1. The document proposes a new experiment involving entanglement and gravitational decoherence using a dual Mach-Zehnder interferometer setup. 2. In the proposed experiment, one interferometer would be placed in a gravitational field, while the other would not. This would result in non-unitary evolution and allow for nonlocal signaling between the two locations. 3. By moving his interferometer in and out of the gravitational field, one experimenter could encode and transmit binary messages to the other, who could decode the messages by observing changes in interference patterns resulting from the non-unitary evolution.

1. 1
A new experiment in nonlocal signaling involving entanglement and
gravitational decoherence
Cristian Dumitrescu*
Abstract. In this article I present a new experimental design related to nonlocal signaling involving
entangled particles in a dual MZ interferometer, also involving gravitational decoherence. I also discuss
the consequences of this design related to the field of quantum computation.
Introduction. A true quantum computer more powerful than a classical computer is still years (or
decades) away. The main problem is overcoming decoherence. There is another way to approach this
problem, and this path is described in this article.
Previous work by other researchers.
In reference [4], Cramer and Herbert consider an experimental design with entangled photons in a path
entangled dual interferometer. Their conclusion is that the intrinsic complementarity between two -
photon interference and one - photon interference blocks any potential nonlocal signal. Without the
coincidence circuits no nonlocal signal can be transmitted from Alice to Bob (in this particular Alice-Bob
EPR setup). In terms of density matrix formalism, nothing that happens at Alice's end has any effect on
Bob's density matrix, even when Bob and Alice's photons are maximally entangled (due to unitary
evolution - conservation of energy).
In reference [8], the experimental design involves a (just one) Mach-Zehnder interferometer in a
gravitational field. They consider interference of a “clock” particle with evolving degrees of freedom (for
example an electron and the “clock” being spin precession) that will not only display a phase shift, but
also reduce visibility of the interference pattern. According to general relativity, proper time flows at
different rates in different regions of space- time. Because of quantum complementarity the visibility of
the interference pattern will drop as the which path information becomes available from the reading of
the proper time of the “clock” going through the interferometer (gravitationally induced decoherence).
In reference [7] a quantum – optics variation of the experiment presented in [8] is discussed. In this
experiment the function of the “clock” is taken by the position of a single photon along the
interferometer arm. Because of general relativistic time dilation, the arrival time of the photon should
depend on the altitude of its trajectory above the source of the gravitational field (Earth in this case). In
an experiment with a single photon travelling in a superposition along two paths of an interferometer
(each located at a different height above the source of the gravitational field), a reduction of the

2. 2
interferometric visibility is expected for relative time dilations larger than the photon’s coherence time
(the which path information of the photon can be read from its time of arrival and interference is lost).
The connection between impossibility proofs of FTL information transfer and unitary evolution.
In this section I present a mathematical proof that FTL (faster than light) information transfer is
impossible if we assume unitary evolution in quantum mechanics (as in [6]). Unitary evolution is related
to energy conservation, and this is an important point related to the experiment that I propose, because
the mathematical model of the experiment that I propose in the next section cannot assume unitarity
(for reason that will be presented later).
So, Alice and Bob share pairs of entangled particles. The basis of ket-vectors ⎸𝑎 〉 describe everything
that Alice can interact with. The ket – vectors ⎸𝑏 〉 describe everything that Bob can interact with. The
tensor product states ⎸𝑎𝑏 〉 describe the combination of Alice’s and Bob’s systems. Alice and Bob’s
system might have interacted in the past but now are separated.
The Alice and Bob wave function is 𝜓 (𝑎, 𝑏) and it may be entangled.
Alice’s complete description of her system (and measuring apparatus) is contained in her density
matrix , where we have:
𝜌 𝑎,𝑎′ = ∑ 𝜓∗
𝑏 (𝑎′
, 𝑏) · 𝜓(𝑎, 𝑏)
Can Bob, at his end, do anything to instantly change Alice’s density matrix, assuming that Bob’s
evolution (his system’s evolution) must be unitary? Bob’s system evolution is described by a unitary
matrix 𝑈𝑏,𝑏′ . The matrix 𝑈 represents whatever happens to Bob’s system, whether or not he does an
experiment. The final wave function is:
𝜓 𝑓𝑖𝑛𝑎𝑙(𝑎, 𝑏) = ∑ 𝑈𝑏,𝑏′𝑏′ · 𝜓(𝑎, 𝑏′) .
The complex conjugate is then:
𝜓 𝑓𝑖𝑛𝑎𝑙
∗
(𝑎′, 𝑏) = ∑ 𝜓∗
𝑏′′ (𝑎′
, 𝑏′′) · 𝑈 𝑏′′,𝑏
†
Alice’s new density matrix is then:
𝜌 𝑎,𝑎′,𝑓𝑖𝑛𝑎𝑙 = ∑ 𝜓∗
𝑓𝑖𝑛𝑎𝑙𝑏 (𝑎′
, 𝑏) · 𝜓 𝑓𝑖𝑛𝑎𝑙(𝑎, 𝑏) = ∑ 𝜓∗
𝑏,𝑏′,𝑏′′ (𝑎′
, 𝑏′′) · 𝑈 𝑏′′,𝑏
†
· 𝑈 𝑏,𝑏′ · 𝜓(𝑎, 𝑏′) .
The combination 𝑈𝑏′′,𝑏
†
· 𝑈𝑏,𝑏′ represents just the matrix product 𝑈†
· 𝑈 , but U is assumed unitary.
That means that 𝑈†
· 𝑈 is the unit matrix 𝛿 𝑏′′,𝑏′ .
As a consequence we have:
𝜌 𝑎,𝑎′,𝑓𝑖𝑛𝑎𝑙 = ∑ 𝜓∗
𝑏 (𝑎′
, 𝑏) · 𝜓(𝑎, 𝑏)

