Questions tagged [entanglement]

For questions about the principle and application of quantum entanglement. It is a physical phenomenon which occurs when pairs or groups of particles are generated, interact, or share spatial proximity in ways such that the quantum state of each particle cannot be described independently of the state of the other(s), even when the particles are separated by a large distance—instead, a quantum state must be described for the system as a whole. (Wikipedia)

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56 views

How does a $d\times\ell$ matrix of rank $\ell$ and with singular values all equal to 1 imply it is maximally entangled

From this question, gls states that given $\Pi\equiv\sum_i |\eta_i\rangle\!\langle i|$ and $\Psi\equiv\sum_i|\psi_i\rangle\!\langle i|$, if $\Pi^\dagger\Psi=I_{d\times\ell}$, then $\Psi$ is "...
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Can a single qutrit in superposition be considered entangled?

Often in quantum computing the idea of quantum superposition is introduced well before the concept of entanglement. I suspect this may be because our conception of (classical) computing privileges ...
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Can $|\Psi\rangle\simeq\sum_k |u_k\rangle|v_k\rangle$ be maximally entangled even if $\{|u_k\rangle\}_k,\{|v_k\rangle\}_k$ are not orthonormal?

Let $\newcommand{\ket}[1]{\lvert#1\rangle}\{\ket{u_k}\}_k,\{\ket{v_k}\}_k\subset\mathcal H$ be orthonormal bases in an $N$-dimensional space. It then follows that the state $$\ket\Psi = C\sum_{k=1}^N \...
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Is there any difference between a quantum- and classically-controlled gate if I know my basis?

Consider an unrealistic 2-qubit plus 1 ancilla bit-flip error correction code (images generated by quirk), where I know by some means or other that an error may have happen on qubit0 (represented by ...
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53 views

What linear map is needed for acting on a maximally entangled state?

I was reading a textbook and I encountered this question. I was wondering why we don't consider $M^\dagger$ instead of $M^{T}$, so I didn't show this relation, could you please help me to show below ...
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What does a quantum NOT operation do to an entangled set of qubits?

Quantum computing is not my field, so answers understandable to a layman will be most useful. Please forgive any incorrect terminology in my question! Assume that a set of the states of N qubits ...
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1answer
58 views

How are Franson Interferometers used to prove security in Photonic QKD Experiments?

I am currently reading this paper about Quantum Key Distribution Protocols which use Franson Interferometers to secure against eavesdroppers. I am having trouble understanding how the interferometers ...
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Can local projections increase entanglement?

Consider a generic bipartite pure state $\newcommand{\ket}[1]{\lvert #1\rangle}\ket\Psi\equiv \sum_k \sqrt{p_k}\ket{u_k}\otimes\ket{v_k}\in\mathcal X\otimes\mathcal Y$, where $p_k\ge0$ are the Schmidt ...
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Keeping data around in an entangled state: use cases

I'm following the IBM Quantum roadmap and really excited to see what the next 3 years bring. As part of the unveiling, they mentioned that the 1000 Qubit machine goal will really stabilize things with ...
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Is there a measurable of entanglement for a many-body system?

After having a discussion with a quantum computing colleague, a question came up: is there any meaningful way to measure entanglement (or something related to it) in a solid-state many body system ...
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Give an explicit derivation of the exact formula for the two-qubit absolute separability Hilbert-Schmidt probability $\approx 0.00365826$

The two-qubit eigenvalue ($\lambda_i$ >= 0, $i=1,\ldots,4$, $\lambda_4=1-\lambda_1-\lambda_2-\lambda_3$) condition of Verstraete, Audenaert, de Bie and de Moor AbsoluteSeparability (p. 6) for ...
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What would be measured if you measure two entangled qubits at exactly the same time?

What would be measured if you measure two entangled qubits at exactly the same time?
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Can Alice and Bob distinguish entangled state coefficients?

Suppose Alice and Bob share the quantum state $\frac{1}{\sqrt 2}(|x\rangle + (-1)^b |y\rangle)$ for some $x\neq y \in \{0,1\}^2$ and $b \in \{0,1\}$. They both do not know $x,y$, and use some ...
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Is entanglement nonincreasing on average by local operations for all possible ensemble decompositions?

