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Sci Adv. 2017 September; 3(9): e1602485.

Published online 2017 September 22. doi: 10.1126/sciadv.1602485

PMCID: PMC5612281

Mohamed Nawareg,^{1,}^{2,}^{*}^{†} Sadiq Muhammad,^{1,}^{†} Pawel Horodecki,^{3} and Mohamed Bourennane^{1,}^{‡}

Received 2016 October 11; Accepted 2017 September 1.

Copyright © 2017 The Authors, some rights reserved;
exclusive licensee American Association for the Advancement of Science. No claim to
original U.S. Government Works. Distributed under a Creative Commons Attribution
NonCommercial License 4.0 (CC BY-NC).

This is an open-access article distributed under the terms of the
Creative Commons
Attribution-NonCommercial license, which permits use, distribution,
and reproduction in any medium, so long as the resultant use is **not**
for commercial advantage and provided the original work is properly
cited.

Entanglement is one of the most puzzling features of quantum theory and a principal resource for quantum information processing. It is well known that in classical information theory, the addition of two classical information resources will not lead to any extra advantages. On the contrary, in quantum information, a spectacular phenomenon of the superadditivity of two quantum information resources emerges. It shows that quantum entanglement, which was completely absent in any of the two resources separately, emerges as a result of combining them together. We present the first experimental demonstration of this quantum phenomenon with two photonic three-partite nondistillable entangled states shared between three parties Alice, Bob, and Charlie, where the entanglement was completely absent between Bob and Charlie.

Quantum entanglement leads to the most counterintuitive effects in physics (*1*, *2*) and an important quantum resource, which plays a
central role in the field of quantum information and communication. Therefore, the
investigation of entanglement properties of quantum states is crucial. The
characterization of entanglement for multipartite and mixed systems is still under
intense research (*3*).
Entanglement can be easily destroyed by decoherence processes as a result of unwanted
coupling with the environment. This uncontrollable interaction introduces noise and
transform, for example, maximally entangled states into mixed states. Therefore, it is
critical to know which mixed states can be distilled to maximally entangled states with
the help of local operations and classical communication (LOCC) and then be valuable
again for further information processing (*4*, *5*). It has been discovered that there is a new class of
entangled states where no entanglement can be distilled, and it has been called bound
entanglement (*6*, *7*). On the contrary, the distillable
entanglement is called free entanglement. After this discovery of bound entanglement,
the impression was that this type of entanglement is completely useless for quantum
information processing. However, it has been shown that, even in the bipartite case,
there is an option to pump entanglement of many bound entangled states into one weakly
entangled pair to beat the quantum teleportation fidelity threshold that is unbeatable
otherwise (*8*). This process is
called activation of bound entanglement, and it was the first manifestation of
superadditivity of quantum communication resources. Later, it turned out that bound
entanglement can lead to various superadditivity of that kind in the multipartite case
(*9*). Bound entanglement also
turned out to be useful, somewhat surprisingly, for quantum key distillation (*10*) [see the study by Dobek
*et al*. (*11*)
for an experimental realization], which eventually paved the way to streaking
superadditivity or the activation of quantum bipartite channels (*12*) where the channel corresponding to bound
entanglement is activated by a 50:50 erasure channel. Independently, it has been shown
that multipartite bound entanglement is a useful resource for other quantum
communication tasks. Not only can it be superactivated in a specific situation (*13*), one can use it for remote
quantum information concentration as well (*14*). It has also been shown that von Neumann measurements
on special bound entangled states allow generation of a new classical secrecy
phenomenon, which is called multipartite bound information (*5*). All of these make bound entangled states
intriguing objects of quantum information, justifying the term “black
hole” of the quantum information field in the sense that the entanglement goes in
but is impossible to recover because of the nondistillability (*15*). However, because the bound entanglement can be
activated as seen above, analogically, one can say the “black hole can
evaporate” in the sense that it can become entangled and therefore become
useful.

