[Show abstract][Hide abstract]ABSTRACT: We report a method that exploits a connection between quantum contextuality and graph theory to reveal any form of quantum contextuality in high-precision experiments. We use this technique to identify a graph which corresponds to an extreme form of quantum contextuality unnoticed before and test it using high-dimensional quantum states encoded in the linear transverse momentum of single photons. Our results open the door to the experimental exploration of quantum contextuality in all its forms, including those needed for quantum computation.
[Show abstract][Hide abstract]ABSTRACT: We show that, regardless of the dimension of the Hilbert space, there exists no set of rays revealing state-independent contextuality with less than 13 rays. This implies that the set proposed by Yu and Oh in dimension three [Phys. Rev. Lett. 108, 030402 (2012)] is actually the minimal set in quantum theory. This contrasts with the case of Kochen-Specker sets, where the smallest set occurs in dimension four.
Full-text Article · Jun 2016 · Journal of Physics A Mathematical and Theoretical
[Show abstract][Hide abstract]ABSTRACT: Quantum nonlocality can be revealed "via local contextuality" in qudit-qudit
entangled systems with d > 2, that is, through the violation of inequalities
containing Alice-Bob correlations that admit a local description, and
Alice-Alice correlations (between the results of sequences of measurements on
Alice's subsystem) that admit a local (but contextual) description. A
fundamental question to understand the respective roles of entanglement and
local contextuality is whether nonlocality via local contextuality exists when
the parties have only qubit-qubit entanglement. Here we respond affirmatively
to this question. This result further clarifies the connection between
contextuality and nonlocality and opens the door for observing nonlocality via
local contextuality in actual experiments.
[Show abstract][Hide abstract]ABSTRACT: The qubit, the simplest quantum system and unit of quantum information, is sometimes compared to a "quantum coin": a coin with infinitely many sets of two sides which can only be tossed when specifying the desired set. However, this picture fails to capture the richness of the quantum world, where qubit measurements are not necessarily binary. Consequently, when pairs of entangled qubits are measured locally, quantum theory predicts correlations that can neither be explained as produced by locally tossing classical coins nor explained by locally tossing quantum coins. However, this last prediction was unconfirmed until now since it requires the observation of a very small effect on an almost perfectly entangled qubit-qubit state. Here we present an experiment on pairs of entangled photonic qubits violating by more than 8 standard deviations a new Bell-like correlation inequality, which is valid only for binary quantum measurements. By also providing device-independent evidences that our system is best described by two qubits, we prove that quantum measurements on a qubit can be fundamentally non-binary. Since non-binary measurements on a qubit cannot be sharp, this constitutes the first device-independent certification of a genuine generalized quantum measurement.
[Show abstract][Hide abstract]ABSTRACT: The free will theorem states that if experimenters have free will in the sense that their choices are not a function of the past, so must some elementary particles. The theorem goes beyond Bell's theorem as it connects the two fundamental resources behind quantum technologies: single-particle contextuality, which supplies the power for quantum computation, and two-particle non-locality, which allows for quantum secure communication. The theorem relies on three axioms: (i) There is a maximum speed for propagation of information, (ii) single particles can exhibit contextuality, (iii) two separated particles can exhibit Einstein-Podolsky-Rosen (EPR) correlations. Here we report the first experimental test of the free will theorem. We used pairs of hyper-entangled photons entangled in path and polarization and enforced the conditions for invoking axiom (i) by measuring each photon in a different laboratory. We certified axiom (ii) by testing the violation of the Peres-Mermin non-contextuality inequality and axiom (iii) by showing EPR correlations between the two laboratories. The three axioms imply an upper bound on the sum of the correlations among the outcomes of sequential measurements in the same laboratory and the correlations between the outcomes in both laboratories. We observed a violation of this bound by more than 66 standard deviations. This reveals that quantum non-locality can be produced when single-particle contextuality is combined with correlations which are not non-local by themselves. Our results demonstrate the resources needed for quantum computation and quantum secure communication simultaneously in the same experiment and open the door to quantum machines that efficiently achieve both tasks.
