| Topic: |
Science > Physics |
| User: |
"cyberdude" |
| Date: |
16 Oct 2003 07:05:09 PM |
| Object: |
What is quantum entanglement? |
Hi,
What is quantum entanglement? Please assume that I only know elementary
quantum physics.
David
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| User: "Nicolaas Vroom" |
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| Title: Re: What is quantum entanglement? |
19 Oct 2003 06:19:56 AM |
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"cyberdude" <quake_earthNOSPAM@hotmail.com> schreef in bericht
news:bmnbnl$gml$1@news.ust.hk...
Hi,
What is quantum entanglement? Please assume that I only know elementary
quantum physics.
IMO if you want to understand entanglement than you also have
to study the concept of superposition and parallelism.
To find an user you can use http://www.google.com/
Two very good documents, which discusses this issue, are in
Nature 20 feb 2003 Volume 421 Issue no 6925.
1. "The qubit duet" by G. Blatter page 797
2. "Quantum oscillations in two coupled charge qubits" page 823.
The first article explains:
Superposition is a "one particle" property
Entanglement is a chracteristic of two or more particles.
Parallelism is important if you want to calculate
"a table of multiplication" using quantum mechanics.
Suppose you want to calculate:
0*5, 1*5, 2*5, 3*5, 4*5, 5*5, 6*5 and 7*5
The answer is 0,5,10,15,20,25,30 and 35
To implement this you get someting in the order of:
H * 5 = R1
H is the Hadamard operation performed on 3 Qubits.
The Hadamard operation represents the numbers
0,1,2,3,4,5,6 and 7 in an entangled state.
The number 5 is a constant and requires also 3 Qubits.
R1 is the output register consisting of 6 Qubits
which contains the answers also in an entangled state.
* represents a multiplication operation.
This operation is performed with unitary logic.
In fact this operation is the most difficult part because
it uses the concept of parallelism.
Parallelism implies that more than one multiply operations
are performed in parallel i.e. at the same time.
I doubt that this is the case.
The first document also mentions the word:
"deterministic entanglement"
This means that the two constituents (qubits) must
interact in a controlled manner.
I think in order to perform "valid" quantum computations
they always must include deterministic entanglement.
As I mentioned before you also have to study superposition.
The concept of superposition is part of the
Schrodinger cat thought experiment.
(See more in recent thread Entanglement in sci.physics.research)
In this experiment there are three events.
1. The release of a "photon" or alpha particle
by a radio active particle.
2. The capture of this particle. This is the moment of the release
of the poisonuous gas and the Cat dies.
3. Observation of the experiment by one or more Observers.
Events 1 and 2 are closely linked. Event 2 is always after Event 1
and is almost simultaneous with event 1.
Event 3 can before or after event 2.
Before event 3 the state of the cat is in a superposition
of both being alive and dead.
IMO event 3 completely takes place in the mind or brain of
each observer.
IMO Schrodinger cat type superposition can not be used
to perform any type of quantum computation.
Nicolaas Vroom
David
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| User: "Laurel Amberdine" |
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| Title: Re: What is quantum entanglement? |
17 Oct 2003 12:20:24 AM |
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On Fri, 17 Oct 2003 00:05:09 +0000 (UTC), cyberdude <quake_earthNOSPAM@hotmail.com> wrote:
Hi,
What is quantum entanglement? Please assume that I only know elementary
quantum physics.
Hmm. I attempted to explain this to someone a couple weeks ago. You
might try searching google groups for the subject "Enganglement and
Quantum Computers".
(I'd actually offer my explanation of entanglement but doing that last
time made me feel ill. I'm not at all qualified to explain these things,
but no one else was doing it.)
If you have any more questions after reading the previous messages, I can
try to clarify.
--
- Laurel * * * http://amberdine.com
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| User: "ghytrfvbnmju7654" |
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| Title: Re: What is quantum entanglement? |
17 Oct 2003 06:10:48 PM |
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cyberdude <quake_earthNOSPAM@hotmail.com> wrote in message news:<bmnbnl$gml$1@news.ust.hk>...
Hi,
What is quantum entanglement? Please assume that I only know elementary
quantum physics.
David
A state is said to be entangled if the result of a
measurement on one object affects the probabilities
of the results of measurements on the other object.
For example, suppose we have two two-state objects,
A and B. We'll call their possible states 0 and 1.
..6|A1,B1> + .8|A2,B2>
would be an example of an entangled state. Suppose
we measure A, and it turns out to be 1. Then we
are left with the state:
|A1,B1>
So we would know that B is also 1. But if A had
been 2, we would have been known B was 2.
