Lev Vaidman
A brief review of the time-symmetrized quantum formalism originated by Aharonov, Bergmann and Lebowitz is presented. Symmetry of various measurements under the time reversal is analyzed. Time-symmetrized counterfactuals are introduced. It is argued that the time-symmetrized formalism demonstrates novel profound features of quantum theory and that recent criticism of the formalism is unfounded.
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Recently, several authors have criticized the time-symmetrized quantum theory originated by the work of Aharonov et al. (1964). The core of this criticism was a proof, appearing in various forms, which showed that the counterfactual interpretation of time-symmetrized quantum theory cannot be reconciled with standard quantum theory. I, (Vaidman, 1996a, 1997) have argued that the apparent contradiction is due to a logical error and introduced consistent time-symmetrized quantum counterfactuals. Here I repeat my arguments defending the time-symmetrized quantum theory and reply to the criticism of…
Recently, several authors have criticized time-symmetrized quantum theory originated by the work of Aharonov et al. (1964). The core of this criticism was the proof, which appeared in various forms, showing that counterfactual interpretation of time-symmetrized quantum theory cannot be reconciled with the standard quantum theory. I argue here that the apparent contradiction appears due to inappropriate usage of traditional time asymmetric approach to counterfactuals, and that the contradiction disappears when the problem is analyzed in terms of time-symmetric counterfactuals. I analyze various…
Recently, several authors have criticized the time-symmetrized quantum theory originated by the work of Aharonov et al. (1964). The core of this criticism was a proof, appearing in various forms, which showed that the counterfactual interpretation of time-symmetrized quantum theory cannot be reconciled with standard quantum theory. I argue here that the apparent contradiction is due to a logical error. I analyze the concept of counterfactuals in quantum theory and introduce time-symmetrized counterfactuals. These counterfactuals do not lead to any contradiction with the predictions of quantum …
Counterfactuals in quantum theory are briefly reviewed and it is argued that they are very different from counterfactuals considered in the general philosophical literature. The issue of time symmetry of quantum counterfactuals is considered and a novel time-symmetric definition of quantum counterfactuals is proposed. This definition is applied for analyzing several controversies related to quantum counterfactuals.
The symmetrized product for quantum mechanical observables is defined. It is seen as consisting of the ordinary multiplication and the application of the superoperator that orders the operators of coordinate and momentum. This superoperator is defined in a way that allows obstruction free quantization when the observables are considered from the point of view of the algebra. Then, the operatorial version of the Poisson bracket is defined. It is shown that it has all properties of the Lie bracket and that it can substitute the commutator in the von Neumann equation.
Variance is a ubiquitous quantity in quantum information theory. Given a basis, we consider the averaged variances of a fixed diagonal observable in a pure state under all possible permutations on the components of the pure state and call it the symmetrized variance. Moreover we work out the analytical expression of the symmetrized variance and find that such expression is in the factorized form where two factors separately depends on the diagonal observable and quantum state. By shifting the factor corresponding to the diagonal observable, we introduce the notion named the standard symmetrize…
Uncertainty of quantum channels based on symmetrized \r{ho}-absolute variance and modified Wigner-Yanase skew information
本文提出了基于对称化ρ-绝对方差的不确定性关系，将其推广至量子信道，并利用Cauchy-Schwarz不等式建立了更紧的不确定性关系，通过示例验证了结果的紧致性。
Recent authors have raised objections to the counterfactual interpretation of the Aharonov-Bergmann-Lebowitz (ABL) rule of time symmetrized quantum theory (TSQT). I distinguish between two different readings of the ABL rule, counterfactual and non-counterfactual, and confirm that TSQT advocate L. Vaidman is employing the counterfactual reading to which these authors object. Vaidman has responded to the objections by proposing a new kind of time-symmetrized counterfactual, which he has defined in two different ways. It is argued that neither definition succeeds in overcoming the objections, exc…
In this paper, we give a quantum circuit that calculates symmetrized functions. Our algorithm applies the original Grover's algorithm or a variant thereof such as AFGA (adaptive fixed point Grover's algorithm). Our algorithm uses AFGA in conjunction with two new techniques we call "targeting two hypotheses" and "blind targeting". Suppose AFGA drives the starting state $|s\rangle$ to the target state $|t\rangle$. When targeting two hypotheses, $|t\rangle$ is a superposition $a_0|0\rangle + a_1|1\rangle$ of two orthonormal states or hypotheses $|0\rangle$ and $|1\rangle$. When targeting blindly,…
