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Questions tagged [quantum-state]

Questions about or related to quantum states. Consider using the density-matrix tag when relevant.

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Are there separable $\rho$ that cannot be decomposed with less than $\operatorname{rank}(\rho)^2$ pure product states?

In What separable $\rho$ only admit separable pure decompositions with more than $\mathrm{rank}(\rho)$ terms?, examples were given of separable states $\rho$ with separable decompositions requiring ...
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Weak Schur sampling and state distinguishability

Consider the task of distinguishing between the following two $n$ qubit quantum states. $$ \rho = \frac{\mathbb{I}}{2^{n}}.$$ $$ \sigma = \frac{1}{2^{n/2}}\sum_{x \in \{0, 1\}^{n/2}} |x\rangle\langle ...
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How large can we make the fidelity between mixed states by allowing unitaries?

For pure states, it is known that one can always find a unitary that relates the two i.e. for any choice of states $\vert\psi\rangle$ and $\vert\phi\rangle$, there exists a unitary $U$ such that $U\...
JRT's user avatar
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Postselection and hardness of estimating amplitudes

Let $A$ be a class of quantum circuits such that \begin{equation} \text{Post}A = \text{Post}BQP, \end{equation} where $\text{Post}$ indicates post-selection. Is only this amount of information ...
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Encoding bosonic degrees of freedom

A well-known way of encoding $N$ levels of a harmonic (bosonic) oscillator is as follows: \begin{equation} |n\rangle = |1\rangle^{\otimes n} \otimes |0\rangle^{\otimes N-n+1} \quad,\qquad ...
mavzolej's user avatar
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Why can a point in anti-de Sitter space be modeled as a logical qutrit and how is its error correction done?

This isn't my area but the recent Quanta article How Space and Time Could Be a Quantum Error-Correcting Code struck me as interesting. They mention: In their paper[1] conjecturing that holographic ...
Sanchayan Dutta's user avatar
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How exactly is the stated composite state of the two registers being produced using the $R_{zz}$ controlled rotations?

This is a sequel to How are two different registers being used as "control"? I found the following quantum circuit given in Fig 5 (page 6) of the same paper i.e. Quantum Circuit Design for ...
Sanchayan Dutta's user avatar
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Is circuit cutting equivalent in anyway to quantum teleportation?

I've been introduced recently to circuit cutting, and after seeing the 4 orthogonal measurements with their 8 corresponding initializations but no initial transfer of classical info, the first thing ...
Guillermo Abad Lopéz's user avatar
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Volume law spread after Hamiltonian evolution

Start with an $n \times n$ lattice, with each qubit initialized to the state $|0\rangle$. Then, apply the Hadamard gate on each qubit. Then, evolve the system under the Hamiltonian \begin{equation} ...
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Are X-state separability and PPT- probabilities the same for the two-qubit, qubit-qutrit, two-qutrit, etc. states?

On p. 3 of "Separability Probability Formulas and Their Proofs for Generalized Two-Qubit X-Matrices Endowed with Hilbert-Schmidt and Induced Measures" (https://arxiv.org/abs/1501.02289), it is ...
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Holevo bound and indistinguishability of non-orthogonal quantum states

I was trying to understand the fact that non-orthogonal quantum states cannot be reliably distinguished and I came across this link. The explanation finishes with the result that the probability of ...
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How to construct a quantum circuit that given $|\psi_0\rangle,|\psi_1\rangle$ outputs $\frac{1}{c}(|\psi_0\rangle+|\psi_1\rangle)$?

Suppose I have two arbitrary quantum states $\lvert \psi_1 \rangle $ and $\lvert \psi_2 \rangle$. Further suppose that we know $U_1$ such that $\lvert \psi_1 \rangle = U_1 \lvert 0 \rangle$, but we ...
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How is this Variational Quantum Singular Value Decomposition paper efficient in any way?

Link to paper here. This algorithm seems neat but the unitary decomposition of the matrix M generally takes an exponential number of Pauli basis elements in the number of qubits $N$, therefore an ...
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How to implement a gate that generate a uniform superposition of all permutation of element

I'm looking for a quantum circuit that permits generating a uniform superposition of all possible permutations for example if we have as input $|0123\rangle$ the output will be the uniform ...
malak sa's user avatar
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How to find the Choi state of a bipartite quantum channel?

The Choi state of a quantum channel $\mathcal{N}_A$ acting on a system $\rho_A \in \mathcal{H}^A$ is given by: $Choi(\mathcal{N}_A) =( \mathcal{I}_{A'} \otimes \mathcal{N}_A)|\Phi^+\rangle \langle\...
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Reduced density matrix of a Haar random state and its Schmidt decomposition

Consider a Haar random quantum state $|\psi\rangle$. Note that $$\rho =\mathbb{E}[|\psi\rangle\langle \psi|] = \frac{\mathbb{I}_{n}}{2^{n}}.$$ $\mathbb{I}_n$ is the identity operator on $n$ qubits. ...
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How to find minimum time needed for Hamiltonian evolution?