[Show abstract][Hide abstract]ABSTRACT: Contextuality provides a unifying paradigm for nonclassical aspects of
quantum probabilities and resources of quantum information. Unfortunately, most
forms of quantum contextuality remain experimentally unexplored due to the
difficulty of performing sequences of projective measurements on individual
quantum systems. Here we show that two-point correlations between dichotomic
compatible observables are sufficient to reveal any form of contextuality. This
allows us to design simple experiments that are more robust against
imperfections and easier to analyze, thus opening the door for observing
interesting forms of contextuality, including those requiring quantum systems
of high dimensions. In addition, this result allows us to connect contextuality
to communication complexity scenarios and reformulate a recent result relating
contextuality and quantum computation.
[Show abstract][Hide abstract]ABSTRACT: A unifying principle explaining the numerical bounds of quantum correlations
remains elusive despite the efforts devoted to identify it. Here we show that
these bounds are indeed not exclusive to quantum theory: for any abstract
correlation scenario with compatible measurements, a suited classical wave
theory produces probability distributions indistinguishable from those of
quantum theory, and therefore share the same bounds. We demonstrate this
finding by implementing classical microwaves propagating along meter-size
transmission-line circuits and reproduce the probabilities of three emblematic
quantum experiments. Our results show that what distinguishes quantum theory is
not the set of numerical bounds, but the fact that it is produced without the
resources used by classical systems. The implications of this observation are
discussed.
Full-text Article · Nov 2015 · Physical Review Letters
[Show abstract][Hide abstract]ABSTRACT: We present an implementation of photonic qubit precertification that performs
the delicate task of detecting the presence of a flying photon without
destroying its qubit state, allowing loss-sensitive quantum cryptography and
tests of nonlocality even over long distance. By splitting an incoming single
photon in two via parametric down-conversion, we herald the photon's arrival
from an independent photon source while preserving its quantum information with
up to $92.3\pm0.6$ % fidelity. With reduced detector dark counts,
precertification will be immediately useful in quantum communication.
Full-text Article · Oct 2015 · Physical Review Letters
[Show abstract][Hide abstract]ABSTRACT: Measurement scenarios containing events with relations of exclusivity represented by pentagons, heptagons,
nonagons, etc., or their complements are the only ones in which quantum probabilities cannot be described
classically. Interestingly, quantum theory predicts that the maximum values for any of these graphs cannot be
achieved in Bell inequality scenarios. With the exception of the pentagon, this prediction remained experimentally unexplored. Here we test the quantum maxima for the heptagon and the complement of the heptagon using three- and five-dimensional quantum states, respectively. In both cases, we adopt two different encodings: linear transverse momentum and orbital angular momentum of single photons. Our results exclude maximally noncontextual hidden-variable theories and are in good agreement with the maxima predicted by quantum theory.
[Show abstract][Hide abstract]ABSTRACT: Motivated by some recent news, a journalist asks a group of physicists:
"What's the meaning of the violation of Bell's inequality?" One physicist
answers: "It means that non-locality is an established fact". Another says:
"There is no non-locality; the message is that measurement outcomes are
irreducibly random". A third one says: "It cannot be answered simply on purely
physical grounds, the answer requires an act of metaphysical judgement".
Puzzled by the answers, the journalist keeps asking questions about quantum
theory: "What is teleported in quantum teleportation?" "How does a quantum
computer really work?" Shockingly, for each of these questions, the journalist
obtains a variety of answers which, in many cases, are mutually exclusive. At
the end of the day, the journalist asks: "How do you plan to make progress if,
after 90 years of quantum theory, you still don't know what it means? How can
you possibly identify the physical principles of quantum theory or expand
quantum theory into gravity if you don't agree on what quantum theory is
about?" Here we argue that it is becoming urgent to solve this too long lasting
problem. For that, we point out that the interpretations of quantum theory are,
essentially, of two types and that these two types are so radically different
that there must be experiments that, when analyzed outside the framework of
quantum theory, lead to different empirically testable predictions. Arguably,
even if these experiments do not end the discussion, they will add new elements
to the list of strange properties that some interpretations must have,
therefore they will indirectly support those interpretations that do not need
to have all these strange properties.
