Measurements transfer information about a system to the apparatus, and then further on -- to observers and (often inadvertently) to the environment. I show that even imperfect copying essential in such situations restricts possible unperturbed outcomes to an orthogonal subset of all possible states of the system, thus breaking the unitary symmetry of its Hilbert space implied by the quantum superposition principle. Preferred outcome states emerge as a result. They provide framework for the ``wavepacket collapse'', designating terminal points of quantum jumps, and defining the measured observable by specifying its eigenstates. In quantum Darwinism, they are the progenitors of multiple copies spread throughout the environment -- the fittest quantum states that not only survive decoherence, but subvert it into carrying information about them -- into becoming a witness.
The coherence-breaking channels play a significant role in quantum information theory. We study the coherence-breaking channels and give a method to amend the coherence-breaking channels by applying unitary operations. For given incoherent channel $Φ$, we give necessary and sufficient conditions for the channel to be a coherence-breaking channel and amend it via unitary operations. For qubit incoherent channels $Φ$ that are not coherence-breaking ones, we consider the mapping $Φ\circΦ$ and present the conditions for coherence-breaking and channel amendment as well.
We consider Markovian dynamics of a finitely dimensional open quantum system featuring a weak unitary symmetry, i.e., when the action of a unitary symmetry on the space of density matrices commutes with the master operator governing the dynamics. We show how to encode the weak symmetry in quantum stochastic dynamics of the system by constructing a weakly symmetric representation of the master operator: a symmetric Hamiltonian, and jump operators connecting only the symmetry eigenspaces with a fixed eigenvalue ratio. In turn, this representation simplifies both the construction of the master op…
The explicit dynamics of the moments for the GKSL equation is obtained. In our case the GKSL equation corresponds to Poisson stochastic processes which lead to unitary jumps. We consider squeeze operators as the unitary jumps.
Energy level splitting from the unitary limit of contact interactions to the near unitary limit for a few identical atoms in an effectively one-dimensional well can be understood as an example of symmetry breaking. At the unitary limit in addition to particle permutation symmetry there is a larger symmetry corresponding to exchanging the $N!$ possible orderings of $N$ particles. In the near unitary limit, this larger symmetry is broken, and different shapes of traps break the symmetry to different degrees. This brief note exploits these symmetries to present a useful, geometric analogy with gr…
A recent experiment by Minev et. al [arXiv:1803.00545] demonstrated that in a dissipative (artificial) 3-level atom with strongly intermittent dynamics it is possible to "catch and reverse" a quantum jump "mid-flight": by the conditional application of a unitary perturbation after a fixed time with no jumps, the system was prevented from getting shelved in the dark state, thus removing the intermittency from the dynamics. Here we offer an interpretation of this phenomenon in terms of the dynamical large deviation formalism for open quantum dynamics. In this approach, intermittency is seen as t…
We report a bulk optics experiment demonstrating the possibility of restoring the entanglement distribution through noisy quantum channels by inserting a suitable unitary operation (filter) in the middle of the transmission process. We focus on two relevant classes of single-qubit channels consisting in repeated applications of rotated phase damping or rotated amplitude damping maps, both modeling the combined Hamiltonian and dissipative dynamics of the polarization state of single photons. Our results show that interposing a unitary filter between two noisy channels can significantly improve …
An unknown quantum state of a single system cannot be discovered, as a measured system is reprepare: it jumps into an eigenstate of the measured observable. This impossibility of finding the quantum state and other symptoms usually blamed on wave-packet collapse follow (as was recently demonstrated for pure states of measured systems) from unitarity (which does not, however, allow for a literal collapse) and from the repeatability of measurements: Continuous unitary evolution and repeatability suffice to establish the discreteness that underlies quantum jumps. Here we consider mixed states of …
We pose and resolve a seeming paradox about spontaneous symmetry breaking in the quantum theory of infinite systems. For a symmetry to be spontaneously broken, it must not be implementable by a unitary operator. But Wigner's theorem guarantees that every symmetry is implemented by a unitary operator that preserves transition probabilities between pure states. We show how it is possible for a unitary operator of this sort to connect the folia of unitarily inequivalent representations. This result undermines interpretations of quantum theory that hold unitary equivalence to be necessary for phys…