Database search can be looked upon as Hamiltonian evolution, with kinetic and potential energy operators. Let the evolution follow the Schrodinger equation: $$i\frac{d}{dt}|\psi⟩= H|ψ⟩$$ with $H = E|s⟩...
Sudhir Kumar Sahoo's user avatar
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Schur transform and the outcome probabilities for a particular type of state

I was reading about the Schur transform and its applications in knowing about an unknown quantum state. Consider $\rho^{\otimes k}$, which means $k$ copies of an unknown $n$ qubit quantum density ...
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Can changing reference frames generate entanglement in identical particles?

Suppose we have a pair of qubits, physically realised as two spin-half particles in some separable pure state $|\psi\rangle$, separated by a distance '$l$', large enough to be regarded as ...
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Can a triplet be a qutrit?

Original question A triplet is a space that consist of three states that have the same total angular momentum (spin 1). If we restrict ourselves to a set of quantum gates that keep triplet states in ...
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How to efficiently construct quantum circuits of oracles in multi-target quantum search?

In standard Grover's quantum search with only one target or its extension of multi-target quantum search, one of the two key parts is to quantize the boolean function $$f(x):\{0,1,\cdots,N-1\}\...
Chao-Hua Yu's user avatar
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What does it mean that a qubit is a triple $(H,X,Z)$ with $H$ Hilbert space and $X,Z$ Pauli operators?

In this paper, http://users.cms.caltech.edu/~vidick/teaching/fsmp/fsmp.pdf, it gives the definition of a qubit as follows: A qubit is a triple $(H, X, Z)$ consisting of a separable Hilbert space H and ...
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Minmax theorem for optimization over isometries and states

I have the following minmax problem and I am wondering if the order of the minimum and maximum can be interchanged and if yes, why? Let $\|\cdot\|_1$ be the trace norm defined as $\|\rho\|_1 = \text{...
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Permutation invariant states have permutation invariant purifications - proof?

I don't remember where I came across the statement but I'm pretty sure it is true and am interested in understanding why it holds. For any $n-$ register state $\rho^n \in H^{\otimes n}$ that is ...
JRT's user avatar
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What was the meaning of Lossless Quantum compression?

I was reading few questions regarding lossless quantum compression on stack exchange, then out of curiosity, I started reading this article. After reading I end up being confused about what does ...
User1086's user avatar
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How does the quantum Fisher information provide bounds for the estimation of output states?

Assume you have some quantum process $Q$ (e.g. quantum state tomography) that intakes initialised states $\rho_{i}$, $i=1,\ldots,n$ and gives some output $\rho'_i$. $$ \rho_1 \to Q \to \rho'_1 \\ \...
Marion's user avatar
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States used in lossless quantum compression?

I was reading about quantum compression in this article and have some doubts regarding an example mentioned. Specifically, I have two questions: In example they represented $|a\rangle = \dfrac{1}{\...
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If $\rho \approx_{\varepsilon}\sigma$, how to find $\Pi\rho\Pi$ to ensure that $\text{supp}(\Pi\rho\Pi)\subset\text{supp}(\sigma)$?

Let $\rho$ and $\sigma$ be positive semidefinite operators with trace less than or equal to 1. Let $\rho\approx_{\varepsilon}\sigma$ i.e. they are close in some distance, such as the trace distance. ...
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Calculating Dot Product of Two States

I've been reading Peter Wittek's Quantum Machine Learning. In chapter 10.2 of this book, the author explains how we can calculate the dot product of two states: To evaluate the dot product of two ...
MetaInformation's user avatar
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Can we characterise how correlated the expectation values associated with a pair of observables are?

Consider a state $\rho$ and two observables $P$ and $Q$. Is there a good way to characterise how correlated the associated expectation values are? Be it in terms of mutual information or something ...
glS's user avatar
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Quantum Boltzmann machine: How do you sample from the Boltzmann distribution on a quantum computer?

I am reading through the following article https://arxiv.org/abs/1601.02036. Eq. (22) describes one of the terms of the gradient of the log-likelihood cost function, which can be estimated using ...
QCQCQC's user avatar
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Is the set of two-qubit absolutely separable states convex?