On the other hand,
pr|A1,B1> + ps|A1,B2> + qr|A2,B1> + qs|A2,B2>
(where p, q, r, & s are arbitrary complex numbers)
is not entangled.
Disclaimer: I am a only a student. Errors may be
present. For the most reliable information, I
recommend the nearest college library.
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| User: "Alfred Einstead" |
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| Title: Re: What is quantum entanglement? |
24 Oct 2003 03:14:07 AM |
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cyberdude <quake_earthNOSPAM@hotmail.com> wrote:
What is quantum entanglement?
It's a property that pertains to physics systems that are composed
of two or more parts.
Please assume that I only know elementary quantum physics.
That's fine, since it's not a quantum question at all, but a question
about the properties of states and state spaces -- which is generic
to all physics. You can also meaningfully ask whether and how it's
present in classical physics, as well; and the definition is
exactly the same in all contexts.
However, the answer is no. It's something that's absent in
classical physics.
In classical physics, if a system A+B were in a pure state, then
the "relative state" of A and B would each also be pure.
A and B can never be entangled when A+B is pure.
In quantum mechanics, if A+B is in a pure state, then the relative
states of A and B will each be mixed when A & B are entangled.
(Note the use of subjunctive in the classical case).
For reference, a mixed state is a mixture or two or more pure
states; e.g. (a discrete mixture) W = p W1 + q W2, W1, W2 pure
states; p+q = 1; p,q > 0; or e.g. (a continuous mixture)
W = integral W_k p_k dk; with p_k >= 0; integral p_k dk = 1,
all the W_k's pure states.
The best way of thinking of them is that "pure state" means
"single system", or "single world" if pertaining to the entire
system, and "mixed state" means "mixture of several
systems in parallel", or more simply "ensemble" (and best
captures the concept of "multiple worlds", if pertaining
to the system as a whole -- but note the presumption above
of the overall system A+B being in a pure state).
States in classical physics are always mixed. Pure states
wouldn't be physically realizable even if classical physics
were valid (and their inaccessibility is, in fact, the main
reason why classical physics can't be valid).
Finally, is the question of what a relative state is.
Classically, if system A has (pure) states W1,W2; system B has
(pure) states W3,W4; the combined system A+B has (pure) states
W1,W3; W1,W4; W2,W3; W2,W4. Suppose A+B is in the state
W = p W1,W3 + q W1,W4 + r W2,W3 + s W2,W4
p + q + r + s = 1; p, q, r, s >= 0
The relative states of A and B are respectively:
W_A = (p+q) W1 + (r+s) W2,
W_B = (p+r) W3 + (q+s) W4.
The process of adding up over system B to get the respective
parts of W_A is referred to as "tracing over B"; likewise for
"tracing over A" to get W_B.
If W had been a pure state, that would mean only one of the p,q,r,s
would be 1, and the others 0. Then, it would follow that one of the
p+q or r+s would be 1, the other 0, so that W_A would be pure too;
likewise for W_B.
For a quantum system, things are more complex. The simplest
state space is that [a qubit] given by a family of the form:
A: (W_A(u,v,w): u^2+v^2+w^2=1).
Suppose system A has these as its pure states, and that system
B has a similar state space:
B: (W_B(x,y,z): x^2+y^2+z^2=1).
Then the state space for the combined system is not just the
juxtaposition of the two:
(W_A(u,v,w),W_B(x,y,z): u^2+v^2+w^2=1=x^2+y^2+z^2)
but something much larger:
A+B: (W(m,n,p,q,r,s,t): m^2+n^2+p^2+q^2+r^2+s^2+t^2=1).
The extra space is occupied by the entangled states.
The unentangled states are those formed as:
W_A(u,v,w),W_B(x,y,z) --> W(ux,uy,uz,vx,wx,vy-wz,vz+wy).
Tracing W(m,n,p,q,r,s,t) over B creates a mixed state of the
form:
(1/2 + z) W_A(u1,v1,w1) + (1/2 - z) W_A(u2,v2,w2)
for some |z| <= 1/2, and u1,v1,w1; u2,v2,w2, all rather complex
expressions in terms of m,n,p,q,r,s,t; which I'm not inclined
to work out here. The only time you'll get purity (z = +1/2
or -1/2) is when the state arises from the W_A,W_B combination
of the form above. Thus, the result of tracing
W(ux,uy,uz,vx,wx,vy-wz,vz+wy)
over B is
W_A(u,v,w);
and the result of tracing over A is
W_B(x,y,z).
Descriptions get a lot simpler when (pure) states are represented
as Hilbert space vectors -- amd this is where the stuff that
pertains specifically to quantum physics appears.