Quantum adiabatic evolutions find a broad range of applications in quantum physics and quantum technologies. The traditional form of the quantum adiabatic theorem limits the speed of adiabatic evolution by the minimum energy gaps of the system Hamiltonian. Here, we experimentally show using a nitrogen-vacancy center in diamond that, even in the presence of vanishing energy gaps, quantum adiabatic evolution is possible. This verifies a recently derived necessary and sufficient quantum adiabatic theorem and offers paths to overcome the conventionally assumed constraints on adiabatic methods. By …
We show that there exist Gaussian channels which are amendable. A channel is amendable if when applied twice is entanglement breaking while there exists a unitary filter such that, when interposed between the first and second action of the map, prevents the global transformation from being entanglement breaking [Phys. Rev. A 86, 052302 (2012)]. We find that, depending on the structure of the channel, the unitary filter can be a squeezing transformation or a phase shift operation. We also propose two realistic quantum optics experiments where the amendability of Gaussian channels can be verifie…
It has been recently proved that a quantum jump may be reversed by a unitary process provided the initial state is restricted by some conditions. The application of such processes for preventing decoherence, for example in quantum computers, was suggested. We shall show that in the situation when the quantum jump is reversible it supplies no information about the initial state additional to the information known beforehand. Therefore the reversibility of this type does not contradict the general statement of quantum measurement theory: a measurement cannot be reversed. As a consequence of this…
We show a new remarkable connection between the symmetric form of a quantum stochastic differential equation (QSDE) and the strong resolvent limit of Schrödinger equations in Fock space: the strong resolvent limit is unitary equivalent to QSDE in the adapted (or Ito) form, and the weak limit is unitary equivalent to the symmetric (or Stratonovich) form of QSDE. We prove that QSDE is unitary equivalent to a symmetric boundary value problem for the Schrödinger equation in Fock space. The boundary condition describes standard jumps of the phase and amplitude of components of Fock vectors belongin…
We study a set of new functionals (called entanglement--breaking indices) which characterize how many local iterations of a given (local) quantum channel are needed in order to completely destroy the entanglement between the system of interest over which the transformation is defined and an external ancilla. The possibility of contrasting the noisy effects introduced by the channel iterations via the action of intermediate ({\it filtering}) transformations is analyzed. We provide some examples in which our functionals can be exactly calculated. The differences between unitary and non-unitary f…
Dual-unitary quantum circuits can be used to construct 1+1 dimensional lattice models for which dynamical correlations of local observables can be explicitly calculated. We show how to analytically construct classes of dual-unitary circuits with any desired level of (non-)ergodicity for any dimension of the local Hilbert space, and present analytical results for thermalization to an infinite-temperature Gibbs state (ergodic) and a generalized Gibbs ensemble (non-ergodic). It is shown how a tunable ergodicity-inducing perturbation can be added to a non-ergodic circuit without breaking dual-unit…
Under unitary evolution, systems move gradually from state to state. An unstable atom has amplitude in its original state after many lifetimes ($τ_L$). But in the laboratory, transitions seem to go instantaneously, as suggested by the term "quantum jump." The problem studied here is whether the "jump" can be assigned a duration, in theory and in experiment. Two characteristic times are defined, jump time ($τ_J$) and passage time ($τ_P$). Both use Zeno time, $τ_Z$, defined in terms of $H$ and its initial state as $τ_Z \equiv \hbar/\sqrt{<ψ| (H-E_ψ)^2 |ψ>}$, with $E_ψ\equiv <ψ|H|ψ>$. $τ_J$ is de…
Continuous-time quantum error correction (CTQEC) is a technique for protecting quantum information against decoherence, where both the decoherence and error correction processes are considered continuous in time. Given any [[n,k,d]] quantum stabilizer code, we formulate a class of protocols to implement CTQEC, involving weak coherent measurements and weak unitary corrections. Under this formalism, we show that the minimal required size of the ancillary system is n-k+1 qubits, and we propose one scheme that meets this minimal requirement. Furthermore, we compare our method with other known sche…
Quantum mechanics still provides new unexpected effects when considering the transport of energy and information. Models of continuous time quantum walks, which implicitly use time-reversal symmetric Hamiltonians, have been intensely used to investigate the effectiveness of transport. Here we show how breaking time-reversal symmetry of the unitary dynamics in this model can enable directional control, enhancement, and suppression of quantum transport. Examples ranging from exciton transport to complex networks are presented. This opens new prospects for more efficient methods to transport ener…
From barren plateaus through fertile valleys: Conic extensions of parameterised quantum circuits
Institut für Theoretische Physik Leibniz Universität Hannover（汉诺威莱布尼茨大学理论物理研究所）；Institute for Quantum Information RWTH Aachen University（亚琛工业大学量子信息研究所）