Rapid and efficient wavefront correction for spatially entangled photons using symmetrized optimization
提出对称化遗传算法（sGA）用于空间纠缠光子的自适应波前校正，利用偶宇称分量影响双光子相关性的洞见将参数空间减半，实现比标准遗传算法更快的收敛与更高的增强效果，从而有效校正复杂介质中的纠缠退化。
Quantum correlations, in particular those, which enable to violate a Bell inequality \cite{BELL}, open a way to advantage in certain communication tasks. However, the main difficulty in harnessing quantumness is its fragility to, e.g, noise or loss of particles. We study the persistency of Bell correlations of GHZ based mixtures and Dicke states. For the former, we consider quantum communication complexity reduction (QCCR) scheme, and propose new Bell inequalities (BIs), which can be used in that scheme for higher persistency in the limit of large number of particles $N$. In case of Dicke stat…
Twisted rapid passage is a type of non-adiabatic rapid passage that generates controllable quantum interference effects that were first observed experimentally in 2003. It is shown that twisted rapid passage sweeps can be used to implement a universal set of quantum gates that operate with high-fidelity. The gate set consists of the Hadamard and NOT gates, together with variants of the phase, pi/8, and controlled-phase gates. For each gate g in the universal set, sweep parameter values are provided which numerical simulations indicate will produce a unitary operation that approximates g with e…
The transit times are obtained for a symmetrized (two identical bosons) and an antisymmetrized (two identical fermions) quantum colliding configuration. Considering two identical particles symmetrically impinging on a one-dimensional barrier, we demonstrate that the phase time and the dwell time give connected results where, however, the exact position of the scattered particles is explicitly determined by the phase time (group delay). For the antisymmetrized wave function configuration, an unusual effect of {\em accelerated} transmission is clearly identified in a simultaneous tunneling of tw…
Symmetrized Liouvillian Gap in Markovian Open Quantum Systems
本文针对马尔可夫开放量子系统，提出对称化Liouvillian间隙，为稳态自相关函数的瞬态衰减提供严格上界，数值验证其优于标准间隙。
This paper is the answer to the paper by Kastner [Found. Phys., to be published, quant-ph/9807037] in which she continued the criticism of the counterfactual usage of the Aharonov-Bergman-Lebowitz rule in the framework of the time-symmetrized quantum theory, in particular, by analyzing the three-box ``paradox''. It is argued that the criticism is not sound. Paradoxical features of the three-box example has been explained. It is explained that the elements of reality in the framework of time-symmetrized quantum theory are counterfactual statements and, therefore, even conflicting elements of re…
Modular Self-Duality, Symmetrized Relative Entropy, and Bogoliubov--Kubo--Mori Susceptibility in Quantum Field Theory
本文研究了量子场论中局部态的模自对偶性、对称相对熵和Bogoliubov-Kubo-Mori可变性，提出了一种算子代数框架，通过固定点构造和对称Araki相对熵，得到了类型III Bogoliubov-Kubo-Mori可变性系数的显式表达式。
Symmetrized Block-Product Periodic Marginals in Infinite Translation-Invariant Quantum Chains
该研究针对无限平移不变量子链提出对称化块积周期边际方法，结合半定规划松弛与矩阵乘积态近似，可诊断周期序、给出基态能量上界，在多自旋模型测试中验证了其有效性。
The Symmetrized Holographic Entropy Cone
本文提出对全息熵锥进行对称化投影的方法，以研究一般参与方数下的极值结构，并据此证明全息熵在量子熵中随参与方数指数稀少。
Fourier Symmetrization for Geometric Quantum Machine Learning
本研究通过傅里叶表示分析对称性对量子傅里叶模型表达能力的影响，提出对称化与随机编码方法，并在量子物理信息神经网络中验证其有效性，降低误差。
Noncommuting observables cannot be simultaneously measured, however, under local hidden variable models, they must simultaneously hold premeasurement values, implying the existence of a joint probability distribution. We study the joint distributions of noncommuting observables on qubits, with possible criteria of positivity and the Fréchet bounds limiting the joint probabilities, concluding that the latter may be negative. We use symmetrization, justified heuristically and then more carefully via the Moyal characteristic function, to find the quantum operator corresponding to the product of n…
It is widely accepted that a Born probability of 1 is sufficient for the existence of a corresponding element of reality. Recently Vaidman has extended this idea to the ABL probabilities of the time-symmetrized version of quantum mechanics originated by Aharonov, Bergmann, and Lebowitz. Several authors have objected to Vaidman's time-symmetrized elements of reality without casting doubt on the widely accepted sufficiency condition for `ordinary' elements of reality. In this paper I show that while the proper truth condition for a quantum counterfactual is an ABL probability of 1, neither a Bor…
For quantum systems with externally time-varied Hamiltonians a definition of operators of system's energy change rate (work per unit time) and entropy production observables is suggested and discussed in the context of rigorous statistical equalities (generalized fluctuation-dissipation relations) under the Jordan-symmetrized chronological operator ordering rule.