The state corresponding to W_A(u,v,w) is just something of the form:
u |b> + (v+iw) |p>;
that corresponding to W_B(x,y,z) is something of the form:
x |d> + (y+iz) |q>;
and that corresponding to W(m,n,p,q,r,s,t) is of the form:
m |bd> + (n+ip) |bq> + (q+ir) |pd> + (s+it) |pq>.
The unentangled states are
W(ux,uy,uz,vx,wx,vy-wz,vz+wy)
= ux |bd> + u(y+iz) |bq> + (v+iw)x |pd> + (v+iw)(y+iz) |pq>
= (u |b> + (v+iw) |p>) (x |d> + (y+iz) |q>)
= W_A(u,v,w) W_B(x,y,z).
The state corresponding to the vector u|b>+(v+iw)|p> is
u^2 |b><b| + (uv+iuw)|b><p| + (uv-iuw)|p><b| + (v^2+w^2)|p><p|.
A general mixed state has the form
P |b><b| + (R+iS) |b><p| + (R-iS) |p><b| + Q |p><p|
P + Q = 1, PQ - 1/4 <= R^2 + S^2 <= PQ.
This is a mixture of two vector states, with mixing coefficients
1/2 +/- sqrt(1/4+R^2+S^2-PQ).
The state corresponding to the vector for W(m,n,p,q,r,s,t) is
m^2 |bd><bd|
+ (mn+imp)|bq><bd| + (mn-imp)|bd><bq|
+ (mq+imr)|pd><bd| + (mq-imr)|bd><pd|
+ (ms+imt)|pq><bd| + (ms-imt)|bd><pq|
+ (n^2+p^2)|bq><bq| + (q^2+r^2)|pd><pd| + (s^2+t^2)|pq><pq|
+ ((nq+pr)+i(nr-pq))|pd><bq| + ((nq+pr)+i(pq-nr))|bq><pd|
+ ((ns+pt)+i(nt-ps))|pq><bq| + ((ns+pt)+i(ps-nt))|bq><pq|
+ ((qs+rt)+i(qt-rs))|pq><pd| + ((qs+rt)+i(rs-qt))|pd><pq|.
Tracing over B yields the mixed state:
(m^2+n^2+p^2)|b><b|
+ ((mq+ns+pt)+i(mr+nt-ps))|p><b|
+ ((mq+ns+pt)-i(mr+nt-ps))|b><p|
+ (q^2+r^2+s^2+t^2)|p><p|
Tracing over A yields the mixed state:
(m^2+q^2+r^2)|d><d|
+ ((mn+qs+rt)+i(mp+qt-rs))|q><d|
+ ((mn+qs+rt)-i(mp+qt-rs))|d><q|
+ (n^2+p^2+s^2+t^2)|q><q|.
If you compute the corresponding mixing ratios in the first
case, you'll find they're between 0 and 1 in general, showing
that this is indeed a mixed state.
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| User: "Nicolaas Vroom" |
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| Title: Re: What is quantum entanglement? |
24 Oct 2003 09:41:37 AM |
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"Alfred Einstead" <whopkins@csd.uwm.edu> schreef in bericht
news:e58d56ae.0310240014.29462040@posting.google.com...
cyberdude <quake_earthNOSPAM@hotmail.com> wrote:
What is quantum entanglement?
It's a property that pertains to physics systems that are composed
of two or more parts.
Please assume that I only know elementary quantum physics.
That's fine, since it's not a quantum question at all, but a question
about the properties of states and state spaces -- which is generic
to all physics. You can also meaningfully ask whether and how it's
present in classical physics, as well; and the definition is
exactly the same in all contexts.
However, the answer is no. It's something that's absent in
classical physics.
In classical physics, if a system A+B were in a pure state, then
the "relative state" of A and B would each also be pure.
A and B can never be entangled when A+B is pure.
In quantum mechanics, if A+B is in a pure state, then the relative
states of A and B will each be mixed when A & B are entangled.
1. Why do you make a distinction between classical physics (cp)
and quantum mechanics (qm) ?
I expect that your answer is that quantum mechanics
describes the behaviour of photons and elementary particles.
2. Suppose I throw a dice 600 times and I get
99*1, 101*2, 98*3, 102*4, 97*5 and 103*6
Is this behaviour described by cp or qm
I expect your answer is cp
3. Using a dice (or dices) is there entanglement involved ?
I expect yout answer is no
4. Suppose I have a system which is in entangled state.
Do you know an example ?
Do you have an experiment which can be done with that system ?
What is the outcome of that experiment ?
Can you explain the outcome using cp ?
