X. -F. Qian, K. Konthasinghe, S. K. Manikandan, D. Spiecker, A. N. Vamivakas, J. H. Eberly
We experimentally observe that quantum duality of a single photon is controlled by its self-entanglement through a three-way quantum coherence identity $V^2+D^2+C^2=1$. Here V, D, C represent waveness, particleness, and self-entanglement respectively.
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We establish duality for monogamy of entanglement: whereas monogamy of entanglement inequalities provide an upper bound for bipartite sharability of entanglement in a multipartite system, we prove that the same quantity provides a \emph{lower} bound for distribution of bipartite entanglement in a multipartite system. Our theorem for monogamy of entanglement is used to establish relations between bipartite entanglement that separate one qubit from the rest vs separating two qubits from the rest.
Entanglement constraint on wave-particle duality for tripartite systems
本文研究三方系统中全局纠缠对定量波粒二象性的约束关系，并通过 OriginQ 量子计算云平台进行量子态层析实验，从理论和实验两方面证实了该约束的存在。
Entanglement duality in spin-spin interactions
该研究通过分析外磁场中自旋-1/2二聚体的热态纠缠，发现自旋-自旋相互作用的纠缠对偶性，将二聚体分为对称与反对称两类并归入环面纠缠类，揭示了纠缠的拓扑本质。
It was shown recently that entanglement of identical particles has a feature called dualism [Phys. Rev. Lett. 110, 140404 (2013)], which is fundamentally connected with quantum indistinguishability. Here we report an experiment that observes the entanglement duality for the first time with two identical photons, which manifest polarization entanglement when labeled by different paths or path entanglement when labeled by polarization states. By adjusting the mismatch in frequency or arrival time of the entangled photons, we tune the photon indistinguishability from quantum to classical limit an…
Polarization-orbital angular momentum duality assisted entanglement observation for indistinguishable photons
本研究利用参量下转换产生的不可区分光子的偏振与轨道角动量（OAM）变量，演示了全同粒子纠缠的对偶性，提出了对偶辅助的纠缠观测方法，可验证量子不可区分性在信道中的保持，为分布式量子传感和远程纠缠生成提供研究基础。
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 work, 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 attain…
We investigate duality in entanglement of a bipartite multi-photon system generated from a coherent state of light. The system can exhibit polarization entanglement if the two parts are distinguished by their parity, or parity entanglement if the parts are distinguished by polarization. It was shown in [PRL 110, 140404 (2013)] that this phenomenon can be exploited as a method to test indistinguishability of two particles and it was conjectured that one can also test indistinguishability of macroscopic systems. We propose a setup to test this conjecture. Contrary to the previous studies using t…
We experimentally verify the link existing between entanglement and the amount of wave-particle duality in a bipartite quantum system, with superconducting qubits in the IBM Q quantum computer. We consider both pure and mixed states, and study the influence of state purity on the observation of the complementarity "triality" relation of Jakob and Bergou. This work confirms the quantitative completion of local Bohr's complementarity principle by the nonlocal quantum entanglement typical of a truly bipartite quantum system.
We predict that if internal and momentum states of an interfering object are correlated (entangled), then by measuring its internal state we may infer both path (corpuscular) and phase (wavelike) information with much higher precision than for objects lacking such entanglement. We thereby partly circumvent the standard complementarity constraints of which-path detection.
