Search

Assuming a well-behaving quantum-to-classical transition, measuring large quantum systems should be highly informative with low measurement-induced disturbance, while the coupling between system and measurement apparatus is fairly simple and weak. Here, we show that this is indeed possible within the formalism of quantum mechanics. We discuss an example of estimating the collective magnetization of a spin ensemble by simultaneous measuring three orthogonal spin directions. For the task of estimating the direction of a spin-coherent state, we find that the average guessing fidelity and the system disturbance are nonmonotonic functions of the coupling strength. Strikingly, we discover an intermediate regime for the coupling strength where the guessing fidelity is quasioptimal, while the measured state is almost not disturbed.

A variational scheme for the derivation of generalized, symmetry-induced continuity equations for Hermitian and non-Hermitian quantum mechanical systems is developed. We introduce a Lagrangian which involves two complex wave fields and whose global invariance under dilation and phase variations leads to a mixed continuity equation for the two fields. In combination with discrete spatial symmetries of the underlying Hamiltonian, the mixed continuity equation is shown to produce bilocal conservation laws for a single field. This leads to generalized conserved charges for vanishing boundary currents and to divergenceless bilocal currents for stationary states. The formalism reproduces the bilocal continuity equation obtained in the special case of $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics and paraxial optics.

It has been well established that the evolution of an isolated quantum system can appear as undergoing pure dephasing to an observer using an imperfect clock. In this work, we apply this theory to the transport phenomenon in open quantum systems. Starting with a system intrinsically undergoing nonunitary evolution in ideal time, we consider the effect of a realistic clock that approaches Gaussian distribution in the long-time limit. For quantum transport, it eventually leads to a general physical prediction: a stable probability current in a quantum transport system must be robust against any transformation that conforms with a simple formula given by an ideal Gaussian stationary clock. This understanding of quantum transport is demonstrated numerically in a topological insulator, where it also explains the robustness of the quantum Hall response against pure dephasing.

No-go theorems prove that, under reasonable assumptions, classical hidden-variable theories cannot reproduce the predictions of quantum mechanics. Traditional no-go theorems proved that hidden-variable theories cannot predict correctly the values of observables. Recent expectation no-go theorems prove that hidden-variable theories cannot predict the expectations of observables. We prove the strongest expectation-focused no-go theorem to date. It is optimal in the sense that the natural weakenings of the assumptions and the natural strengthenings of the conclusion make the theorem fail. The literature on expectation no-go theorems strongly suggests that the expectation-focused approach is more general than the value-focused one. We establish that the expectation approach is not more general.

Quantum coherence can be used to infer the presence of a detector without triggering it. Here we point out that, according to quantum mechanics, such interaction-free measurements cannot be perfect, i.e., in a single-shot experiment one has strictly positive probability to activate the detector. We formalize the extent to which such measurements are forbidden by deriving a trade-off relation between the probability of activation and the probability of an inconclusive interaction-free measurement. Our description of interaction-free measurements is theory independent and allows derivations of similar relations in models generalizing quantum mechanics. We provide the trade-off for the density cube formalism, which extends the quantum model by permitting coherence between more than two paths. The trade-off obtained hints at the possibility of perfect interaction-free measurements and indeed we construct their explicit examples. Such measurements open up a paradoxical possibility where we can learn by means of interference about the presence of an object in a given location without ever detecting a probing particle in that location. We therefore propose that absence of perfect interaction-free measurement is a natural postulate expected to hold in all physical theories. As shown, it holds in quantum mechanics and excludes the models with multipath coherence.

Quantum theory does not provide a unique definition for the joint probability of two noncommuting observables, which is the next important question after the Born's probability for a single observable. Instead, various definitions were suggested, e.g., via quasiprobabilities or via hidden-variable theories. After reviewing open issues of the joint probability, we relate it to quantum imprecise probabilities, which are noncontextual and are consistent with all constraints expected from a quantum probability. We study two noncommuting observables in a two-dimensional Hilbert space and show that there is no precise joint probability that applies for any quantum state and is consistent with imprecise probabilities. This contrasts with theorems by Bell and Kochen-Specker that exclude joint probabilities for more than two noncommuting observables, in Hilbert space with dimension larger than two. If measurement contexts are included into the definition, joint probabilities are not excluded anymore, but they are still constrained by imprecise probabilities.

