Exact entanglement cost of quantum states and channels under positive-partial-transpose-preserving operations

Xin Wang and Mark M. Wilde
Phys. Rev. A 107, 012429 – Published 26 January 2023

Abstract

This paper establishes single-letter formulas for the exact entanglement cost of simulating quantum channels under free quantum operations that completely preserve positivity of the partial transpose (PPT). First, we introduce the κ-entanglement measure for point-to-point quantum channels, based on the idea of the κ entanglement of bipartite states, and we establish several fundamental properties for it, including amortization collapse, monotonicity under PPT superchannels, additivity, normalization, faithfulness, and nonconvexity. Second, we introduce and solve the exact entanglement cost for simulating quantum channels in both the parallel and sequential settings, along with the assistance of free PPT-preserving operations. In particular, we establish that the entanglement cost in both cases is given by the same single-letter formula, the κ-entanglement measure of a quantum channel. We further show that this cost is equal to the largest κ entanglement that can be shared or generated by the sender and receiver of the channel. This formula is calculable by a semidefinite program, thus allowing for an efficiently computable solution for general quantum channels. Noting that the sequential regime is more powerful than the parallel regime, another notable implication of our result is that both regimes have the same power for exact quantum channel simulation, when PPT superchannels are free. For several basic Gaussian quantum channels, we show that the exact entanglement cost is given by the Holevo-Werner formula [Holevo and Werner, Phys. Rev. A 63, 032312 (2001)], giving an operational meaning of the Holevo-Werner quantity for these channels.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
1 More
  • Received 4 August 2022
  • Accepted 9 January 2023

DOI:https://doi.org/10.1103/PhysRevA.107.012429

©2023 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Xin Wang1,2,* and Mark M. Wilde3,4,†

  • 1Institute for Quantum Computing, Baidu Research, Beijing 100093, China
  • 2Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, Maryland 20742, USA
  • 3Hearne Institute for Theoretical Physics, Department of Physics and Astronomy, Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803, USA
  • 4School of Electrical and Computer Engineering, Cornell University, Ithaca, New York 14850, USA

  • *wangxin73@baidu.com
  • wilde@cornell.edu

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 107, Iss. 1 — January 2023

Reuse & Permissions
Access Options
CHORUS

Article Available via CHORUS

Download Accepted Manuscript
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review A

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×