The simplest single-photon entanglement is the entanglement of the vacuum state and the single-photon state between two path modes. The verification of the existence of single-photon entanglement has attracted extensive research interests. Here, based on the construction of Bell's inequality in wave space, we propose a new method to verify single photon entanglement. Meanwhile, we define the wave state in two-dimensional space relative to the photon number state, and propose a method to measure it. Strong violation of Bell inequality based on joint measurement of wave states indicates the exis…
The entanglement between two bosons or fermions can be accessed if there exists an auxiliary degree of freedom which can be used to label and effectively distinguish the two particles. For some types of entanglement between two indistinguishable particles one can observe duality, i.e., if the entanglement is present in the Hilbert space H and an auxiliary Hilbert space H' is used to label the particles, then if we used H as a label the entanglement would be present in H'. For distinguishable particles this effect does not occur because of superselection rules which prevent superpositions of di…
Recent times have seen a spurt of research activity focused on "completing" certain wave-particle duality relations using entanglement or polarization. These studies use a duality relation involving path-predictability, and not path-distinguishability. Quantum origins of these results are explored here, in the more general framework of multipath quantum interference. Multipath interference with a path-detector is theoretically analyzed to find the connection between predictability and distinguishability. It is shown that entanglement is what quantitatively connects distinguishability with pred…
We consider four norms on tensor product spaces that have appeared in quantum information theory and demonstrate duality relationships between them. We show that the product numerical radius is dual to the robustness of entanglement, and we similarly show that the S(k)-norm is dual to the projective tensor norm. We show that, analogous to how the product numerical radius and the S(k)-norm characterize k-block positivity of operators, there is a natural version of the projective tensor norm that characterizes Schmidt number. In this way we obtain an elementary new proof of the cross norm criter…
We investigate the transformation of entanglement entropy under dualities, using the Kramers-Wannier duality present in the transverse field Ising model as our example. Entanglement entropy between local spin degrees of freedom is not generically preserved by the duality; instead, entangled states may be mapped to states with no local entanglement. To understand the fate of this entanglement, we consider two quantitative descriptions of degrees of freedom and their transformation under duality. The first involves Kraus operators implementing the partial trace as a quantum channel, while the se…
We point out an earlier unnoticed implication of quantum indistinguishability, namely, a property which we call `dualism' that characterizes the entanglement of two identical particles (say, two ions of the same species) -- a feature which is absent in the entanglement of two non-identical particles (say, two ions of different species). A crucial application of this property is that it can be used to test quantum indistinguishability without bringing the relevant particles together, thereby avoiding the effects of mutual interaction. This is in contrast to the existing tests of quantum indisti…
The aim of this paper is to revisit the implications of complementarity when we inject into a Mach Zehnder interferometer particles with internal structure, prepared in special translational-internal entangled (TIE) states. This correlation causes the path distinguishability to be phase dependent in contrast to the standard case. We show that such a TIE state permits us to detect small phase shifts along with almost perfect path distinguishability, beyond the constraints imposed by complementarity on simultaneous which-way and which-phase measurements for standard cases (when distinguishabilit…
Implementation of controlled-rotations using entanglement is considered. We show that the successful probability is closely related to the entanglement and the rotation angle. The successful probability will increase if we increase the entanglement we use or decrease the controlled-rotation angle and the probability will trend to unit when the entangled state trends to a Bell state or the controlled-rotation angle trends to zero.
Quantum Wave-Particle Duality in Free-Electron--Free-Electron Entanglement
该研究通过相对论两电子波包理论，建立自由电子量子波包尺寸与电磁耦合产生的纠缠的直接联系，发现自由漂移可增大QEW宽度以增强纠缠，确立了自由电子波粒二象性与二分纠缠的关联。
We demonstrate controlled entanglement routing between bunching and antibunching path-entangled two-photon states in an unbalanced Mach-Zehnder interferometer (UMZI), in which the routing process is controlled by the relative phase difference in the UMZI. Regarding bunching and antibunching path-entangled two-photon states as two virtual ports, we can consider the UMZI as a controlled entanglement router, which bases on the coherent manipulation of entanglement. Half of the entanglement within the input two-photon state is coherently routed between the two virtual ports, while the other is los…
Kang et al. [Chin. Phys. B 24 (2015) 090306] proposed a controlled mutual quantum entity authentication protocol. We find that the proposed protocol is not secure, that is, Charlie can eavesdrop the shared keys between Alice and Bob without being detected.
We find the nearest product states for arbitrary generalized W states of n qubits, and show that the nearest product state is essentially unique if the W state is highly entangled. It is specified by a unit vector in Euclidean n-dimensional space. We use this duality between unit vectors and highly entangled W states to find the geometric measure of entanglement of such states.