In a recent paper [Phys. Rev. A 95, 052118 (2017)], the authors claim that our criticism, in Phys. Rev. A 94, 052125 (2016), to some quantum speed limit bounds for open quantum dynamics that appeared recently in literature are invalid. According to the authors, the problem with our analysis would be generated by an artifact of the finite-precision numerical calculations. We analytically show here that it is not possible to have any inconsistency associated with the numerical precision of calculations. Therefore, our criticism of the quantum speed limit bounds continues to be valid.

Since the enlightening proofs of quantum contextuality first established by Kochen and Specker, and also by Bell, various simplified proofs have been constructed to exclude the noncontextual hidden variable theory of our nature at the microscopic scale. The conflict between the noncontextual hidden variable theory and quantum mechanics is commonly revealed by Kochen-Specker sets of yes-no tests, represented by projectors (or rays), via either logical contradictions or noncontextuality inequalities in a state-(in)dependent manner. Here we propose a systematic and programmable construction of a state-independent proof from a given set of nonspecific rays in ${\mathbb{C}}^3$ according to their Gram matrix. This approach brings us a greater convenience in the experimental arrangements. Besides, our proofs in ${\mathbb{C}}^3$ can also be generalized to any higher-dimensional systems by a recursive method.

In 2001, Zurek derived the generic minimum scale $a_Z$ for the area of structures of Wigner's quantum phase distribution. Here we show by construction, using superoscillatory functions, that the Wigner distribution can locally show regular spotty structures on scales much below Zurek's scale $a_Z$. The price to pay for the presence of such structures is their exponential smallness. For the case we construct, there is no increased interferometric sensitivity from the presence of patches with superoscillatory structure in phase space.

We show that probability is locally conserved in discrete-time quantum walks, corresponding to a particle evolving in discrete space and time. In particular, for a spatial structure represented by an arbitrary directed graph, and any unitary evolution of a particle which respects that locality structure, we can define probability currents which also respect the locality structure and which yield the correct final probability distribution.

In his recent article [Phys. Rev. A 95, 060101(R) (2017)], Adler questions the usefulness of the bound found in our experimental search for genuine effects of hypercomplex quantum mechanics [Nat. Commun. 8, 15044 (2017)]. Our experiment was performed using a black-box (instrumentalist) approach to generalized probabilistic theories; therefore, it does not assume a priori any particular underlying mechanism. From that point of view our experimental results do indeed place meaningful bounds on the possible effects of “postquantum theories,” including quaternionic quantum mechanics. In his article, Adler compares our experiment to nonrelativistic and Möller formal scattering theories within quaternionic quantum mechanics. With a particular set of assumptions, he finds that quaternionic effects would likely not manifest themselves in general. Although these assumptions are justified in the nonrelativistic case, a proper calculation for relativistic particles is still missing. Here, we provide a concrete relativistic example of Klein-Gordon scattering wherein the quaternionic effects persist. We note that when the Klein-Gordon equation is formulated using a Hamiltonian formalism it displays a so-called “indefinite metric,” a characteristic feature of relativistic quantum wave equations. In Adler's example this is directly forbidden by his assumptions, and therefore our present example is not in contradiction to his work. In complex quantum mechanics this problem of an indefinite metric is solved in a second quantization. Unfortunately, there is no known algorithm for canonical field quantization in quaternionic quantum mechanics.

One of the most important and useful entropic uncertainty relations concerns a $d$-dimensional system and two mutually unbiased measurements. In such a setting, the sum of two information entropies is lower bounded by $lnd$. It has recently been shown that projective measurements subject to operational mutual unbiasedness can also be constructed in a continuous domain, with the help of periodic coarse graining. Here we consider the whole family of Rényi entropies applied to these discretized observables and prove that such a scheme does also admit the entropic uncertainty relations mentioned above.

We discuss how, in appropriately designed configurations, solenoids carrying a semifluxon can be used as topological energy barriers for charged quantum systems. We interpret this phenomenon as a consequence of the fact that such solenoids induce nodal lines in the wave function describing the charge, which on itself is a consequence of the Aharonov-Bohm effect. Moreover, we present a thought experiment with a cavity where two solenoids are sufficient to create bound states.

