3
diagonal coincidence lines that reduces the frequency cor-
relation, thereby allowing us to tune the entropy of the
QFC. In this work, we demonstrate a novel pumping
and filtering scheme32 in PPLN waveguide-based QFC
to maneuver its entropy, by tailoring its joint spectral
intensity (JSI). Further, gaining control over the direc-
tion of quantum walk (QW), although very critical to
QIP and quantum information transport33, has been in-
deed difficult34,35, and often impossible due to its in-
herent stochastic nature. Unidirectional one and two-
dimensional QW from separable two-particle states have
been shown theoretically36. Nevertheless, the experimen-
tal demonstration of obtaining a definitive control over
the directions of QWs in photonic systems is still scarce.
To address this issue, we study quantum walks initiated
from such high-dimensional quantum states with variable
entropies37 and demonstrate control.
Quantum superpositions enable QWs38,39 to po-
tentially speedup certain computational tasks such
as database searches, tests of graph isomorphism,
ranking nodes in a network40, quantum many-body
simulations39, boson sampling41, universal quantum
computing42,43, and quantum state preparation44. En-
tanglement generation, localization, and quantum infor-
mation transport through QW even find applications
in exotic fields of studies, notably, in explaining the
energy transfer mechanism within photosynthesis45, in
neural network46, for topology identification47, and in
neuroscience48. Being robust and immune to decoher-
ence at room temperature, QW realized in photonic
platforms are advantageous over other platforms such
as cold atom, Bose-Einstein condensates (BEC), opti-
cal lattices, trapped ions, etc.49. However, QW imple-
menting spatial49, polarization40, angular momentum50
degrees of freedom of photon either require large over-
head to alter the depth of the QW40 or necessitate
modifying the physical layout to attain the tunability
of the duration of QW49,51. Recently, QWs exhibiting
enhanced ballistic transport (bosonic) or strong energy
confinement (fermionic) have been demonstrated52 using
high-dimensional bi-photon quantum frequency combs
(QFCs)52, which do not require any change of the device
arrangement. However, no control over the directions
of the demonstrated QWs52 could be achieved, which
were initiated from the maximally entangled states. Re-
cently, Floquet engineered discrete- and continuous-time
QWs and their control have been reported numerically
by using time-dependent coins34, and by tweaking the
node-coupling coefficients35. The role of space-dependent
coins53, and initial conditions54 on QWs are also stud-
ied extensively. Lately, the directionality of QW in BEC
has been observed55,56. Quantum photonic states having
tunable entropies extend our accessibility to the Hilbert
space. Consequently, richer dynamics of QWs instigated
from such states are expected yet have not been observed
to date. For the first time to the best of our knowledge,
here we experimentally demonstrate the coherent con-
trol of the direction and steering of quantum walk ini-
tiated from a high-dimensional bi-photon quantum fre-
quency comb with tunable state entropies leading to a
completely new paradigm of QWs. Procuring precise
control over a nonclassical stochastic process involving
a high-dimensional Hilbert space may have immense im-
plications in, e.g., quantum search, transport of quantum
information, and atomic interference.
II. DESCRIPTION AND CHARACTERISTICS
OF NON-MAXIMALLY ENTANGLED QFCS
Biphoton quantum frequency combs providing a route
to generate complex high-dimensional states10 can play
a major role in discrete-variable photonic quantum com-
puting. They are either generated by monochromatically
exciting one of the resonating modes of a microresonator
(MR) or by pumping a nonlinear waveguide typically be-
low the parametric threshold6with the help of an ar-
ray of equidistant optical filters. We adopted the lat-
ter approach at the moderate expense of reduced bright-
ness and second-order correlation (g(2)) because of the
increased design flexibility of choosing the QFC free-
spectral range (FSR), also necessary to synchronize with
the RF-driving frequency to perform the quantum state
tomography (QST).
A scheme for the generation of non-maximally en-
tangled QFCs from pulse excitation is shown in Fig.
1. A programmable filter (PF1) configuration is used
to discretize the SPDC spectra from a femtosecond
(fs) laser-driven PPLN-waveguide to create a bi-photon
QFC8. The distance between the adjacent bandpass
filters (BPFs) defines the free spectral range (FSR) of
the QFC. The femtosecond (fs)-laser allows producing a
broad single-mode frequency bandwidth for each photon
with respect to CW-pumping52,57,58. Together with a
special filter, this may result in multiple anti-diagonal
lines in the JSI. Due to the presence of multiple lines,
one particular idler mode is spectrally connected to sev-
eral signal modes (instead of one, as it would be in a
maximally entangled state). This effectively reduces the
entanglement of the system as explained in Fig. 1. One
can create a variety of JSIs with several frequency anti-
correlation line configurations by changing the spectral
profile of the excitation or by altering the FSRs. To
simulate such versatile JSIs, we develop a mathemati-
cal model (see Supplementary Information), where we
assume that the BPF corresponding to the 0-th (central)
mode is placed matching with the center of the quasi-
phase-matching (QPM) bandwidth (i.e., the degenerate
angular frequency (fd) = pump-frequency (fp)/2) of the
PPLN.
Initially we model the corresponding JSI of the QFC
assuming there exists an equal number of frequency anti-
correlation lines (i.e., symmetrical) surrounding the cen-
tral antidiagonal. The quantum-state representing the
p−th adjacent anti-diagonals with respect to the central
anti-diagonal (p= 0) of such QFC having Nnumber of