compared to bipartite systems.