[Show abstract][Hide abstract]ABSTRACT: The interpretation of quantum theory is one of the longest-standing debates
in physics. Type-I interpretations see quantum probabilities as determined by
intrinsic properties of the world. Type-II interpretations see quantum
probabilities as not directly dealing with intrinsic properties of the world
but with relational experiences between an observer and the world. It is
usually believed that deciding between these two types cannot be made simply on
purely physical grounds but it requires an act of metaphysical judgement. Here
we show that, although the problem is undecidable within the framework of
quantum theory, it is decidable, under some assumptions, within the framework
of thermodynamics. We prove that type-I interpretations are incompatible with
the following assumptions: (i) the decision of which measurement is performed
on a quantum system can be made independently of the system, (ii) a quantum
system has limited memory, and (iii) Landauer's principle is valid. We consider
an ideal experiment in which an individual quantum system is submitted to a
sequence of quantum projective measurements that leave the system in pure
quantum states. We show that in any type-I interpretation satisfying (i)-(iii)
the system must reset its internal state, which implies that a minimum amount
of heat per measurement has to be dissipated into the system's environment. We
calculate a lower bound to the heat dissipated per measurement assuming that
the measurements are chosen from a set of size $2^n$. Then, we show that this
lower bound becomes infinite in the limit of $n$ tending to infinity. This
leads to the conclusion that either type-I interpretations are untenable or at
least one of the assumptions (i)-(iii) has to be abandoned.
[Show abstract][Hide abstract]ABSTRACT: Device-independent quantum communication will require a loophole-free violation of Bell inequalities.
In typical scenarios where line of sight between the communicating parties is not available, it is convenient
to use energy-time entangled photons due to intrinsic robustness while propagating over optical fibers. Here
we show an energy-time Clauser-Horne-Shimony-Holt Bell inequality violation with two parties separated
by 3.7 km over the deployed optical fiber network belonging to the University of Concepción in Chile.
Remarkably, this is the first Bell violation with spatially separated parties that is free of the postselection
loophole, which affected all previous in-field long-distance energy-time experiments. Our work takes a
further step towards a fiber-based loophole-free Bell test, which is highly desired for secure quantum
communication due to the widespread existing telecommunication infrastructure.
[Show abstract][Hide abstract]ABSTRACT: Contextuality is a fundamental feature of quantum theory and a necessary
resource for quantum computation and communication. It is therefore important
to investigate how large can contextuality be in quantum theory. Contextuality
witnesses can be expressed as a sum $S$ of $n$ probabilities, such that $1 \le
\alpha < \vartheta \le n$ are, respectively, the maximum of $S$ for
noncontextual theories and for the theory under consideration. A theory allows
for absolute maximal contextuality if it has scenarios in which
$\vartheta/\alpha$ tends to $n$. Here we show that quantum theory allows for
absolute maximal contextuality despite what is suggested by the examination of
the quantum violations of Bell and noncontextuality inequalities considered in
the past. Our proof is not constructive and does not single out explicit
scenarios. Nevertheless, we identify scenarios in which quantum theory allows
for almost absolute maximal contextuality.