Companion question on MathOverflow Let us order the four nonnegative eigenvalues, summing to 1, of a two-qubit density matrix ($\rho$) as \begin{equation} 1 \geq x \geq y \geq z \geq (1-x-y-z) \geq 0. ...
Paul B. Slater's user avatar
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Preparing a state given access to projector

Let's say I am given access to a magical box that lets me apply a projector $|\psi\rangle \langle\psi|$, where $|\psi\rangle$ is a quantum state. I do not know anything about $|\psi\rangle$: just that ...
BlackHat18's user avatar
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Quantum Ising model correlation function query

In this paper on quantum Ising model dynamics, they consider the Hamiltonian $$\mathcal{H} = \sum_{j < k} J_{jk} \hat{\sigma}_{j}^{z}\hat{\sigma}_{k}^{z}$$ and the correlation function $$\mathcal{G}...
John Doe's user avatar
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Preparation of states that correspond to efficiently integrable probability distributions

I have been trying to implement methods from paper Creating superpositions that correspond to efficiently integrable probability distributions by Grover and Rudolph. It is stated that there exists an ...
Amir Naveh's user avatar
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Finding separable decompositions of bipartite X-states using the methodology of Li and Qiao

Two recent papers of Jun-Li Li and Cong-Feng Qiao (arXiv:1607.03364 and arXiv:1708.05336) present "practical schemes for the decomposition of a bipartite mixed state into a sum of direct products of ...
Paul B. Slater's user avatar
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What proportions of certain sets of PPT-two-retrit states are bound entangled or separable?

For two particular (twelve-and thirteen-dimensional) sets of two-retrit states (corresponding to 9 x 9 density matrices with real off-diagonal entries), I have been able to calculate the Hilbert-...
Paul B. Slater's user avatar
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A question on a subset of projectors onto symmetric subspace

Use $\text{perm}_t$ to denote the set of all permutations among $t$ items. For any particular subset $S\subseteq\{0,1\}^n$ and any $\sigma\in \text{perm}_t$, we define \begin{align} P_S(\sigma) = \...
BlackHat18's user avatar
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Complexity of the quantum circuits that are needed to implement communication protocol?

Consider the following simultaneous communication problem. Alice and Bob do not share any entanglement or any common randomness, and cannot communicate directly with each other. As inputs, x is given ...
Ruben Hoba's user avatar
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Is it possible to convert a qudit to a qubit?

I am trying to write a Qiskit code for a algorithm which uses qudits. I want to use qubits instead because $p$ value can go pretty high. Is it mathematically possible to convert qudit to qubit for ...
videet.acharya's user avatar
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Entangling attack on BB84 protocol

I am trying to solve the exercise 5.3 from the book "A Gentle Introduction to Quantum Computing". The exercise reads as follows: Suppose Eve attacks the BB84 quantum key distribution of ...
Jorge Vázquez Pérez's user avatar
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What does the $\sigma_z$ operator correspond to in the context of a Transmon qubit?

In the context of the transmon qubit and an LC circuit with a coupling capacitor and driving voltage. We can write the charge operator $Q$ as $-iQ_{ZPF}\sigma_y$ (since we defined $Q$ using the ladder ...
bubakazouba's user avatar
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Hyperspherical parametrization of a multi-qubit state

Can anyone please explain me in simple words how the hyperspherical coordinates can be used to parameterise multi-qubit states? The state of an $n$-qubit system can be thought of as a point on the $\...
Michael_1812's user avatar
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Deriving Bloch vector $dr$ from master equation

I am trying to derive the Bloch vector $dr$ for a measurement of a observable in any arbitrary direction $\theta$. For context this is the setup and derivation I have for continuous measurement along ...
Ian's user avatar
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Is there a measure similar to the Helstrom measurement which can distinguish between more than 2 pure quantum states?

My understanding is the Helstrom measurement distinguishes between 2 pure quantum states. Is there a measure similar to the Helstrom measurement which can distinguishes between more than 2 pure ...
Leockl's user avatar
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Are there different orderings of the fifteen SU(4) generators in common use?

I've recently performed certain analyses (Archipelagos of Total Bound and Free Entanglement) pertaining to eq. (50) in Separable Decompositions of Bipartite Mixed States , that is \begin{equation} ...
Paul B. Slater's user avatar
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Find the qutrit analogue of certain qubit and ququart formulas of Li and Qiao for testing separability

In eqs. (33), (43)-(46), (56) of their paper, "Separable Decompositions of Bipartite Mixed States" https://arxiv.org/abs/1708.05336, Li and Qiao present a number of formulas pertinent to testing the ...
Paul B. Slater's user avatar
3 votes
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Please clarify the following orthogonal property (quantum anonymous voting)

I am a beginner at QC, currently going through a paper on Quantum Anonymous Voting. Please clarify the orthogonal property described in the following scenario. Consider $n$ voters $V_{0}, V_{1}, V_{2}...
qcnoob's user avatar
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Understanding shared Bell states from quantum entanglement

I'm trying to understand an entanglement swapping derivation provided in this PDF (pages 2 - 3) I have several things about this process that I don't understand, and I was hoping someone could ...
Yuerno's user avatar
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How to define initial state $\rvert \Psi(0) \rangle \equiv \rvert 1, -1 \rangle \otimes \rvert 0 \rangle_{\text{cav}} $ of a system in QuTiP?

Say, we have a $\require{mhchem}\ce{^87Rb}$ atom having an electric dipole transition on the $D_{1}$ line and we have two hyperfine ground states, one on $F = 1$ and one on $F = 2$ level. So, we take ...
Mun's user avatar
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