Here, we report on the first experiment when, metaphorically speaking, “adding
two zeros” results in a “nonzero value” or when, in more precise
words, the resource (a specific type of free entanglement), which is completely absent
in any of the two ingredients, emerges as a result of putting the two ingredients
together. Here, the three-partite bound entangled state has been synthesized, and after
the interaction with some special free entangled state, the new quantum entanglement has
been established, which could not be made out of any of the states (or an arbitrary
number of copies of them) of each of the two classes alone. This is also the first
observation of three-qubit bound entanglement activation. Note that, at the same time,
we experimentally produced the first representative of bound entanglement that can be
used for the generation of multipartite bound information (*16*).

It is known that there is more than one type of entanglement in the multipartite case.
The most celebrated is the Greenberger-Horne-Zeilinger (GHZ) versus W state
nonequivalence (*17*, *18*). In the case of mixed states,
there are different types of states that are also not equivalent. Below, we shall
describe the situation when one has two different types of mixed state entanglement,
each of them unable to perform some task; however, the combination of the two resources
(in terms of local interaction and classical communication) resolves this
impossibility.

Consider the family of tripartite states ρ =
ρ^{ABC} for which the partial transposition of the
indices on the, say, first system is positive; that is, one has the nonnegative
eigenvalues of partially transposed matrix ${\mathrm{\rho}}^{{\mathrm{\Gamma}}_{\mathit{A}}}$ produced from the matrix representation of the
original state with the elements
[ρ_{ij,kl,mn}]
=
[ρ^{ABC}]_{ij,kl,mn}
by swapping the first two indices corresponding to the row and column of the first
subsystem *A*, namely,${[{\mathrm{\rho}}_{\mathit{i}\mathit{j},\mathit{k}\mathit{l},\mathit{m}\mathit{n}}]}^{{\mathrm{\Gamma}}_{\mathit{A}}}={[\mathrm{\rho}]}_{\mathit{j}\mathit{i},\mathit{k}\mathit{l},\mathit{m}\mathit{n}}$. This is just a positive partial transpose (PPT) test
attributed to Peres (*19*)
performed with respect to system *A*. Note that it means that the
partially transposed matrix is a legitimate state. It is known that this property
makes it impossible for one to distill, via LOCC, any maximally entangled state
between party *A* (on which transpose was checked) and any of the
other parties (*B* or *C*), or both [see Horodecki
*et al*. (*7*)]. Distilling a maximally entangled bipartite pure state
with a subsystem *X*, requires the PPT condition for the original
multipartite state to be violated with respect to *X* from the very
beginning. It must be so because the positivity is conserved under LOCC (*7*). An even more demanding
condition follows immediately: Because bipartite entanglement fails PPT test if and
only if both of its subsystems fail, then to distill entanglement between the two
parties *X* and *Y* out of some multipartite state, the
violation of the test is needed with respect to each of the two parties
*X* and *Y* independently; that is, one must have
neither ${\mathrm{\rho}}^{{\mathrm{\Gamma}}_{\mathit{X}}}$ nor ${\mathrm{\rho}}^{{\mathrm{\Gamma}}_{\mathit{Y}}}$ positive. Otherwise, on the basis of the fact that
any two-qubit entanglement is distillable (*5*), one may write ${\mathcal{D}}_{\mathit{X}:\mathit{Y}}(\mathrm{\rho})>0$ to denote that pure entanglement between
*X* and *Y* can be distilled. To have distillability
of singlets between them, this requirement of simultaneous violation of the PPT
condition by the two systems is generally necessary for a multipartite system made of
qubits. This fact, which is briefly summarized in Fig.
1, follows from the result stating that any two-qubit state violating the
PPT condition is distillable (*5*). Dür and Cirac (*9*) have designed a tripartite state
ρ^{ABC} that has the property that two of its
partial transpositions, ${\mathrm{\rho}}^{{\mathrm{\Gamma}}_{\mathit{A}}}$ and ${\mathrm{\rho}}^{{\mathrm{\Gamma}}_{\mathit{B}}}$, are positive, but the third,
${\mathrm{\rho}}^{{\mathrm{\Gamma}}_{\mathit{C}}}$, is not (see Fig.
2). There is some entanglement in this state (because it violates the PPT
entanglement test). However, there is no chance to distill any pure entanglement out
of it because there is no pair of qubits that violate the PPT test. Thus, the state
is bound entangled and is denoted as

$$\mathcal{D}({\mathrm{\rho}}_{\text{bound}})=0$$

(1)

which expresses the fact that no pure entanglement can be distilled among any number of parties. It does not allow any distillability between any two parties, which we denote, as mentioned before, by writing ${\mathcal{D}}_{\mathit{B}:\mathit{C}}({\mathrm{\rho}}_{\text{bound}})=0$. This can be easily seen from Fig. 2, where the three-qubit state described above has been symbolically depicted.