We know for a pure state conversion $|\psi \rangle \rightarrow_\textrm{LOCC} |\phi \rangle$ via local operation and classical communication (LOCC), an entanglement monotone should not increase, that ...
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Effect of quantum entanglement on measurement

I'm taking a quantum information systems class and thought of this while trying to wrap my head around some material, so I apologize if this comes off as dumb or founded on misunderstandings. Say you ...
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Is the square root of SWAP gate "maximally entangling"?

I'm not sure if this is a good question for the site, but here goes. On the "Quantum logic gate" Wikipedia page, it is said that: The $\sqrt{\mathrm{SWAP}}$ gate is not, however maximally ...
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Is this a Bell test?

Inspired by this article which uses a $|+\rangle$ state as a control for a $CSWAP$, I realised you can conditionally measure a qubit by (maybe) swapping it with an empty ancilla, measuring it and (...
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Example of a two-qudit state whose measurement outcomes are independent in one basis but dependent in another

If you have a pure composite system whose two subsystems are in a product state, then the outcomes of measuring the subsystems (in any basis) are statistically independent. If the subsystems are ...
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Prove entanglement in the final state of the Deutsch-Jozsa circuit

I am asked to prove the following: Consider the Deutsch-Jozsa circuit. The output of the circuit is of the form $|\psi\rangle \otimes \frac{1}{\sqrt{2}}(|0\rangle-|1\rangle)$. Prove that the state$|\...
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Defining dimension of an operator in qutip

My main question: Can someone please explain to me how the list of array is used to define the dimension in qutip? Context: If I have my density operator ...
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Is there a name for $Z_{1}(|\mathrm{GHZ}\rangle)$?

The GHZ state is defined as $|\mathrm{GHZ}\rangle = \frac{|000\rangle + |111\rangle}{\sqrt{2}}$. Is there a name for the phase flipped GHZ state, i.e. $Z_1(|\mathrm{GHZ}\rangle)=\frac{|000\rangle - |...
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Reduced Density Matrix Equation of Motion to describe an Ellipse

Given a pure two qubit state $|\psi_{AB}\rangle$. If we trace out system $B$, the remaining density matrix $\rho_A = Tr_B|\psi_{AB}\rangle\langle\psi_{AB}|$, can be represented as a point lying ...
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Are all pure entangled states `robust'?

Let $\mathcal{H}_A \otimes \mathcal{H}_B$ be the tensor product of two finite dimensional Hilbert spaces, let $d = \operatorname{dim}(\mathcal{H}_A \otimes \mathcal{H}_B)$ and let $| \psi \rangle \in \...
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In the three-qubit bit flip code, why can the first bit flip without impacting the entanglement with the other qubits?

The principle of the three-qubit Bit Flip Code is straight forward at first sight. Using CNOT you basically encode $$a|0\rangle + b|1\rangle $$ to $$ a|000\rangle + b|111\rangle$$ using ...
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How to get the state of an individual qubit in a composite system?

Given a composite system with $N$ qubits represented by some $2^N$-dimensional vector, how would I get the quantum state of an individual qubit? Note that I understand some states are not separable ...
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Generalized construction of W basis

Although this question deals with the construction of a W-state, I was looking for a general way to find all the orthogonal W-states, given a number of qubits. For example, for three qubits, the first ...
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191 views

What separable $\rho$ only admit separable pure decompositions with more than $\mathrm{rank}(\rho)$ terms?

As shown e.g. in Watrous' book (Proposition 6.6, page 314), a separable state $\rho$ can always be written as a convex combination of at most $\mathrm{rank}(\rho)^2$ pure, separable states. More ...
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Prove that $A\preceq B$ implies $A=\Psi(B)$ for some channel $\Psi$

Define $\newcommand{\PP}{\mathbb{P}}\newcommand{\ket}[1]{\lvert #1\rangle}\newcommand{\tr}{\operatorname{tr}}\newcommand{\ketbra}[1]{\lvert #1\rangle\!\langle #1\rvert}\PP_\psi\equiv\ketbra\psi$, and ...
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131 views

How does one go about constructing a mixed entangled state?

In general, an entangled state is one which cannot be decomposed as $\sum_{i}p_{i} \bigl(\rho_{i}^A\otimes\rho_{i}^B\bigr)$. But such an entangled state could still be mixed in principle. How would ...
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How to get the relative phase of an entangled pair of qubits

I have an extension to the following question: How to get the relative phase of a qubit? How do I get the relative phase of a pair of entangled qubits such as $$\frac{1}{\sqrt{2}}(|00\rangle+e^{i\...
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Is there a way to construct a quantum circuit/oracle to check if 2 qubits in an unknown pure state are entangled?

