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Quantum Steering in the Gaussian World
Ioannis Kogias, A. Lee, S. Ragy and G. AdessoUniversity of Nottingham
To appear on arXiv: [quant-ph]
’82: Signalling faster than light? The “no-cloning” theorem.(Wootters & Zurek)
’85: A computing machine that obeys the QM laws was shown to be faster than any classical one. (D. Deutsch) Parallelism Interference
’94: Two enormously important problems were found to be solved efficiently on a quantum machine:
Find prime factors of an integer (RSA) “discrete log” problem
(P. Shor)
’95: Shannon’s information theory was extended to the Quantum domain (B. Schumacher)
Some history . . . Implications
for Black hole information
paradox
Q Cryptography
Q Metrology
Q Communicati
on
Q Channel Superactivation
Super-dense coding
Q Error-
Correcting
Codes
Schemes for fault-tolerant Q Computation
Gravitational waves
Relativistic Q
Information
Exploit Quantum Correlations
What is “Quantum Correlations” ?
• Distant systems A & B
• Non-interacting
• State
• Measure both A & B
𝑃 (𝑎 ,𝑏∨𝐴 ,𝐵; 𝜌 𝐴𝐵 )
The probability of getting is:
Correlation function
Entanglement
Steering
Non-locality
Classes of Q. Correlations
≠∑𝜆
𝑝𝜆 𝑃 (𝑎∨𝐴; 𝜌𝜆 , 𝐴 ) 𝑃 (𝑏∨𝐵 ; 𝜌𝜆 , 𝐵 )
If cannot be expressed as:
≠∑𝜆
𝑝𝜆 𝑃 (𝑎∨𝐴; 𝜆 ) 𝑃 (𝑏∨𝐵; 𝜌𝑖 , 𝐵 )
≠∑𝜆
𝑝𝜆 𝑃 (𝑎∨𝐴; 𝜆 ) 𝑃 (𝑏∨𝐵 ; 𝜆 )
Independent of Hilbert space
Obey Uncertainty
relations
¿𝜑 ⟩= 1
√2( ¿00 ⟩+¿11 ⟩ )
Wherever there is independence from Hilbert space…
…It corresponds to a device-independent entanglement detection.
Steering: 1-side device independence
Nonlocality: Total device independence
Device independent Quantum Cryptography! ! ! !
(A. Acin et al., PRL 98 230501, 2007)
An important gap . . .
Gaussian States
Perfectly manipulated in the lab
х Lack a measure of steerability (Strength)х Detailed study of their steering properties
I. Kogias, A. Lee, S. Ragy and G. Adesso(to appear on arXiv soon)