Quantum Error Correction for Long-Distance Quantum Communication - - PowerPoint PPT Presentation
Quantum Error Correction for Long-Distance Quantum Communication Institute of Physics, University of Mainz Peter van Loock Quantum Error Correction for Long-Distance Quantum Communication Institute of Physics, University of Mainz Peter van
Institute of Physics, University of Mainz
Institute of Physics, University of Mainz
Ultrafast Long-Distance Quantum Communication Old versus New Quantum Repeaters: QED vs. QEC Photon Loss Codes
Ultrafast Long-Distance Quantum Communication with Linear Optics Old versus New Quantum Repeaters: QED vs. QEC Photon Loss Codes
1.) Original Quantum Repeaters (Briegel et al., DLCZ,…): use entanglement distribution, swapping, purification (loss, local errors) 2.) Quantum repeaters with purification (loss) and QECC (local errors) 3.) Quantum repeaters with QECC only (loss and local errors)
in
in
2
att
in
in
in in
in
in att
in
in
in in PS
PS
succ att
QED
PS
in
in
QED
in
in
QED
….need to detect the qubit non-destructively
BM
Bell measurement detects syndrome and „recovers“ in one step: no loss = 2-photon detection, photon lost =1-photon detection
classical channel
in
BM
classical channel
in
Complications: on-demand generation of local Bell states Bell measurement with unit success probability never beats direct transmission
BM
classical channel
in
att att BM succ
( for any )
distribute known, entangled states distribute different copies in each segment QED/entanglement purification quantum memories two-way classical communication
) 3 / 2 ( log ) / ( log swap distr
swap 2 2
P L L
distr
distr
swap
distr
distr
swap
1 / swap / distr
L L L L
Entanglement Purification (Quantum Error Detection) Entanglement Distribution Entanglement Swapping Quantum Memories
2 2 distr
L.M. Duan, M.D. Lukin, J.I. Cirac, P. Zoller, Nature 414, 413 (2001)
2 2 distr
2
no-loss space
2 2 distr
2
loss space: only QED, not QEC!
distribute known, entangled states distribute different copies in each segment QED/entanglement purification quantum memories two-way classical communication Problems: very slow, limited by CC rates, good memories required
W.J. Munro et al., Nat. Photon. 4, 792 (2010)
implementation-independent HQR with encoding secret key rates in QKD
,
N.K. Bernardes and P.v.L., PRA 86, 052301 (2012)
A.G. Fowler et al., Phys. Rev. Lett. 104, 180503 (2010) W.J. Munro et al., Nature Photon. 6, 777 (2012)
parity loss codes topological surface codes
Leung‘s bosonic code: exact Leung‘s AD code:
approximate
m m m m n n m m m n
) , (
Quantum Parity Code (QPC):
T.C. Ralph, A.J.F. Hayes, and A. Gilchrist., PRL 95, 100501 (2005)
) , ( ) , ( ) , ( ) , ( ) , ( ) , (
m n m n m n m n m n m n
QPC(n,n) corrects (n – 1) photon losses
) 1 , 1 (
QPC(1,1):
) 1 , 1 ( ) 1 , 1 (
QPC(2,2):
) 2 , 2 ( ) 2 , 2 (
(is exact!)
, 1 1 1 ,
j i m j ij j i ij
Quantum Parity Code (QPC):
stabilizers for physical Pauli operators independent stabilizers QPC(2,2):
22 12 21 11 22 21 12 11
like code
) , ( in m n
) , ( m n
BM
) , ( m n
) , ( m n
…replace DR-qubit/Bell states/BM‘s by QPC-encoded qubit/Bell states/BM‘s, use stabilizer formalism and exploit transversality of QPC code as a CSS code
classical channel
) , ( in m n
) , ( m n
BM
) , ( m n
) , ( m n
classical channel
…many physical BM‘s for one logical BM via many physical CNOTs and many physical Hadamards: need nonlinear operations, matter-light interactions,…
) , ( in m n
) , ( m n
BM
) , ( m n
) , ( m n
…replace matter-qubit-based QPC-Bell states by optical QPC-Bell states and nonlinear light-matter interactions by static linear optics
classical channel
) , ( in m n
) , ( m n
BM
) , ( m n
) , ( m n
…replace matter-qubit-based QPC-Bell states by optical QPC-Bell states and nonlinear light-matter interactions by static linear optics
classical channel
, BM succ
l l nm nm l l
att 0 /
) , ( in m n
) , ( m n
BM
) , ( m n
) , ( m n
…replace matter-qubit-based QPC-Bell states by optical QPC-Bell states and nonlinear light-matter interactions by static linear optics
classical channel
What is ? Can we again exploit „transversality“?
l
, BM
BM of QPC(2,2) encoded Bell states:
BM of QPC(2,2) encoded Bell states:
QPC-encoded BM works asymptotically well with linear optics (no loss) and it even still works in the presence of losses !
n l
, BM
succ /
succ