A Reversible Theory of Entanglement and its Relation to the Second Law
@article{Brando2010ART, title={A Reversible Theory of Entanglement and its Relation to the Second Law}, author={Fernando G. S. L. Brand{\~a}o and Martin Bodo Plenio}, journal={Communications in Mathematical Physics}, year={2010}, volume={295}, pages={829-851} }
We consider the manipulation of multipartite entangled states in the limit of many copies under quantum operations that asymptotically cannot generate entanglement. In stark contrast to the manipulation of entanglement under local operations and classical communication, the entanglement shared by two or more parties can be reversibly interconverted in this setting. The unique entanglement measure is identified as the regularized relative entropy of entanglement, which is shown to be equal to a…
56 Citations
Entanglement theory and the second law of thermodynamics
- Physics
- 2008
Entanglement is central both to the foundations of quantum theory and, as a novel resource, to quantum information science. The theory of entanglement establishes basic laws that govern its…
No second law of entanglement manipulation after all
- Physics
- 2021
We prove that the theory of entanglement manipulation is asymptotically irreversible under all non-entangling operations, showing from first principles that reversible entanglement transformations…
An Extension of Entanglement Measures for Pure States
- PhysicsAnnalen der Physik
- 2020
To quantify the entanglement is one of the most important topics in quantum entanglement theory. An entanglement measure is built from measures for pure states. Conditions when the entanglement…
Relative Entropy and Squashed Entanglement
- Computer Science
- 2014
A monogamy-like inequality involving the relative entropy of entanglement and its one-way LOCC variant is achieved, and a commensurate and faithful lower bound for squashedEntanglement is obtained, in the form of one- way LOCC relative entropy, which gives a strengthening to the strong subadditivity of von Neumann entropy.
Faithful Squashed Entanglement
- Computer Science
- 2011
This paper presents a lower bound for squashed entanglement in terms of a distance to the set of separable states, and shows that multiple provers are not more powerful than a single prover when the verifier is restricted to LOCC operations thereby providing a new characterisation of the complexity class QMA.
Resource Theory of Entanglement with a Unique Multipartite Maximally Entangled State.
- PhysicsPhysical review letters
- 2019
It is proved that the resource theory of GME that is formulated here has a unique maximally entangled state, the generalized GHZ state, which can be transformed to any other state by the allowed free operations.
Semidefinite optimization for quantum information
- Computer Science
- 2018
A framework of semidefinite programs to evaluate the classical and quantum communication capabilities of quantum channels in both the non-asymptotic and asymptotic regimes is developed and the first general SDP strong converse bound on the classical capacity of an arbitrary quantum channel is established.
Entanglement Theory and the Quantum Simulation of Many-Body Physics
- Physics
- 2008
In this thesis we present new results relevant to two important problems in quantum information science: the development of a theory of entanglement and the exploration of the use of controlled…
Second Law of Entanglement Dynamics for the Non-Asymptotic Regime
- Physics2021 IEEE Information Theory Workshop (ITW)
- 2021
A refined second law ofEntanglement dynamics that holds for the non-asymptotic regime of entanglement manipulation is established.
Entanglement manipulation and distillability beyond LOCC
- Physics
- 2017
When a quantum system is distributed to spatially separated parties, it is natural to consider how the system evolves when the parties perform local quantum operations with classical communication…
References
SHOWING 1-10 OF 54 REFERENCES
Entanglement theory and the second law of thermodynamics
- Physics
- 2008
Entanglement is central both to the foundations of quantum theory and, as a novel resource, to quantum information science. The theory of entanglement establishes basic laws that govern its…
Quantifying entanglement with witness operators
- Computer Science
- 2005
An infinite family of new entanglement quantifiers is introduced, having as its limits the best separable approximation measure and the generalized robustness, and provides sharper bounds to d_(min) and E_D than the negativity in most the states.
Entanglement and thermodynamical analogies
- Physics, Computer Science
- 1998
A scheme of the search of representative state for given entanglement which can be viewed as an analogue of the Jaynes maximum entropy principle is proposed and proposes a concept of local orthogonality of ensembles which leads to the mixed states with distillableEntanglement equal to entanglements of formation.
Robustness of entanglement
- Physics
- 1999
In the quest to completely describe entanglement in the general case of a finite number of parties sharing a physical system of finite-dimensional Hilbert space an entanglement magnitude is…
Entanglement measures and purification procedures
- Physics, Computer Science
- 1998
It is argued that the statistical basis of the measure of entanglement determines an upper bound to the number of singlets that can be obtained by any purification procedure.
Entanglement purification via separable superoperators
- Computer Science, Physics
- 1997
This work uses the fact that every EPP is a separable superoperator to give a new upper bound on the rate of EPPs on Bell- diagonal states, and thus on the capacity of Bell-diagonal channels.
Max- Relative Entropy of Entanglement, alias Log Robustness
- Computer Science, Physics
- 2008
Properties of the max-relative entropy of entanglement, defined in Ref. 10, are investigated, and its significance as an upper bound to the one-shot rate for perfect entanglement dilution, under a…
Teleportation, entanglement and thermodynamics in the quantum world
- Physics
- 1998
Quantum mechanics has many counter-intuitive consequences which contradict our intuition which is based on classical physics. Here we discuss a special aspect of quantum mechanics, namely the…
Concentrating partial entanglement by local operations.
- PhysicsPhysical review. A, Atomic, molecular, and optical physics
- 1996
Any pure or mixed entangled state of two systems can be produced by two classically communicating separated observers, drawing on a supply of singlets as their sole source of entanglement.
Entanglement measures under symmetry
- Physics, Mathematics
- 2001
We show how to simplify the computation of the entanglement of formation and the relative entropy of entanglement for states, which are invariant under a group of local symmetries. For several…