Now, consider the following situation shown in Fig.
2 [see the study by Dür and Cirac (*9*)]. The three parties share the abovementioned
three-qubit state ${\mathrm{\rho}}_{\text{bound}}^{\mathit{A}\mathit{B}\mathit{C}}$, which is bound entangled because both
${\mathrm{\rho}}_{\text{bound}}^{{\mathrm{\Gamma}}_{\mathit{A}}}$ and ${\mathrm{\rho}}_{\text{bound}}^{{\mathrm{\Gamma}}_{\mathit{B}}}$ are positive. This state satisfies
$\mathcal{D}({\mathrm{\rho}}_{\text{bound}})=0$. In particular, the distillable entanglement
restricted to parties *B* and *C* is also
zero

$${\mathcal{D}}_{\mathit{B}:\mathit{C}}({\mathrm{\rho}}_{\text{bound}})=0$$

(2)

However, in addition, the parties share another tripartite state
${\mathrm{\rho}}_{\text{free}}^{{\mathit{A}}^{\prime}{\mathit{B}}^{\prime}{\mathit{C}}^{\prime}}$. It has free entanglement with respect to subsystems
*A*′ and *B*′ but still has no
distillability power with respect to the specified cut

$${\mathcal{D}}_{{\mathit{B}}^{\prime}:{\mathit{C}}^{\prime}}({\mathrm{\rho}}_{\text{free}})=0$$

(3)

Originally, the bound entangled state is the following one designed by Dür and
Cirac (*9*)

$${\mathrm{\rho}}_{\text{bound}}^{\mathit{A}\mathit{B}\mathit{C}}=\frac{1}{3}|{\mathrm{\Psi}}_{\text{GHZ}}\rangle \langle {\mathrm{\Psi}}_{\text{GHZ}}|+\frac{2}{3}\frac{\mathit{P}}{4}$$

(4)

where the GHZ state
$|{\mathrm{\Psi}}_{\text{GHZ}}\rangle =\frac{1}{\sqrt{2}}(|000\rangle +|111\rangle )$ and the projection *P* projects onto
{|010, |011, |100, |101}, that is,
|010010| + |011011| + |100100| +
|101101|, whereas the free entangled state is defined as

$${\mathrm{\rho}}_{\text{bound}}^{{\mathit{A}}^{\prime}{\mathit{B}}^{\prime}{\mathit{C}}^{\prime}}={[|{\mathrm{\Psi}}^{+}\rangle \langle {\mathrm{\Psi}}^{+}|]}_{{\mathit{A}}^{\prime}{\mathit{B}}^{\prime}}\otimes {[|\mathrm{\Omega}\rangle \langle \mathrm{\Omega}|]}_{{\mathit{C}}^{\prime}}$$

(5)

where one of the states is just a
maximally entangled state between *A*′ and
*B*′, $|{\mathrm{\Psi}}^{+}\rangle =\frac{1}{\sqrt{2}}(|00\rangle +|11\rangle )$, whereas |Ω is either some qubit state
or just a vacuum state (no photon).

Let us stress once again the fact that no pure entanglement between Bob and Charlie
parts can be created from an arbitrary number of copies of any of the state
ρ_{bound} or ρ_{free}, because these states satisfy
Eqs. 2 and 3, respectively. Now, as depicted in Fig. 3, this no-go property disappears when the two
states are allowed to be processed together. Then, party *A* (Alice)
performs the joint measurement—projection onto a maximally entangled state or
the complement three-dimensional projector. If the measurement is successfully
concluded (projection onto singlet), then Alice sends the message to Bob and Charlie
who may then verify that they now share some free entangled state that can be further
distilled to the singlet form. The probability of Alice’s joint measurement
that led to a successful projection onto the singlet state is
^{2}/_{3}.