[Show abstract][Hide abstract]ABSTRACT: Quantum theory introduces a cut between the observer and the observed system,
but does not provide a definition of what is an observer. Based on an
informational definition of observer, Grinbaum has recently predicted an upper
bound on bipartite correlations in the Clauser-Horne-Shimony-Holt (CHSH) Bell
scenario equal to 2.82537, which is slightly smaller than the Tsirelson bound
of standard quantum theory, but is consistent with all the available
experimental results. Not being able to exceed Grinbaum's limit would support
that quantum theory is only an effective description of a more fundamental
theory and would have a deep impact in physics and quantum information
processing. Here we present a test of the CHSH Bell inequality on photon pairs
in maximally entangled states of polarization in which a value 2.8276+-0.00082
is observed, violating Grinbaum's bound by 2.72 standard deviations and
providing the smallest distance with respect to Tsirelson's bound ever
reported, namely, 0.0008+-0.00082. This sets a new lower experimental bound for
Tsirelson's bound, strengthening the value of principles that predict
Tsirelson's bound as possible explanations of all natural limits of
correlations, and has important consequences for cryptographic security,
randomness certification, characterization of physical properties in
device-independent scenarios, and certification of quantum computation.
Full-text Article · Jun 2015 · Physical Review Letters
[Show abstract][Hide abstract]ABSTRACT: There is a tension in quantum theory between the existence of a widely
accepted way to axiomatize the theory and the lack of similarly accepted
intuitive principles from which the theory can be derived. This tension is
present at the very definition of what measurements are admissible. The usual
assumption is that all measurements which do not produce negative probabilities
are valid measurements. However, besides simplicity, there is no conceptional
reason for such an assumption. Here we show that this assumption leads to a
very particular prediction that can be experimentally tested: in certain
situations, the number of outcomes of a measurement is, by itself, a quantum
phenomenon. For reaching this conclusion, we consider minor modifications of
quantum theory in which all measurements are produced from quantum measurements
with a limited number of outcomes and classical measurements, and show that any
of these modifications is accessible to falsification by particular
high-precision Bell-type experiments. Our analysis reveals that the results of
previous experiments provide evidence that nature cannot be explained with the
simplest of these modifications in which all measurements are essentially
quantum dichotomic. This supports standard quantum theory versus a natural and
almost indistinguishable alternative, but leaves as an open challenge to
perform experiments which allow us to exclude other alternatives such as
essentially trichotomic quantum theories and more general dichotomic theories.
[Show abstract][Hide abstract]ABSTRACT: Device-independent (DI) quantum communication will require a loophole-free
violation of Bell inequalities. In typical scenarios where line-of-sight
between the communicating parties is not available, it is convenient to use
energy-time entangled photons due to intrinsic robustness while propagating
over optical fibers. Here we show an energy-time Clauser-Horne-Shimony-Holt
Bell inequality violation with two parties separated by 3.7 km over the
deployed optical fiber network belonging to the University of Concepci\'on in
Chile. Remarkably, this violation is free of the post-selection loophole
affecting all previous in-field long-distance energy-time experiments. Our work
takes a further step towards a fiber-based loophole-free Bell test, which is
highly desired for secure quantum communication due to the widespread existing
telecommunication infrastructure.
[Show abstract][Hide abstract]ABSTRACT: Clock synchronization for nonfaulty processes in multiprocess networks is indispensable for a variety of technologies. A reliable system must be able to resynchronize the nonfaulty processes upon some components failing causing the distribution of incorrect or conflicting information in the network. The task of synchronizing such networks is related to Byzantine agreement (BA), which can classically be solved using recursive algorithms if and only if less than one-third of the processes are faulty. Here we introduce a nonrecursive quantum algorithm, based on a quantum solution of the detectable BA, which achieves clock synchronization in the presence of arbitrary many faulty processes by using only a single quantum system.
[Show abstract][Hide abstract]ABSTRACT: We solve the problem of whether a set of quantum tests reveals
state-independent contextuality and use this result to identify the simplest
set of minimal dimension. We also show that identifying state-independent
contextuality graphs [R. Ramanathan and P. Horodecki, Phys. Rev. Lett. 112,
040404 (2014)] is not sufficient for revealing state-independent contextuality.