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Quantum Correlation Measures
Quantum
Entanglement
Information Theoretic
Correlation
Entanglement of Formation Logarithmic Negativity
Entanglement content Peres-Horodecki criterion
Few known
measures
Quantum Correlation Measures
Quantum
Entanglement
Information Theoretic
Correlation
Entanglement of Formation Logarithmic Negativity
Quantum Discord Quantum Work Deficit
Entanglement content Peres-Horodecki criterion
Classical information theory Thermodynamics perspective
Few known
measures
Freezing of Discord and Its Allies
• Initial two qubit state:
• Independent local environments act on each qubit
Freezing of Discord and Its Allies
• Initial two qubit state:
• Independent local environments act on each qubit
• Evolution:
Freezing of Discord and Its Allies
• Initial two qubit state:
• Independent local environments act on each qubit
• Evolution:
• Bit-flip (BF), phase-flip (PF), bit-phase-flip channels
Freezing of Discord and Its Allies
Entanglement usually decays and dies..
Yu & Eberly, Science (2009)
Dynamics under noisy channels: there are several types...
Freezing of Discord and Its Allies
Entanglement usually decays and dies..
Yu & Eberly, Science (2009)
Dynamics under noisy channels: there are several types...
Quantum correlations are robust!
Werlang et. al., PRA (2009)
Freezing of Discord and Its Allies
Entanglement usually decays and dies..
Yu & Eberly, Science (2009)
Dynamics under noisy channels: there are several types...
Quantum correlations are robust!
Werlang et. al., PRA (2009)
Play with the initial state
Maziero et. al., PRA (2009)
Freezing of Discord and Its Allies
Entanglement usually decays and dies..
Yu & Eberly, Science (2009)
Dynamics under noisy channels: there are several types...
Quantum correlations are robust!
Werlang et. al., PRA (2009)
Play with the initial state
Maziero et. al., PRA (2009)
.., and there is freezing!
Mazzola et. al., PRL (2010),
Aaronson et. al., PRA (2013),
Cianciaruso et. al., Sci. Rep. (2015)
Freezing of Discord and Its Allies
Initial state Bell diagonal (BD) state
Two sets of conditions:
1.
2.
Freezing of Discord and Its Allies
Initial state Bell diagonal (BD) state
Two sets of conditions:
1.
2.
Universal for (almost) all the discord-like measures…Aaronson et. al., PRA (2013), Cianciaruso et. al., Sci. Rep. (2015)
Freezing of Discord and Its Allies
BD state + magnetization in x direction:
TC, T Das, D Sadhukhan, A K Pal, A Sen(De), U Sen, PRA (2015)
Freezing of Discord and Its Allies
Universality no longer exists…
One-way quantum work deficit…
Work deficit
Freezing of Discord and Its Allies
Universality no longer exists…
One-way quantum work deficit…
Work deficit Discord
Freezing of Discord and Its Allies
Universality no longer exists…
One-way quantum work deficit…
Work deficit Discord
Different phase diagram
Different set of conditions
Freezing of Discord and Its Allies
Universality no longer exists…
One-way quantum work deficit…
Work deficit Discord
Different phase diagram
Different set of conditions
Freezing of Entanglement
Open evolution:
System
…
…
…
…
……
…
…Door
Environment
𝑇𝐸
𝑇𝑆
𝐻𝐸 = 𝐵𝜎𝑍
Repeated Quantum Interaction
Freezing of Entanglement
Open evolution:
Repeated Quantum Interaction
System
…
…
…
…
……
…
…Door
Environment
𝑇𝐸
𝑇𝑆
𝐻𝐸 = 𝐵𝜎𝑍
Freezing of Entanglement
Open evolution:
Repeated Quantum Interaction
System
…
…
…
…
……
…
…Door
Environment
𝑇𝐸
𝑇𝑆
𝐻𝐸 = 𝐵𝜎𝑍
Freezing of Entanglement
Open evolution:
Repeated Quantum Interaction
System
…
…
…
…
……
…
…Door
Environment
𝑇𝐸
𝑇𝑆
𝐻𝐸 = 𝐵𝜎𝑍
Quantum master equation:
where…
Freezing of Entanglement
System:
TC, T Das, D Sadhukhan, A K Pal, A Sen(De), U Sen, PRA (2016)
1 2 3 4 5
Can be solved “exactly” using successive Jordan-Wigner and
Fourier transformation.
Freezing of Entanglement
Freezing:
PM-II phase
𝜏𝐹(𝑖,𝑖+1)
: Freezing terminal
for spin pair (i,i+1)
Monotonic: 𝜏𝐹(𝑖,𝑖+1)
≥ 𝜏𝐹𝑗,𝑗+1
; 𝑖 > 𝑗
Freezing of Entanglement
Freezing:
PM-II phase
𝜏𝐹(𝑖,𝑖+1)
: Freezing terminal
for spin pair (i,i+1)
Monotonic: 𝜏𝐹(𝑖,𝑖+1)
≥ 𝜏𝐹𝑗,𝑗+1
; 𝑖 > 𝑗
Both in PM-I and PM-II phase
Scale invariance
Freezing of Entanglement
Freezing:
𝜏𝐹(𝑖,𝑖+1)
: Freezing terminal
for spin pair (i,i+1)
XXZ model
XY phase
Alt. fld. XY model
AFM phase
Freezing of Entanglement
Freezing:
𝜏𝐹(𝑖,𝑖+1)
: Freezing terminal
for spin pair (i,i+1)
Non-Monotonic
XXZ model
XY phase
Alt. fld. XY model
AFM phase
Freezing of Entanglement
Freezing:
𝜏𝐹(𝑖,𝑖+1)
: Freezing terminal
for spin pair (i,i+1)
Non-Monotonic
XXZ model
XY phase
Alt. fld. XY model
AFM phase
No scale invariance
Freezing of Entanglement
Freezing:
𝜏𝐹(𝑖,𝑖+1)
: Freezing terminal
for spin pair (i,i+1)
Non-Monotonic
XXZ model
XY phase
Alt. fld. XY model
AFM phase
No scale invariance
QIClib: New general purpose quantum information and
computing library written in C++11
https://titaschanda.github.io/QIClib/
A New Quantum Library
QIClib: New general purpose quantum information and
computing library written in C++11
https://titaschanda.github.io/QIClib/
1. Partial trace, partial transpose etc.
2. Matrix functions
3. Entropic functions
4. Different entanglement measures
5. Schmidt decomposition, purification etc.
6. State of the art random object generators
7. Apply arbitrary (control) quantum gates
8. Pseudo quantum measurements
9. Easily implement quantum circuits
10. Discord type measures
etc.
A New Quantum Library
QIClib: New general purpose quantum information and
computing library written in C++11
https://titaschanda.github.io/QIClib/
1. Partial trace, partial transpose etc.
2. Matrix functions
3. Entropic functions
4. Different entanglement measures
5. Schmidt decomposition, purification etc.
6. State of the art random object generators
7. Apply arbitrary (control) quantum gates
8. Pseudo quantum measurements
9. Easily implement quantum circuits
10. Discord type measures
etc.
A New Quantum Library
QIClib: New general purpose quantum information and
computing library written in C++11
https://titaschanda.github.io/QIClib/
1. Partial trace, partial transpose etc.
2. Matrix functions
3. Entropic functions
4. Different entanglement measures
5. Schmidt decomposition, purification etc.
6. State of the art random object generators
7. Apply arbitrary (control) quantum gates
8. Pseudo quantum measurements
9. Easily implement quantum circuits
10. Discord type measures
etc.
A New Quantum Library
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