We investigate the minimum entanglement cost of the deterministic implementation of two-qubit controlled-unitary operations using local operations and classical communication (LOCC). We show that any such operation can be implemented by a three-turn LOCC protocol, which requires at least 1 ebit of entanglement when the resource is given by a bipartite entangled state with Schmidt number 2. Our result implies that there is a gap between the minimum entanglement cost and the entangling power of controlled-unitary operations. This gap arises due to the requirement of implementing the operations w…
We propose a method for generation of genuine multipartite entangled states in a short-range Ising spin chain with periodic global pulses of magnetic field. We consider an integrable and a non-integrable Floquet system that are periodic in time and have constant quasi-energy gaps with degeneracies. We start with all spins polarized along one direction and show that they evolve into states with high entanglement by calculating the average entanglement entropy and geometric measure of entanglement. We show that some of these states have a high number of parties involved in the entanglement by ca…
We propose an alternative scenario for the generation of entanglement between rotational quantum states of two polar molecules. This entanglement arises from dipole-dipole interaction, and is controlled by a sequence of laser pulses simultaneously exciting both molecules. We study the efficiency of the process, and discuss possible experimental implementations with cold molecules trapped in optical lattices or in solid matrices. Finally, various entanglement detection procedures are presented, and their suitability for these two physical situations is analyzed.
We consider a system of multiple qubits without any quantum control. We show that one can mediate entanglement between different subsystems in a controlled way by adding a (locally) controlled auxiliary system of the same size that couples via an always-on, distant dependent interaction to the system qubits. Solely by changing the internal state of the control system, one can selectively couple it to selected qubits, and ultimately generate different kinds of entanglement within the system. This provides an alternative way for quantum control and quantum gates that does not rely on the ability…
The dual of an entanglement-assisted quantum error-correcting (EAQEC) code is defined from the orthogonal group of a simplified stabilizer group. From the Poisson summation formula, this duality leads to the MacWilliams identities and linear programming bounds for EAQEC codes. We establish a table of upper and lower bounds on the minimum distance of any maximal-entanglement EAQEC code with length up to 15 channel qubits.
Quantum entanglement is essential to the development of quantum computation, communications, and technology. The controlled SWAP test, widely used for state comparison, can be adapted to an efficient and useful test for entanglement of a pure state. Here we show that the test can evidence the presence of entanglement (and further, genuine n-qubit entanglement), can distinguish entanglement classes, and that the concurrence of a two-qubit state is related to the test's output probabilities. We also propose a multipartite measure of entanglement that acts similarly for n-qubit states. The number…
This is a perspective on "k-stretchability of entanglement, and the duality of k-separability and k-producibility" by Szilárd Szalay, published in Quantum 3, 204 (2019).
Usually duality process keeps energy spectrum invariant. In this paper, we provide a duality, which keeps entanglement spectrum invariant, in order to diagnose quantum entanglement of non-Hermitian non-interacting fermionic systems. We limit our attention to non-Hermitian systems with a complete set of biorthonormal eigenvectors and an entirely real energy spectrum. The original system has a reduced density matrix $ρ_\mathrm{o}$ and the real space is partitioned via a projecting operator $\mathcal{R}_{\mathrm o}$. After dualization, we obtain a new reduced density matrix $ρ_{\mathrm{d}}$ and a…
Using a single circular Rydberg atom, we have prepared two modes of a superconducting cavity in a maximally entangled state. The two modes share a single photon. This entanglement is revealed by a second atom probing, after a delay, the correlations between the two modes. This experiment opens interesting perspectives for quantum information manipulation and fundamental tests of quantum theory.