The entanglement verification protocol relies on the PPT test that reports
entanglement between Bob’s and Charlie’s laboratories, but among the
specially chosen qubit subspaces $\{{|00\rangle}_{\mathit{B}{\mathit{B}}^{\prime}}{|11\rangle}_{\mathit{B}{\mathit{B}}^{\prime}}{|0\rangle}_{\mathit{C}}{|1\rangle}_{\mathit{C}}\}$, we omitted the trivial vacuum state
${|\mathrm{\Omega}\rangle}_{{\mathit{C}}^{\prime}}$ on system *C*′. It is well
known that non-PPT bound entangled states do not exist in a 2 ×
*N* system and that all non-PPT 2 × *N*
entangled states are distillable (*3*). In this sense, we have here the LOCC protocol mapping
ρ_{bound} ρ_{free} →
σ_{free}, where Eqs.
2 and 3 show initially zero
distillable entanglement between Bob and Charlie with the input states
(ρ_{bound} and ρ_{free}) but finally give free
entanglement, that is, ${\mathcal{D}}_{\mathit{B}{\mathit{B}}^{\prime}:\mathit{C}{\mathit{C}}^{\prime}}({\mathrm{\sigma}}_{\text{free}})>0$.

Because the total protocol on Fig.
3—being LOCC—cannot create free entanglement (this is a standard
property of LOCC operation), we have to conclude eventually that the condition
${\mathcal{D}}_{\mathit{B}{\mathit{B}}^{\prime}:\mathit{C}{\mathit{C}}^{\prime}}({\mathrm{\rho}}_{\text{bound}}\otimes {\mathrm{\rho}}_{\text{free}})>0$ must have held initially despite vanishing Eqs. 2 and 3. Thus, as already mentioned, we have here the first realization
of the extreme superadditivity of quantum resources, which means that although we
have complete absence of some quantum information ingredient (free entanglement
between Bob and Charlie) in any of the two resources, when one allows the two of them
to interact, the ingredient surprisingly emerges. One of the crucial elements here
for which this “something out of nothing” type of effect is to be
guaranteed is that one really has to prepare bound entanglement in the experiment.
Moreover, this protocol can also be viewed as activation of three-qubit bound
entanglement. In this context, we like to mention that there was an unsuccessful
experimental attempt to activate four-qubit bound entanglement (*20*).

Finally, it is informative to further examine our protocol from the resource theory
perspective governed by the LOCC paradigm (defined by separated locations and quantum
operations used as free resources). Namely, at a first look, the protocol presented
seems to be viewed as an entanglement swapping experiment transferring the
entanglement from *B* to whatever *A* was entangled to
(in this case, systems *B* and *C*). However, this
perspective misses the resource framework aspect here, where the locations are
essential as dictated by the LOCC paradigm. From this perspective, having just three
locations (for example, local regions)—$\stackrel{~}{\mathit{A}}$ (with particles *A*,
*A*′), $\stackrel{~}{\mathit{B}}$ (with particles *B*,
*B*′), and $\stackrel{~}{\mathit{C}}$ (with particles *C*,
*C*′)—rather than physical systems is more important.
Now, in usual entanglement swapping, it is that one free (distillable) entangled
state shared between locations $\stackrel{~}{\mathit{A}}$ and $\stackrel{~}{\mathit{B}}$ and another free (distillable) entangled state shared
between locations $\stackrel{~}{\mathit{A}}$ and $\stackrel{~}{\mathit{C}}$ initially. After successful joint measurement at
$\stackrel{~}{\mathit{A}}$, $\stackrel{~}{\mathit{B}}$ and $\stackrel{~}{\mathit{C}}$ become entangled. In contrast, in our activation
protocol, one free (distillable) entangled state is shared between locations
$\stackrel{~}{\mathit{A}}$ and $\stackrel{~}{\mathit{B}}$ and another bound (nondistillable) entangled state is
shared between locations $\stackrel{~}{\mathit{A}}$, $\stackrel{~}{\mathit{B}}$, and $\stackrel{~}{\mathit{C}}$, but no entanglement is shared between locations
$\stackrel{~}{\mathit{A}}$ and $\stackrel{~}{\mathit{C}}$, as opposed to the previous case.