Feynman's sum-over-histories formulation of quantum mechanics has been considered a useful calculational tool in which virtual Feynman histories entering into a coherent quantum superposition cannot be individually measured. Here we show that sequential weak values, inferred by consecutive weak measurements of projectors, allow direct experimental probing of individual virtual Feynman histories, thereby revealing the exact nature of quantum interference of coherently superposed histories. Because the total sum of sequential weak values of multitime projection operators for a complete set of orthogonal quantum histories is unity, complete sets of weak values could be interpreted in agreement with the standard quantum mechanical picture. We also elucidate the relationship between sequential weak values of quantum histories with different coarse graining in time and establish the incompatibility of weak values for nonorthogonal quantum histories in history Hilbert space. Bridging theory and experiment, the presented results may enhance our understanding of both weak values and quantum histories.

We study how vacuum neutrino oscillations can be affected by a causal, nonlinear and state-dependent modification of quantum field theory that may be interpreted using the many-worlds formulation of quantum mechanics. The effect is induced by a Higgs-neutrino Yukawa interaction that causes a nonlinear interference between the neutrino mass eigenstates. This leads to a tiny change in the oscillation pattern of light, active neutrinos. At large baselines where the oscillations disappear, the nonlinear effect is also suppressed and does not source correlations between the mass eigenstates once they are entangled with the environment. Our example provides a way to compute effects of nonlinear quantum mechanics and field theory that may probe the possible physical reality of many worlds.

Wave-particle duality is a bizarre feature at the heart of quantum mechanics which refers to the mutually exclusive dual attributes of quantum objects as the wave and the particle. Quantum eraser presents a counterintuitive aspect of the wave-particle duality. In this paper, we show that quantum eraser can be quantitatively understood in terms of the recently developed duality-entanglement relation. In other words, we show that wave-particle-entanglement triality captures all the physics of the quantum erasure. We find that a controllable partial erasure of the which-path information is attainable, enabling the partial recovery of the quantum interference and extending the scope of the conventional quantum eraser protocols.

Producing contextual correlations in sequences of measurements on single quantum systems faces two major problems. One is the experimental difficulty of performing sequences of ideal measurements on high-dimensional quantum systems, a problem that also affects other forms of quantum temporal correlations. The other is the simulability with classical light of existing contextuality experiments with photons. Here, we introduce a scheme that solves both problems. We show that, by encoding quantum information in $n\ge 2$ indistinguishable bosons in $m\ge 2$ modes, targeting observables exploiting the bunching-antibunching of bosons, and performing ideal measurements by dispersively coupling these systems with auxiliary qubits, it is possible to realize sequential quantum measurements on high-dimensional quantum systems and produce contextuality which cannot be simulated by classical light, as it relies on indistinguishability and higher-order interference.

We analyze the structure of the space of temporal correlations generated by quantum systems. We show that the temporal correlation space under dimension constraints can be nonconvex. For the general case, we provide the necessary and sufficient dimension of a quantum system needed to generate a convex correlation space for a given scenario. We further prove that this dimension coincides with the dimension necessary to generate any point in the temporal correlation polytope. As an application of our results, we derive nonlinear inequalities to witness the nonconvexity for qubits and qutrits in the simplest scenario, and present an algorithm which can help to find the minimum for a certain type of nonlinear expressions under dimension constraints.

We revisit quantum-classical hybrid systems of the Sudarshan type under the light of Galilean covariance. We show that these kinds of hybrids cannot be given as a unitary representation of the Galilei group and at the same time conserve the total linear momentum unless the interaction term only depends on the relative canonical velocities.

We address the problem of reconstructing quantum theory from the perspective of an agent who makes bets about the outcomes of possible experiments. We build a general Bayesian framework that can be used to organize the agent's beliefs and update them when new information becomes available. Our framework includes as special cases classical and quantum probability theory, as well as other forms of probabilistic reasoning that may arise in future physical theories. Building on this framework, we develop a notion of an ideal experiment, which in quantum theory coincides with the notion of projective measurement. We then prove that, in every general Bayesian theory, ideal experiments must satisfy the exclusivity principle, a property of projective measurements that plays a central role in the characterization of quantum correlations. Our result suggests that the set of quantum correlations may be completely characterized in terms of Bayesian consistency conditions.