We propose an exact equivalence between the entanglement spectra of two completely different free-fermion systems at zero temperature. This equivalence follows from a position-momentum duality where the physical roles of the occupied band and real space projectors are exchanged. We examine the physical consequences of this duality in multi-band models, and as an example also physically motivate the equivalence of the entanglement spectrum of a real space partitioned two-band topological insulator with that of a bilayer Fermi gas with an interlayer partition. This duality has an interesting rel…
Recently, Paolo Facchi et al. [Phys. Rev. A. 77, 060304 (R) (2008)] introduced the notion of maximally multipartite entangled states of n qubits. Here, we give a criterion for faithful controlled teleportation of an arbitrary two-qubit state via a five-qubit entangled state and obtain the general relation between the genuine five-qubit entangled state and controlled teleportation. This criterion can be extended to teleportation of an arbitrary N-qubit state using 2N+1-qubit entangled state. Furthermore, we study the optimal match of measuring basis and quantum channel.
Geometric measure of entanglement of quantum graph states prepared with controlled phase shift operators
该研究推导了受控相移算符制备的任意图加权图态中单量子比特与系统其余部分的纠缠几何度量及态参数关系，并在Qiskit Aer模拟器与ibmq lima量子处理器上验证了两比特情形的解析结果。
In this paper, a novel protocol for bidirectional controlled quantum teleportation (BCQT) is proposed. Based on entanglement swapping of initiate Bell state, two users can teleport an unknown single-qubit state to each other under the permission of the supervisor. This proposed protocol would be utilized to a system in which a controller controls the communication in one direction only. Indeed, just one of the users needs the permission of the controller to reconstruct the unknown quantum state. In comparison to the existing BCQT protocols which their quantum channels are cluster and brown sta…
We investigate the dynamical behavior of the atom-photon entanglement in a V-type three-level quantum system using the atomic reduced entropy. It is shown that an atom and photons are entangled at the steady-state; however disentanglement can also be achieved in an especial condition. It is demonstrated that in the presence of quantum interference induced by spontaneous emission, the reduced entropy and the atom-photon entanglement are phase-dependent. Non-stationary solution is also obtained when the quantum interference due to the spontaneous emission is completely included.
Duality between imperfect resources and measurements for propagating entanglement in networks
本文提出基于非锐化双量子比特测量的网络纠缠传播单向与双向协议，证明含噪及非最大纠缠资源在适当参数下可获得更高单配偶性分数。
We investigate minimal control power (MCP) for controlled dense coding defined by the channel capacity. We obtain MCPs for extended three-qubit Greenberger-Horne-Zeilinger (GHZ) states and generalized three-qubit $W$ states. Among those GHZ states, the standard GHZ state is found to maximize the MCP and so does the standard $W$ state among the $W$-type states. We find the lower and upper bounds of the MCP and show for pure states that the lower bound, zero, is achieved if and only if the three-qubit state is biseparable or fully separable. The upper bound is achieved only for the standard GHZ …
We show that an absolute coherent phase of a laser can be used to manipulate the entanglement of photon pairs of two-photon laser. Our focus is on the generation of a continuous source of entangled photon pairs in the double $Λ$ (or Raman) scheme. We study the dependence of steady state entanglement on the phase and laser parameters. We obtain a relationship between entanglement and two-photon correlation. We derive conditions that give steady state entanglement for the Raman-EIT scheme and use it to identify region of steady state macroscopic entanglement. No entanglement is found for the dou…
Quantum entanglement is notorious for being a very fragile resource. Significant efforts have been put into the study of entanglement degradation in the presence of a realistic noisy environment. Here, we present a theoretical and an experimental study of the decoherence properties of entangled pairs of qubits. The entanglement dynamics of maximally entangled qubit pairs is shown to be related in a simple way to the noise representation in the Bloch sphere picture. We derive the entanglement level in the case when both qubits are transmitted through any arbitrary unital Pauli channel, and comp…
Random quantum states and operations are of fundamental and practical interests. In this work, we investigate the entanglement properties of random hypergraph states, which generalize the notion of graph states by applying generalized controlled-phase gates on an initial reference product state. In particular, we study the two ensembles generated by random Controlled-Z(CZ) and Controlled-Controlled-Z(CCZ) gates, respectively. By applying tensor network representation and combinational counting, we analytically show that the average subsystem purity and entanglement entropy for the two ensemble…
