“Werner state”的意思、由来-开放百科全书

词条

Werner state

释义

Multipartite Werner states
References

A Werner state^[1] is a {{nowrap|d × d}}-dimensional bipartite quantum state density matrix that is invariant under all unitary operators of the form . That is, it is a quantum state ρ that satisfies

for all unitary operators U acting on d-dimensional Hilbert space.

Every Werner state is a mixture of projectors onto the symmetric and antisymmetric subspaces, with the relative weight p_sym being the only parameter that defines the state.

where

are the projectors and

is the permutation operator that exchanges the two subsystems.

Werner states are separable for p_sym ≥ {{frac|1|2}} and entangled for p_sym < {{frac|1|2}}. All entangled Werner states violate the PPT separability criterion, but for d ≥ 3 no Werner state violates the weaker reduction criterion. Werner states can be parametrized in different ways. One way of writing them is

where the new parameter α varies between −1 and 1 and relates to p_sym as

Multipartite Werner states

Werner states can be generalized to the multipartite case.^[2] An N-party Werner state is a state that is invariant under for any unitary U on a single subsystem. The Werner state is no longer described by a single parameter, but by N! − 1 parameters, and is a linear combination of the N! different permutations on N systems.

References

1. ^{{cite journal |author=Reinhard F. Werner |year=1989 |title=Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model |journal=Physical Review A |volume=40 |issue=8 |pages=4277–4281 |doi=10.1103/PhysRevA.40.4277 |bibcode=1989PhRvA..40.4277W |pmid=9902666}}
2. ^Eggeling et al. (2008)

1 : Quantum mechanics

随便看

开放百科全书收录14589846条英语、德语、日语等多语种百科知识，基本涵盖了大多数领域的百科知识，是一部内容自由、开放的电子版国际百科全书。