I expect: No.
Can you explain the outcome using qm ?
I expect: Yes.
SNIP
The best way of thinking of them is that "pure state" means
"single system", or "single world" if pertaining to the entire
system, and "mixed state" means "mixture of several
systems in parallel", or more simply "ensemble" (and best
captures the concept of "multiple worlds", if pertaining
to the system as a whole -- but note the presumption above
of the overall system A+B being in a pure state).
You should describe those concepts using an example.
States in classical physics are always mixed. Pure states
wouldn't be physically realizable even if classical physics
were valid (and their inaccessibility is, in fact, the main
reason why classical physics can't be valid).
Finally, is the question of what a relative state is.
SNIP
5. Suppose I have a system which is in either
the entangled state or in the not entangled state
Do you know an example ?
How do you switch between states ?
Do you have an experiment which can be done with that system ?
What is the outcome of that experiment in both states ?
I expect the questions 4 and 5 are not easy.
Nicolaas Vroom
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| User: "Sam Wormley" |
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| Title: Re: What is quantum entanglement? |
16 Oct 2003 07:29:34 PM |
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cyberdude wrote:
Hi,
What is quantum entanglement? Please assume that I only know elementary
quantum physics.
David
You might enjoy:
Entanglement: The Greatest Mystery in Physics
Amir D Aczel
2002 John Wiley & Sons/Four Walls Eight
Windows 302pp 16.99/$28.00hb
There are two kinds of books about quantum
mechanics. There are those in which we learn
about abstract concepts such as Hilbert spaces,
state vectors and density matrixes, but where the
author never addresses - or only pays lip-service
to - the question of what quantum mechanics
actually means. This is the approach often taken in
textbooks. The other, quite opposite, approach
focuses on the interpretative question - drawing all
kinds of conclusions and analogies, talking about
telepathy and other mysteries, and perhaps even
claiming that quantum mechanics transcends
Western philosophy.
Neither approach is very helpful when one wants
to understand what quantum mechanics really
means in a deep philosophical sense. Amir Aczel's
new book on entanglement - falling as it does into
neither category - avoids such pitfalls.
Anton Zeilinger from the Institute of Experimental
Physics at the University of Vienna reviews the
book in the May issue of Physics World; email
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| User: "cyberdude" |
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| Title: Re: What is quantum entanglement? |
23 Oct 2003 09:16:04 PM |
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Sam Wormley <swormley1@mchsi.com> wrote:
You might enjoy:
Entanglement: The Greatest Mystery in Physics
Amir D Aczel
2002 John Wiley & Sons/Four Walls Eight
Windows 302pp 16.99/$28.00hb
There are two kinds of books about quantum
...
I have borrowed the book and read part of it. It was written in plain
English and is very readable. It tells the history of Quantum Mechanics
or how scientists discovered it. There are also min-biographies of the
brilliant physicists we know well such as Einstein, Planck, Von Neuman,
and Schrodinger. It also describes the framework of Quantum Mechanics in
a simple way. But it has left so many questions that even scientists
don't have satisfying answers. They include why in the quantum world,
things are in quanta; that quantum entanglement is myterious in that
signals may transfer in space with superluminal speed; quantum
superposition is a phenomenon we can't perceive in our daily experience.
It seems a good book for studying quatum mechanics if one is tired of the
ways the standard QM books present the theories.
David
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| User: "Sam Wormley" |
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| Title: Re: What is quantum entanglement? |
23 Oct 2003 11:10:05 PM |
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cyberdude wrote:
Sam Wormley <swormley1@mchsi.com> wrote:
You might enjoy:
Entanglement: The Greatest Mystery in Physics
Amir D Aczel
2002 John Wiley & Sons/Four Walls Eight
Windows 302pp 16.99/$28.00hb
There are two kinds of books about quantum
...
I have borrowed the book and read part of it. It was written in plain
English and is very readable. It tells the history of Quantum Mechanics
or how scientists discovered it. There are also min-biographies of the
brilliant physicists we know well such as Einstein, Planck, Von Neuman,
and Schrodinger. It also describes the framework of Quantum Mechanics in
a simple way. But it has left so many questions that even scientists
don't have satisfying answers. They include why in the quantum world,
things are in quanta; that quantum entanglement is myterious in that
signals may transfer in space with superluminal speed; quantum
superposition is a phenomenon we can't perceive in our daily experience.
It seems a good book for studying quatum mechanics if one is tired of the
ways the standard QM books present the theories.
David
The book brings you up to date on many recent entanglement experiments, the
Einstein-Podolsky-Rosen paradox and Bell's inequality theorem.
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