3. 3
This is exactly the initial density matrix related to Alice’s system. Nothing that happens at Bob’s end has
any immediate effect on Alice’s density matrix. No FTL signal is possible, assuming unitary evolution.
On the other hand, if U is not unitary, I see no reason why it should always be the case that the identity
∑ 𝜓∗
𝑏 (𝑎′
, 𝑏) · 𝜓(𝑎, 𝑏) = ∑ 𝜓∗
𝑏,𝑏′,𝑏′′ (𝑎′
, 𝑏′′) · 𝑈 𝑏′′,𝑏
†
· 𝑈𝑏,𝑏′ · 𝜓(𝑎, 𝑏′) should always hold. Alice’s
density matrix (that governs the results of local measurements) changes. In fact, if U is not unitary, the
equality above will not likely be true. Even more happens when we work with non – unitary operators.
The whole mathematical framework of quantum mechanics collapses (for example the trace is not well
defined any more, and many other unpleasant things). This means that a new mathematical framework
is needed in order to study these phenomena.
The proposed experiment.
Let's consider a path entangled dual interferometer experiment involving entangled particles (electrons,
for example), when one MZ - interferometer is in a gravitational field (see fig. 1). When we consider the
density matrix of the system composed of the entangled particles in the two MZ interferometers, and
when we consider the partial trace over system B (Bob's subsystem situated in a gravitational field),
then we see that the interference visibility will also be affected for system A, Alice's subsystem (this can
be seen by performing the calculations). This opens the door for nonlocal signaling since Bob can send
binary messages to Alice by moving his MZ - interferometer in and out of the gravitational field, and
Alice using statistical analysis, can decode Bob's message based on high or low visibility of her
interference pattern (and no coincidence circuits necessary). Note that for every bit of information
transferred, Alice has to perform a statistical analysis of many particles. In this case the evolution of the
system represented by the entangled particles going through the dual MZ interferometers in the
presence of a gravitational field (for Bob's subsystem) is not unitary (and all FTL information transfer
impossibility proofs are based on unitarity). I am aware that the conventional mathematical framework
of QFT is causal at any time scales, so any attempt to consider FTL schemes within this framework is
futile. Note though that the experiment that I propose involves gravity, so any mathematical model of
this experimental design would go beyond QFT.
Considering the connection between Lorentz invariance and causality, it seems to me that this
experimental design (its consequences in terms of results of experiment) will not be compatible with
macroscopic causality. This means that computation with CTC’s (closed timelike curves) might be
possible
As I said before, unitary evolution is related to conservation of energy. The experiment that I propose
involves gravitational decoherence, and in this case the systems involved in the experiment that I
propose cannot follow unitary evolution. As another example of what could happen (related to time
dilation), in reference [5] the gravitational redshift was first described by Pund and Rebka, who verified
that the frequency of electromagnetic radiation depends on the altitude difference between the emitter
and receiver.

4. 4
Following a protocol they agreed upon, both Bob and Alice will analyse batches of N particles (many
such groups). Bob wants to send a binary message to Alice. When he wants to send a binary 1, he places
his interferometer in the gravitational field (as seen in fig. 1) and he will notice the reduction of
interferometric visibility. Because of non-unitary evolution, Alice will also notice the reduction of the
interferometric visibility. She will then know that Bob intended to send her the bit of information 1 (with
a high confidence level). When Bob wants to send a binary 0, he places his interferometer away from
the gravitational field. As a consequence neither Bob or Alice will notice any reduction of the
interferometric visibility, and Alice will know that Bob intended to send her the bit of information 0.
Basically, Bob can send any message encoded in binary, and the message will be received by Alice
instantaneously (the statistical analysis that Alice follows, in order to decode the message takes some
time, but nonlocal signalling seems to be possible). Based on the equivalence principle, other possible
designs could be considered.
Conclusions. In references [1] and [2] it is shown the power of computation with CTC’s (closed timelike
curves). Basically, the method involves forcing nature to solve hard problems efficiently, just in order to
make the universe causally consistent. This article can be seen as mostly a review article, except for the
proposed experiment, which is original. This would open the door for a different kind of quantum
computer, and solving hard problems efficiently in any domain of activity would be possible. I also want
to emphasize the following points. In the transactional interpretation of quantum mechanics (see
Fig 1. This is the basic design of the dual interferometer experiment involving entangled particles when Bob’s MZ
interferometer is in a gravitational field (represented by the solid red arrow on the left). In this figure, only one
operational mode is shown, when Bob’s interferometer is in a gravitational field.
Alice
receiver
Bob,
sender
Beam
splitters
Phase
shifter
Phase
shifter
Source of
entangled
particles
Detectors
Detectors g