We introduce a family of highly symmetric bipartite quantum states in arbitrary dimensions. It consists of all states that are invariant under local phase rotations and local cyclic permutations of the basis. We solve the separability problem for a subspace of these states and show that a sizable part of the family is bound entangled. We also calculate some of the Schmidt numbers for the family in $d = 3$, thereby characterizing the dimensionality of entanglement. Our results allow us to estimate entanglement properties of arbitrary states, as general states can be symmetrized to the considere…
We consider entanglement in a system of fixed number of identical particles. Since any operation should be symmetrized over all the identical particles and there is the precondition that the spatial wave functions overlap, the meaning of identical-particle entanglement is fundamentally different from that of distinguishable particles. The identical-particle counterpart of the Schmidt basis is shown to be the single-particle basis in which the one-particle reduced density matrix is diagonal. But it does not play a special role in the issue of entanglement, which depends on the single-particle b…
In this paper we present the two-state vector formalism of quantum mechanics. It is a time-symmetrized approach to standard quantum theory particularly helpful for the analysis of experiments performed on pre- and post-selected ensembles. Several peculiar effects which naturally arise in this approach are considered. In particular, the concept of ``weak measurements'' (standard measurements with weakening of the interaction) is discussed in depth revealing a very unusual but consistent picture. Also, a design of a gedanken experiment which implements a kind of quantum ``time machine'' is descr…
We present a formalism for calculating the non-symmetrized quantum current noise within the Born-Markov approximation for the master equation. The formalism is particularly well suited to obtaining the current noise for quantum transport in mesoscopic devices such as a superconducting single electron transistor (SSET). As an example of the method, we obtain explicit results for the double Josephson-quasiparticle (DJQP) resonance in a SSET. Our calculations reveal the asymmetries that develop in the current noise as well as clarifying the behavior at high frequencies. Our findings are consisten…
The quantum mechanical notion of unobservable causal loop and the anthropic principle
本文提出通过时间对称化补全可逆量子过程描述，揭示不可观测因果环的量子叠加结构，并以此完备人择原理，解释量子加速下的宇宙演化。
Semicoherent Symmetric Quantum Processes: Theory and Applications
本研究在半相干场景下探讨ε-近似量子过程与严格对称性的相互作用，借鉴约尔旦的对称代数形式构建对称化体系，应用于多量子领域，为相干资源有限场景下的量子动力学调控提供新思路。
Here we present the time-bidirectional state formalism (TBSF) unifying in a general manner the standard quantum mechanical formalism with no postselection and the time-symmetrized two-state (density) vector formalism, which deals with postselected states. In the proposed approach, a quantum particle's state, called a time-bidirectional state, is equivalent to a joined state of two particles propagating in opposite time directions. For a general time-bidirectional state, we derive outcome probabilities of generalized measurements, as well as mean and weak values of Hermitian observables. We als…
One of the remarkable notions in the recent development of quantum physics is the weak value related to weak measurements. We emulate it as a two-time conditional expectation in a classical stochastic model. We use the well known symmetrized form of the master equation, which is formally equivalent to the wave equation in quantum mechanics apart from the fact that wave functions are always real. The origin of the unusual behaviors of the weak value such as the negative probability and the abnormal enhancement of some expectations becomes clearer in the present case, where the two-time conditio…
Path Integral Approach to Quantum Fisher Information
本文提出了一种实时路径积分形式的量子 Fisher 信息方法，通过时间积分动作变形的连通对称协方差或传播子中的插入项重新表述，避免显式状态重构，并利用 Schwinger-Keldysh 形式化推导了量子 Fisher 信息的紧凑 semiclassical 表达式。
Repeated measurements as typically occurring in two- or multi-time correlators rely on von Neumann's projection postulate, telling how to restart the system after an intermediate measurement. We invoke the principle of deferred measurement to describe an alternative procedure where co-evolving quantum memories extract system information through entanglement, combined with a final readout of the memories described by Born's rule. The new approach to repeated quantum measurements respects the unitary evolution of quantum mechanics during intermediate times, unifies the treatment of strong and we…
Trace-Norm Overlaps of Quantum States: Interpolation, Equality, and Data-Processing Rigidity
研究量子态迹范数重叠随参数的变化，证明对数凸性、与Rényi散度的联系、数据处理单调性仅在α=1/2成立，并刻画等式条件及交换性判定。
Imaginary pseudo entropy encodes temporal orientation
本文通过校准的副本干涉仪将伪Rényi相位转化为可测量的跃迁方向记录，证明虚部伪熵编码时间方向的可逆区分，并在量子信道下该信息仅递减。
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