IEEE Aerospace and Electronic Systems Magazine - November 2020 - 66

Progress Toward an All-Microwave Quantum Illumination Radar
action, QENR may prove to be strictly less efficient than
joint measurements. However, in real-life situations where
there is already significant environmental noise and loss,
the performance differences may be negligible. Of course
the analysis presented here is valid only for the symmetrical where the signal and idler transmitted powers are identical, the asymmetrical case being more complicated [25].
As we will discuss in the next section, QENR also has
unique advantages over joint measurements, which may
allow it to work at higher power and longer range.

ENTANGLEMENT-TRANSMISSION CHALLENGES

ENHANCEMENT WITHOUT ENTANGLEMENT
Quantifying entanglement of multimode Gaussian states
can be done through various methods differentiating classical from quantum states. In an experiment, however, the
measured state will never be pure and comparing various
measures of entanglement to determine which state is
" more entangled " becomes hazardous. It is instead preferable to have a simple binary outcome certifying that a
state is entangled or not by comparing an entanglementmeasure to a bound separating classical from quantum
states. For two-mode Gaussian states, this can be done
using the so-called positive partial transpose (PPT) criterion [3]. For the sake of keeping the discussion simple, we
will only broadly present the criterion and its implications
for this article.
The PPT criterion relies on the fact that a physical
covariance matrix must remain real, symmetric, and positive definite and that the measured quadratures obey the
Heisenberg uncertainty relations. Interestingly enough,
only classical states still respect the uncertainty relations if
time is reversed on only one of the two modes. Here, time
^ quadrareversal is equivalent to changing the sign of the Q
ture, reversing the sign of the corresponding correlations
between the modes. Mathematically, the PPT criterion dictates that the state is classical if the lowest symplectic
eigenvalue nÀ of the covariance matrix R in (16) is nÀ !
1=2, and nÀ < 1=2 if and only if the state is entangled.
In the symmetrical case where the signal and idler powers
are identical P a ¼ P b ¼ P then nÀ ¼ Var½I^a À hI^a I^b i.
From the covariance matrix (1), the state is entangled if the
measured covariance respects
CQ > P À 1:

(26)

In other words, if the covariance is greater than the measured power minus one unit of vacuum noise, i.e., the classical bound in (18), then the state is entangled and,
therefore, must be quantum. As was done experimentally
by Chang et al. in [8], this certification process is a first
necessary step to ensure that (i) the SPDC source does
indeed produce TMSSs with a covariance (26) as large as
possible, and (ii) the classical noise source is as close to
the ideal as possible by saturating the classical bound.
66

As signal loss reduces the measured covariance, and
that thermal background noise increases the measured
noise power, we can readily understand that entanglement
cannot be retained throughout the round-trip as the
inequality (26) will no longer be respected somewhere
along the way. As we have shown earlier, since it is the
initial correlations at the source that provide the detection
benefits, the loss of entanglement does not preclude a
quantum advantage to be achieved in practice.

While the practical aspects of quantum-enhanced noise
radar are appealing, there are still many challenges and
open questions regarding the implementation of quantum radar with microwave superconducting circuits. For
instance, the very low output power of JPAs is a serious
concern as we must find a way to take the faint and
fragile microwave signals from a well-controlled and
ultracold environment and transmit them unscathed in
the hot and open atmosphere. A possible strategy is to
use several circulators or isolators at different temperature stages along the transmission path designed in such
a way that it would provide minimal transmission losses
toward the atmosphere, while simultaneously strongly
attenuating the large amount of incoming harmful atmospheric noise.
Without a doubt, the successful transmission and
detection of raw, entangled microwave signals in the open
atmosphere would be a groundbreaking result with great
impact for quantum communications and quantum information sciences. Still, increasing the transmitted power
without sacrificing entanglement remains an issue for
practical applications. In the following, we approach the
problem in two different ways: signal amplification and
multiplexing.

AMPLIFICATION OF ENTANGLED SIGNALS
Quantum entanglement is a fragile resource in the presence noise and loss. This fragility is well embodied in the
inequality (26) used to certify the unique quantum signature of entangled states. Indeed, respecting it requires both
very low-noise levels and very high detection efficiency in
order for the detected noise power to be as close to the initial state as possible. The amplification process required to
perform heterodyne detection at room temperature can
then be more than enough to destroy the faint quantum
entanglement. To see this, we use the standard equation
modeling a phase-preserving amplifier where the ampli^ of the input a^ is
fied signal A
^¼
A

pﬃﬃﬃﬃ
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
G a^ þ G À 1 h^y

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