5. 5
reference [3], inspired by the Wheeler – Feynman absorber theory) a transaction is formed between the
emitter and absorber by a superposition of advanced and retarded waves. In a Minkowski diagram of
such an interaction involving the emission and absorption of a particle, the emergence of the
transaction does not occur at some particular location in space or some particular instant in time, but
rather forms along the entire four – vector which connects the emission with the absorption locus. The
transaction involves the interference of retarded and advanced waves. The influence of the transaction
in enforcing the correlations of the quantum events is both nonlocal and temporal. Due to this
interference (destructive interference), there are no advanced (or retarded) waves before the
emission of the particle and after its absorption, but constructive interference reinforces them between
the emitter and the absorber (as points in space - time). Only the completion of this transaction
facilitates the momentum and energy transfer between the emitter and absorber. I emphasize that this
happens in flat space – time (for type one transactions). My suggestion is to study these phenomena in
curved space – time. This would require quantum field theory in curved space – time (as a theoretical
tool). In various EPR experiments (or experiments involving entangled laser beams), if the emitter or the
absorber are in a curved space – time, there is a distinct possibility that the transaction involving the
interference of advanced and retarded waves might not be perfect (as in flat space - time), and
therefore some residual advanced waves might be present, that could be detected (the destructive
interference that cancels them in flat space – time might not be complete in curved space - time). In
fact, a simple experiment (conceptually at least) as directing a laser beam towards a black hole might
open the possibility of detecting advanced waves. Introducing this element of asymmetry in terms of
the curvature of space – time in the emitter or absorber vicinity might open the possibility of detection
of these advanced waves. Once again, I am not thinking about sending messages to the past (at the
macroscopic level), with all the paradoxes that it implies, but rather setting up experiments where the
only way nature can be consistent would be to “promote” low probability events to very likely events, a
way to influence the probability distribution of events (as Professor John Cramer would say). It is also
worth mentioning that the equivalence principle opens the door towards simulating such environments
by putting the emitter and/or absorber in accelerating systems (fast rotation for example). Experimental
tests in order to detect advanced waves were proposed by Partridge (in 1973), Heron and Pegg (in 1974),
Schmidt and Newman (in 1980), and others. The actual performed experiments were unsuccessful, but
none of them took into account the curvature of space – time around the emitter and absorber (in the
context of the transactional interpretation). Only a complete analysis of these proposed experiments in
the context of quantum field theory in curved space – time could estimate the level of feasibility of my
proposed experiments. The experiment described in detail in this article is just one of the class.
References:
1. Aaronson, S. and Watrous, J. “Closed timelike curves make quantum and classical computing
equivalent”, Proc. R. Soc. A. doi:10.1098/rspa.2008.0350.
2. Brun, T. A. “Computers with timelike curves can solve hard problems”, arXiv:gr-qc/0209061v1
18 Sep. 2002.
3. Cramer, J. “Generalized absorber theory and the Einstein – Podolsky – Rosen paradox”, Phys.
Rev. D, volume 22, number 2, pp. 362 – 376, July 1980.

6. 6
4. Cramer, J. and Herbert, N. “An Inquiry into the Possibility of Nonlocal Quantum Communication”,
arXiv:1409.5098v2 [quant-ph] 15Feb. 2015.
5. Pound, R. V. and Rebka, G. A. “Apparent weight of photons”, Phys. Rev. Lett. 4, 337 – 41 (1960).
6. Susskind, L. and Friedman, A. “Quantum Mechanics”, Basic Books, 2014.
7. Zych, M., Costa, F., Pikovski, I. and Brukner, C. ”General relativistic effects in quantum
interference of photons”, arXiv:1026.0965v2 [quant-ph] 6 Nov. 2012.
8. Zych, M., Costa, F., Pikovski, I. and Brukner, C. ”Quantum interferometric visibility as a witness
of general relativistic proper time”, Nature Communications, 18 Oct. 2011.
About the author.
Cristian Dumitrescu graduated from the University of Bucharest with a BSc. In Mathematics in 1988. He
worked as a high school teacher for two years and then as a computer programmer for various
companies in UK, Romania and Canada. Cristian Dumitrescu emigrated to Canada in 1994 and obtained
Canadian citizenship in 1998. In the last 17 years he has been working in a field not related to science,
but has kept mathematics and physics as a favorite hobby.
*Email: cristiand43@gmail.com
cristiand41@hotmail.com