We generate and characterise entangled states of a register of 20 individually controlled qubits, where each qubit is encoded into the electronic state of a trapped atomic ion. Entanglement is generated amongst the qubits during the out-of-equilibrium dynamics of an Ising-type Hamiltonian, engineered via laser fields. Since the qubit-qubit interactions decay with distance, entanglement is generated at early times predominantly between neighbouring groups of qubits. We characterise entanglement between these groups by designing and applying witnesses for genuine multipartite entanglement. Our r…
Two quantum information processing protocols are said to be dual under resource reversal if the resources consumed (generated) in one protocol are generated (consumed) in the other. Previously known examples include the duality between entanglement concentration and dilution, and the duality between coherent versions of teleportation and super-dense coding. A quantum feedback channel is an isometry from a system belonging to Alice to a system shared between Alice and Bob. We show that such a resource may be reversibly decomposed into a perfect quantum channel and pure entanglement, generalizin…
The notions of $k$-separability and $k$-producibility are useful and expressive tools for the characterization of entanglement in multipartite quantum systems, when a more detailed analysis would be infeasible or simply needless. In this work we reveal a partial duality between them, which is valid also for their correlation counterparts. This duality can be seen from a much wider perspective, when we consider the entanglement and correlation properties which are invariant under the permutations of the subsystems. These properties are labeled by Young diagrams, which we endow with a refinement…
Using well known duality between quantum maps and states of composite systems we introduce the notion of Schmidt number of a quantum channel. It enables one to define classes of quantum channels which partially break quantum entanglement. These classes generalize the well known class of entanglement breaking channels.
A tripartite entangled state of bright optical field is experimentally produced using an Einstein-Podolsky-Rosen entangled state for continuous variables and linear optics. The controlled dense coding among a sender, a receiver and a controller is demonstrated by exploiting the tripartite entanglement. The obtained three-mode position correlation and relative momentum correlation between the sender and the receiver and thus the improvements of the measured signal to noise ratios of amplitude and phase signals with respect to the shot noise limit are 3.28dB and 3.18dB respectively. If the mean …
We investigate the entanglement properties of symmetry states of the Schur-Weyl duality. Our approach based on reduced two-qubit density matrices, and concurrence as the measure of entanglement. We show that all kinds of entangled graphs, which describe the entanglement structure in Schur-Weyl states are completely coded in the corresponding Young tableau.
Quantum logic gates are important for quantum computations and quantum information processing in numerous physical systems. While time-bin qubits are suited for quantum communications over optical fiber, many essential quantum logic gates for them have not yet been realized. Here, we demonstrated a controlled-phase (C-Phase) gate for time-bin qubits that uses a 2x2 optical switch based on an electro-optic modulator. A Hong-Ou-Mandel interference measurement showed that the switch could work as a time-dependent beam splitter with a variable spitting ratio. We confirmed that two independent time…
We study the growth of entanglement between two adjacent regions in a tripartite, one-dimensional many-body system after a quantum quench. Combining a replica trick with a space-time duality transformation, we derive an exact, universal relation between the entanglement negativity and Renyi-1/2 mutual information which holds at times shorter than the sizes of all subsystems. Our proof is directly applicable to any translationally invariant local quantum circuit, i.e., any lattice system in discrete time characterised by local interactions, irrespective of the nature of its dynamics. Our deriva…
Investigating controlled teleportation capability of quantum states with respect to $k$-separability
研究将两方标准传态保真度阈值分析扩展至多方受控传态场景，给出了 $N$-qudit $k$-可分态在受控传态中不能超过的阈值，并证明真正多体纠缠非高传态能力的必要前提。