We generalize the hidden symmetry-breaking picture of symmetry-protected topological (SPT) order developed by Kennedy and Tasaki in the context of the Haldane phase. Our generalization applies to a wide class of SPT phases in one-dimensional spin chains, protected by an on-site representation of a finite abelian group. This generalization takes the form of a non-local unitary map that relates local symmetry-respecting Hamiltonians in an SPT phase to local Hamiltonians in a symmetry-broken phase. Using this unitary, we establish a relation between the two-point correlation functions that charac…
Topological matter exhibits exotic properties yet phases characterized by large topological invariants are difficult to implement, despite rapid experimental progress. A promising route toward higher topological invariants is via engineered Floquet systems, particularly in photonics, where flexible control holds the potential of extending the study of conventional topological matter to novel regimes. Here we implement a one-dimensional photonic quantum walk to explore large winding numbers. By introducing partial measurements and hence loss into the system, we detect winding numbers of three a…
Our goal is the discussion of the problem of mathematical interpretation of basic postulates (or `principles') of Quantum Mechanics: transitions to quantum stationary orbits, the wave-particle duality, and the probabilistic interpretation, in the context of semiclassical self-consistent Maxwell--Schrödinger equations. We discuss possible relations of these postulates to the theory of attractors of Hamiltonian nonlinear PDEs and to a new general mathematical conjecture on global attractors of G-invariant nonlinear Hamiltonian partial differential equations with a Lie symmetry group G. This conj…
We show that in the collision of two superfluid fermionic atomic clouds one observes the formation of quantum shock waves as discontinuities in the number density and collective flow velocity. Domain walls, which are topological excitations of the superfluid order parameter, are also generated and exhibit abrupt phase changes by $π$ and slower motion than the shock waves. The domain walls are distinct from the gray soliton train or number density ripples formed in the wake of the shock waves and observed in the collisions of superfluid bosonic atomic clouds. Domain walls with opposite phase ju…
We define the hitting time for a model of continuous-time open quantum walks in terms of quantum jumps. Our starting point is a master equation in Lindblad form, which can be taken as the quantum analogue of the rate equation for a classical continuous-time Markov chain. The quantum jump method is well known in the quantum optics community and has also been applied to simulate open quantum walks in discrete time. This method however, is well-suited to continuous-time problems. It is shown here that a continuous-time hitting problem is amenable to analysis via quantum jumps: The hitting time ca…
In this work spontaneous (non-dynamical) breaking (effective hiding) of the unitary quantum mechanical dynamical symmetry (superposition) is considered. It represents an especial but very interesting case of the general formalism of the spontaneous symmetry breaking (effective hiding). Conceptual analogies with spontaneous breaking of the gauge symmetry in Weinberg-Sallam's electro-weak interaction are pointed out. Also, consequences of the spontaneous superposition breaking in the measurement process are discussed. Measurement can be considered as a typical Landau's continuous phase transitio…
The scaling symmetry in conformal quantum mechanics (CQM) can be broken due to the boundary conditions that follow from the requirement of a unitary time evolution of the Hamiltonian. We show that the scaling symmetry of CQM can be restored by introducing a suitable mixed state, which is associated with a nonvanishing von Neumann entropy. We give an explicit formula for the entropy arising from the mixed state in CQM. Our work provides a direct link between the restoration of a broken symmetry and von Neumann entropy.
QiNN-QJ: A Quantum-inspired Neural Network with Quantum Jump for Multimodal Sentiment Analysis
School of Engineering, Yunnan University（云南大学工程学院）；College of Computer and Data Science, Fuzhou University（福州大学计算机与数据科学学院）；Institute of Cyber-Systems and Control, College of Control Science and Engineering, Zhejiang University（浙江大学控制科学与工程学院智能系统与控制研究所）；Australian Artificial Intelligence Institute, Faculty of Engineering and Information Technology, University of Technology Sydney（新南威尔士大学人工智能研究所）
Understanding which physical processes are symmetric with respect to time inversion is a ubiquitous problem in physics. In quantum physics, effective gauge fields allow emulation of matter under strong magnetic fields, realizing the Harper-Hofstadter, the Haldane models, demonstrating one-way waveguides and topologically protected edge states. Central to these discoveries is the chirality induced by time-symmetry breaking. In quantum walk algorithms, recent work has discovered implications time-reversal symmetry breaking has on the transport of quantum states which has enabled a host of new ex…
We examine the dynamics of a qubit stored in the motional degrees of freedom of an ultra-cold ion in an ion trap which is subject to the decoherence effects of a finite-temperature bath. We discover an encoding of the qubit, in two of the motional modes of the ion, which is stable against the occurrence of either none or one quantum jump. For the case of a zero-temperature bath we describe how to transfer only the information concerning the occurrence of quantum jumps and their types to a measuring apparatus, without affecting the ion's motional state significantly. We then describe how to gen…