In our experiment, the physical qubits are polarized photons, where the computational
basis corresponds to horizontal *H* and vertical *V*
linear polarization |0 = |*H* and |1 =
|*V*. To prepare the three-photon polarization bound
entangled state ρ_{bound}, we used a spontaneous parametric
downconversion (SPDC) process and quantum interference. To experimentally and fully
investigate the properties of a three-qubit bound entangled state, we have evaluated
the three-photon 8 × 8 density matrix ${\mathrm{\rho}}_{\text{bound}}^{\text{exp}}$, by making 27 local polarization measurements in
linear, diagonal, and circular polarization bases
|*H*/*V*, $|+/-\rangle =(|\mathit{H}\rangle \pm |\mathit{V}\rangle )/\sqrt{2}$, and $|\mathit{R}/\mathit{L}\rangle =(|\mathit{H}\rangle \pm \mathit{i}|\mathit{V}\rangle )/\sqrt{2}$. The results of these measurements allow us to
tomographically reconstruct the density matrix ${\mathrm{\rho}}_{\text{bound}}^{\text{exp}}$. Fourfold coincidences were recorded for each
projective measurement.

To guarantee that the reconstruction algorithm does not allow unphysical results, we
used a maximum likelihood technique. Figure 4
shows the real parts of the elements of the density matrix ${\mathrm{\rho}}_{\text{bound}}^{\text{exp}}$ in the *H*/*V* basis.
We observe the symmetric form of the state in the
*H*/*V* basis, one peak on each of the four corners
and four peaks on the diagonal. The preparation fidelity of ${\mathrm{\rho}}_{\text{bound}}^{\text{exp}}$ is 95.4 ± 0.3%, and the fidelities of its
parts GHZ and projectors are 83.8 and 98.5%, respectively.

In Table 1, we list all eigenvalues of the
partially transposed density matrix of the tripartite quantum state
${\mathrm{\rho}}_{\mathit{A}\mathit{B}\mathit{C}}^{\text{exp}}$ corresponding to
*A*/*BC*, *B*/*AC*,
and *C*/*AB* cuts. For the two first cuts, all the
eigenvalues are positive, and in contrast, for the
*C*/*AB* cut, one eigenvalue is negative,
−0.118 ± 0.003, which implies that the state is bound entangled. The SD
of the obtained negative eigenvalue is 64σ (note that the theoretically
expected negativity is −0.1667). We have experimentally applied the witness
(Eq. 6) to our prepared state
${\mathrm{\rho}}_{\text{bound}}^{\text{exp}}$, and we have obtained the result
$\mathit{T}\mathit{r}({\mathcal{W}}_{\mathit{s}}{\mathrm{\rho}}_{\text{bound}}^{\text{exp}})=-0.4785$. The value of the witness for the ideal state bound
is ^{2}/_{3}. The difference is due to the imperfect interference in
the preparation of the GHZ part of the state. Note that this witness is the one that
provides the minimal value (−1) for the maximally entangled state where the
Bob qubit subspace is spanned by the two vectors |*HH* and
|*VV* and the Charlie subspace corresponds to the standard
basis {|*H*, |*V*}.

The superadditivity protocol is performed through a conditional teleportation (with
positive Hong-Ou-Mandel interference), where the party Alice performs a joint Bell
measurement on modes *A* and *A*′. Figure 5 shows the real parts of the elements of
the density matrix ${\mathrm{\rho}}_{(\mathit{B}{\mathit{B}}^{\prime})\mathit{C}}^{\text{exp}}$ of the state shared between Bob and Charlie in the
{|*H*, |*V*} basis. We observe the
symmetric form of the state, one peak on each of the four corners and four peaks on
the diagonal. The preparation fidelity of exp ${\mathrm{\rho}}_{(\mathit{B}{\mathit{B}}^{\prime})\mathit{C}}^{\text{exp}}$ is 92.8 ± 0.3%.

In Table 2, we list all eigenvalues of the
partially transposed density matrix of the bipartite quantum state
${\mathrm{\rho}}_{(\mathit{B}{\mathit{B}}^{\prime})\mathit{C}}^{\text{exp}}$ corresponding to the
*C*/*BB*′ cut. One can observe that one of
the eigenvalues is negative, −0.09 ± 0.003. The SD of the obtained
negative eigenvalue is 60σ. These results imply that the state
${\mathrm{\rho}}_{(\mathit{B}{\mathit{B}}^{\prime})\mathit{C}}^{\text{exp}}$ is free entangled and consequently demonstrate
superadditivity of quantum information resources and the bound entanglement
activation. We have experimentally applied the witness to the state after activation
and have obtained the result, −0.362. Again, this value is smaller compared to
the theoretical value of ^{2}/_{3}. The discrepancy is due to the
imperfection of the dip interference.