We present a way to teleport multi-qubit quantum information from a sender to a distant receiver via the control of many agents in a network. We show that the original state of each qubit can be restored by the receiver as long as all the agents collaborate. However, even if one agent does not cooperate, the receiver can not fully recover the original state of each qubit. The method operates essentially through entangling quantum information during teleportation, in such a way that the required auxiliary qubit resources, local operation, and classical communication are considerably reduced for…
We study the entanglement structure, i.e., the structure of quantum composite system from operational aspects. The structure is not uniquely determined in General Probabilistic Theories (GPTs) even if we impose reasonable postulate about local systems. In this paper, we investigate the possibility that the standard entanglement structure can be determined uniquely by repeatability of measurement processing and its saturated situation called self-duality. Surprisingly, self-duality cannot determine the standard entanglement structure even if we additionally impose local unitary symmetry assumpt…
We consider an infinite spin chain as a bipartite system consisting of the left and right half-chain and analyze entanglement properties of pure states with respect to this splitting. In this context we show that the amount of entanglement contained in a given state is deeply related to the von Neumann type of the observable algebras associated to the half-chains. Only the type I case belongs to the usual entanglement theory which deals with density operators on tensor product Hilbert spaces, and only in this situation separable normal states exist. In all other cases the corresponding state i…
Phase-controlled recoverable entanglement in accelerated detector registers
本文研究四量子比特簇态寄存器中加速探测器对的可恢复纠缠，通过局域制备相位控制噪声保护，在最优相位下固定解码器恢复贝尔对，并推导小间距衰减速率及热浴匹配下的最优时间，最终恢复隐形传态资源。
Wave-particle duality and entanglement are two fundamental characteristics of quantum mechanics. All previous works on experimental investigations in wave{particle properties of single photons (or single particles in general) show that a well-defined interferometer setting determines a well-defined property of single photons. Here we take a conceptual step forward and control the wave-particle property of single photons with quantum entanglement. By doing so, we experimentally test the complementarity principle in a scenario, in which the setting of the interferometer is not defined at any ins…
Geometry-Information Duality: Quantum Entanglement Contributions to Gravitational Dynamics
本文提出时空几何与量子场信息的基本对偶性，通过引入源自量子纠缠熵的信息应力-能量张量修改Einstein场方程，计算了牛顿常数的修正，揭示了量子信息对引力动力学和时空结构的根本性作用。
Describing non-equilibrium properties of quantum many-body systems is challenging due to high entanglement in the wavefunction. We describe evolution of local observables via the influence matrix (IM), which encodes the effects of a many-body system as an environment for local subsystems. Recent works found that in many dynamical regimes the IM of an infinite system has low temporal entanglement and can be efficiently represented as a matrix-product state (MPS). Yet, direct iterative constructions of the IM encounter highly entangled intermediate states - a temporal entanglement barrier (TEB).…
The sources, which generate atom-photon quantum correlations or entanglement based on quantum memory, are basic blocks for building quantum repeaters (QRs). For achieving highly entanglement-generation rates in ensemble-based QRs, spatial-, temporal- and spectral-multimode memories are needed. The previous temporal-multimode memories are based on rephrasing mechanisms in inhomogeneous-broadened media. Here, by applying a train of multi-direction write pulses into a homogeneous-broadened atomic ensemble to induce Duan-Lukin-Cirac-Zoller-like Raman processes, we prepare up to 19 pairs of modes, …
The analysis of the entanglement entropy of a subsystem of a one-dimensional quantum system is a powerful tool for unravelling its critical nature. For instance, the scaling behaviour of the entanglement entropy determines the central charge of the associated Virasoro algebra. For a free fermion system, the entanglement entropy depends essentially on two sets, namely the set $A$ of sites of the subsystem considered and the set $K$ of excited momentum modes. In this work we make use of a general duality principle establishing the invariance of the entanglement entropy under exchange of the sets…
Chaos-controlled switching between entanglement and coherence
通过混沌控制实现纠缠与相干性的可切换切换，揭示了在不同混沌区域中纠缠和相干响应的翻转现象。
Entangling capability of coherently controlled quantum processes
该研究解析表征量子开关和时间翻转两种相干控制量子过程的纠缠能力，推导纠缠相关表达式，扩展分析至多种信道，揭示存在耗散时仍可生成最大纠缠，为相干控制量子过程的纠缠生成提供系统分析。
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