We give an explicit stochastic Hamiltonian model of discontinuous unitary evolution for quantum spontaneous jumps like in a system of atoms in quantum optics, or in a system of quantum particles that interacts singularly with "bubbles" which admit a continual counting observation. This model allows to watch a quantum trajectory in a photodetector or in a cloud chamber by spontaneous localisations of the momentums of the scattered photons or bubbles. Thus, the continuous reduction and spontaneous localization theory is obtained from a Hamiltonian singular interaction as a result of quantum filt…
The passive states of a quantum system minimize the average energy among all the states with a given spectrum. We prove that passive states are the optimal inputs of single-jump lossy quantum channels. These channels arise from a weak interaction of the quantum system of interest with a large Markovian bath in its ground state, such that the interaction Hamiltonian couples only consecutive energy eigenstates of the system. We prove that the output generated by any input state $ρ$ majorizes the output generated by the passive input state $ρ_0$ with the same spectrum of $ρ$. Then, the output gen…
Topological phases and the associated multiple edge states are studied for parity and time-reversal $(\mathcal{PT})$ symmetric non-Hermitian open quantum systems by constructing a non-unitary three-step quantum walk retaining $\mathcal{PT}$ symmetry in one dimension. We show that the non-unitary quantum walk has large topological numbers of the $\mathbb{Z}$ topological phase and numerically confirm that multiple edge states appear as expected from the bulk-edge correspondence. Therefore, the bulk-edge correspondence is valid in this case. Moreover, we study the stability of the multiple edge s…
We investigate unitary operators acting on a tensor product space, with the property that the quantum channels they generate, via the Stinespring dilation theorem, are of a particular type, independently of the state of the ancilla system in the Stinespring relation. The types of quantum channels we consider are those of interest in quantum information theory: unitary conjugations, constant channels, unital channels, mixed unitary channels, PPT channels, and entanglement breaking channels. For some of the classes of bipartite unitary operators corresponding to the above types of channels, we p…
Electronic structure methods typically benefit from symmetry breaking and restoration, specially in the strong correlation regime. The same goes for Ansätze on a quantum computer. We develop a unitary coupled cluster method on the antisymmetrized geminal power (AGP) -- a state formally equivalent to the number-projected Bardeen--Cooper--Schrieffer wavefunction. We demonstrate our method for the single-band Fermi--Hubbard Hamiltonian in one and two dimensions. We also explore post-selection as a state preparation step to obtain correlated AGP and prove that it scales no worse than $\mathcal{O}(…
Characterizing quantum channels from local-unitary invariants
Institute for Quantum Inspired and Quantum Optimization, Hamburg University of Technology（汉堡工业大学量子启发与量子优化研究所）；University of Tsukuba（筑波大学）；Center for Artificial Intelligence Research (C-AIR), University of Tsukuba（筑波大学人工智能研究中心）
A hallmark of topological band theory in periodic media is that bulk properties are not affected by boundary conditions. Remarkably, in certain non-Hermitian lattices the bulk properties are largely affected by boundaries, leading to such major effects as the non-Hermitian skin effect and violation of the bulk-boundary correspondence. Here we unveil that non-unitary discrete-time quantum walks of photons in systems involving gain and loss show rather generally non-Bloch parity-time ($\mathcal{PT}$) symmetry breaking phase transitions, and suggest a bulk probing method to detect such boundary-d…
It has been proposed that measurement in quantum mechanics results from spontaneous breaking of a symmetry of the measuring apparatus and could be a unitary process that preserves coherence. Viewed in this manner, it is argued, non-destructive measurements should preserve this coherence and be reversible. It is shown that experiments with maximally entangled bipartite states can indeed distinguish between projective and unitary measurements.
We study the current-carrying steady-state of a transverse field Ising chain coupled to magnetic thermal reservoirs and obtain the non-equilibrium phase diagram as a function of the magnetization potential of the reservoirs. Upon increasing the magnetization bias we observe a discontinuous jump of the magnetic order parameter that coincides with a divergence of the correlation length. For steady-states with a non-vanishing conductance, the entanglement entropy at zero temperature displays a bias dependent logarithmic correction that violates the area law and differs from the well-known equilib…
Emergence of the classical world from the quantum substrate of our Universe is a long-standing conundrum. I describe three insights into the transition from quantum to classical that are based on the recognition of the role of the environment. I begin with derivation of preferred sets of states that help define what exists - our everyday classical reality. They emerge as a result of breaking of the unitary symmetry of the Hilbert space which happens when the unitarity of quantum evolutions encounters nonlinearities inherent in the process of amplification - of replicating information. This der…