We have prepared for the first time a high-fidelity mixed three-qubit polarization bound entangled state. This state is the first experimental realization of a bound entangled state that can be used for generation of multipartite bound information. Using quantum state tomography, we have fully reconstructed its density matrix and demonstrated all its entanglement properties, which make this state useful for novel multiparty quantum communication schemes, for example, secret sharing and communication complexity reduction. We have also realized the activation scheme. The unique feature of quantum mechanics revealed by the present experiment is its something-out-of-nothing character: The ingredient completely absent in any of the two resources suddenly emerges after putting the two resources together. This phenomenon lies in the very heart of quantum information. We strongly believe that the results reported here will help in the development of novel quantum information and communication protocols and in the deeper understanding of foundations of quantum mechanics.

The three-photon polarization bound entangled state ρ_{bound} can be
obtained as follows: First, we generated the product of two photon pairs in maximally
entangled states ${|{\mathrm{\Psi}}^{+}\rangle}_{{\mathit{a}\mathit{a}}^{\prime}}=({|\mathit{H}\mathit{H}\rangle}_{\mathit{a}{\mathit{a}}^{\prime}}+{|\mathit{V}\mathit{V}\rangle}_{\mathit{a}{\mathit{a}}^{\prime}})/\sqrt{2}$ and ${|{\mathrm{\Psi}}^{+}\rangle}_{{\mathit{b}\mathit{b}}^{\prime}}=({|\mathit{H}\mathit{H}\rangle}_{{\mathit{b}\mathit{b}}^{\prime}}-{|\mathit{V}\mathit{V}\rangle}_{{\mathit{b}\mathit{b}}^{\prime}})/\sqrt{2}$ in modes (*a*,
*a*′) and (*b*, *b*′),
respectively, by SPDC sources (see Fig. 6) (*21*). The two-photon coincidence
rate of these SPDC processes is 2.2 × 10^{5}/s, and the fidelity
for${|{\mathrm{\Psi}}^{+}\rangle}_{\mathit{a}{\mathit{a}}^{\prime}}$ and ${|{\mathrm{\Psi}}^{+}\rangle}_{\mathit{b}{\mathit{b}}^{\prime}}\text{is}96\pm 1\%$. To prepare the three-qubit
|Ψ_{GHZ}, we used the quantum interference at PBS between the
modes in *a*′ and *b*′. To obtain the
indistinguishability of the photons in modes *a*′ and
*b*′, because of their arrival times, we adjusted the path
length of the photon in mode *b*′. The ${|{\mathrm{\Psi}}_{\text{GHZ}}\rangle}_{\mathit{A}\mathit{B}\mathit{C}}=({|\mathit{H}\mathit{H}\mathit{H}\rangle}_{\mathit{A}\mathit{B}\mathit{C}}+{|\mathit{V}\mathit{V}\mathit{V}\rangle}_{\mathit{A}\mathit{B}\mathit{C}})/\sqrt{2}$ was produced in modes *A*,
*B*, and *C*, when the photon in mode
*T* was successfully projected onto the diagonal linear polarization
state and conditioned by a click at the trigger detectors in mode *T*.
Second, to prepare the three-qubit mixed state, we placed an adjustable polarizer in
each of the four photonic paths *a*, *b*,
*a*′, and *b*′. These polarizers consist
of a PBS and three adjustable HWP. The settings of these plates for horizontal,
vertical, and both polarizations states were (45°,0°,0°),
(45°,0°,45°), and (0°,0°,0°), respectively. To
switch between the settings, these plates were mounted on motorized rotation stages (see
Fig. 6). All these settings were controlled by
random number generators to guarantee the needed probability for the preparation of each
of the terms of mixed bound entangled state. All measurements in the four modes
*A*, *B*, *C*, and *T*
were performed with polarization analysis components followed by single-photon detectors
(avalanche photodiode) and a multichannel coincidence unit. The dip interference
visibility was 83 ± 1%. The conditioned three-photon coincidence rate was 300/s.
For quantum state tomography, the measurement time for each setting was 60 s, which
gives an average of 18,000 threefold coincidence events by setting. We note that similar
techniques have been used for the preparation of a four-partite bound entangled state
(*22*–*24*).

To also check one-qubit/two-qubit separability, we constructed a witness
(*25*), with the form

$$\begin{array}{c}{\mathcal{W}}_{\mathit{s}}=\frac{1}{2}({\mathbb{1}}_{\mathit{A}}\otimes {\mathbb{1}}_{\mathit{B}}+{\mathrm{\sigma}}_{\mathit{A}}^{\mathit{z}}\otimes {\mathrm{\sigma}}_{\mathit{B}}^{\mathit{z}})\otimes {\mathbb{1}}_{\mathit{C}}\\ -\frac{1}{2}({\mathrm{\sigma}}_{\mathit{A}}^{\mathit{x}}\otimes {\mathrm{\sigma}}_{\mathit{B}}^{\mathit{x}}-{\mathrm{\sigma}}_{\mathit{A}}^{\mathit{y}}\otimes {\mathrm{\sigma}}_{\mathit{B}}^{\mathit{y}})\otimes {\mathrm{\sigma}}_{\mathit{C}}^{\mathit{x}}\\ +\frac{1}{2}({\mathrm{\sigma}}_{\mathit{A}}^{\mathit{x}}\otimes {\mathrm{\sigma}}_{\mathit{B}}^{\mathit{y}}+{\mathrm{\sigma}}_{\mathit{A}}^{\mathit{y}}\otimes {\mathrm{\sigma}}_{\mathit{B}}^{\mathit{x}})\otimes {\mathrm{\sigma}}_{\mathit{C}}^{\mathit{y}}\\ -\frac{1}{2}({\mathbb{1}}_{\mathit{A}}\otimes {\mathrm{\sigma}}_{\mathit{B}}^{\mathit{z}}-{\mathrm{\sigma}}_{\mathit{A}}^{\mathit{z}}\otimes {\mathbb{1}}_{\mathit{B}})\otimes {\mathrm{\sigma}}_{\mathit{C}}^{\mathit{z}}\end{array}$$

(6)

The activation setup consisted of a quantum interference between the photonic modes
*A* and *A*′ (see Fig. 7). We used a third maximally entangled polarization photon state in
modes *A*′ and *B*′ (created by a third SPDC
process) and the three-qubit bound entangled state in photonic modes *A*,
*B*, and *C*. This interference was realized with the
help of PBS and HWP plates set at 22.5°. To obtain the indistinguishability of
photons *A* and *A*′ due to their arrival times, we
adjusted the path length of the photon in mode *A*′. The zero
delay corresponded to the maximal overlap with a visibility of *V* = 83
± 1 %. The six folded coincidences corresponding to the detection of a photon in
each of the six spatial modes *B*, *B*′,
*C*, *T*, and two modes after the interference were
recorded for each projective measurements. The observed average rate of the six folded
coincidences was 1/s. The measurement time for each setting was 1 hour, which gives an
average of 3600 sixfold coincidence events by setting.

We thank R. Horodecki for helpful comments and useful discussions. **Funding:**
We acknowledge support from the Swedish Research Council (Vetenskapsrådet), the
Knut and Alice Wallenberg Foundation, and European Research Council Advanced Grant
QOLAPS. M.N. was supported by the international Ph.D. project “Physics of future
quantum-based information technologies” (grant MPD/2009-3/4) from the Foundation
for Polish Science. We also acknowledge support from the project Era-Net Chist-Era 7FP
UE. **Author contributions:** P.H. proposed and worked out the theory part of
the project. M.B., M.N., and S.M. designed the experiment. M.N. and S.M. performed and
analyzed the data. M.B. supervised the project. All the authors discussed the results
and wrote the manuscript. **Competing interests:** The authors declare that
they have no competing interests. **Data and materials availability:** All data
needed to evaluate the conclusions in the paper are present in the paper and/or the
Supplementary Materials. Additional data related to this paper may be requested from the
authors. Correspondence and requests for materials should be addressed to M.B.

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