I have 2 qubits which are in an unknown pure state i.e. their density matrix $\rho$ can be expressed as $|\psi\rangle\langle\psi|$. Let the initial state be $|\psi\rangle = c_{00}|00\rangle + c_{01}|...
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1answer
58 views

Lower Bound to Measure Entanglement in Mixed States

Given a mixed state with a $n$ qubit density matrix of the following structure: $$ \rho=\pmatrix{\lambda_1&&&&\nu\\&\lambda_2\\ &&\lambda_{\dots}\\ &&&\lambda_2\...
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Finding a class $C$ of bipartite PPT states such that entanglement of $\rho \in C$ implies entanglement of $\rho + \rho^{\Gamma}$

Consider an entangled bipartite quantum state $\rho \in \mathcal{M}_d(\mathbb{C}) \otimes \mathcal{M}_{d'}(\mathbb{C})$ which is positive under partial transposition, i.e., $\rho^\Gamma \geq 0$. As ...
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What is the deep physical reason behind the existence of bound entanglement? [closed]

In Quantum Information processing, we can extract entanglement from $n$-copies of a weakly entangled state to produce a fully or highly entangled states in $d$-dimensions, using the known distillation ...
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76 views

Separability Criterion for Multipartite GHZ Quantum States

In "SEPARABILITY CRITERION FOR MULTIPARTITE QUANTUM STATES BASED ON THE BLOCH REPRESENTATION OF DENSITY MATRICES" by Hassan and Joag, I found this remarkable thing about entanglement of ...
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Is communication possible with entanglement?

From what I gather, communication is not possible with quantum mechanics. With the experiment on teleportation, entanglement is referred to as coordination and not communication. However, my belief is ...
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Is the Hilbert-Schmidt probability simply zero that a generic rank-2 two-qubit ("pseudo-pure") density matrix is separable?

The multifacted evidence is very compelling--although not yet presented in a formal proof--that the Hilbert-Schmidt probability that a generic (full rank/rank-4) two-qubit density matrix is separable ...
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138 views

How to prepare a quantum circuit for $\frac{1}{\sqrt{3}}(|00\rangle+|01\rangle+|10\rangle)$ starting from $|00\rangle$

How do I prepare a quantum circuit for $\frac{1}{\sqrt{3}}(|00\rangle+|01\rangle+|10\rangle)$ state starting from the $|00\rangle$ state? I have no clue how to do it. I tried with controlled Hadamard ...
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Are the skills learned for a degree in Computer Engineering helpful in learning Quantum Computing? [closed]

Next year, I will be a senior Computer Engineering student. Saying that, I have studied computer organization, electrical circuits, electronics and data structures. Our university provides an ...
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Visualizing "interference" in Quantum Programs

I'd like to develop an intuition about interference in QC programs and was hopeful that some visualization vehicle (like the bloch sphere) would be available to assist in developing an intuition of ...
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56 views

Joint system of RAB after purification of A into R

Given a pure state $|\psi\rangle_{AB}$ on a joint system $AB$, we can consider the reduced density operator $\sigma_A = Tr_B(|\psi \rangle \langle \psi|)$ on $A$ and subsequently purify this state ...
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Predicting rotations with many EPR pairs

I was explaining to a colleague that you can't use EPR pairs to communicate information, as it violates the no-communication theorem. This lead me to thinking... If I have let's say 1,000,000 EPR ...
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397 views

Question about DIY Quantum Computer Prototype

I recently came across these 2 videos on Coursera which show how to build a simple quantum computer that can implement the simplest case of the Deutsch-Jozsa algorithm (which uses only 2 qubits). ...
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61 views

Creative way to clone quantum data?

My goal is to think of a creative way to clone quantum data, specifically, forensically examine a quantum hard drive or memory of the future. No, I don't think I can violate the No Cloning Theorem or ...
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1answer
103 views

Bra-Ket Notation and Proof of a Ket Equation in Two-Party Shared-Entanglement Setting

Disclaimer: I had posted this question previously on the physics StackExchange, but received no response there. My question is two-part. First, imagine a bipartite quantum state $|\Phi \rangle_{AB}$, ...
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63 views

Compute the negativity of maximally entangled bipartite states

The entanglement negativity $\mathcal N(\rho)$ of a (bipartite) state $\rho$ is defined as the absolute value of the sum of the negative eigenvalues of the partial transpose of a state, or ...
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Why does the entanglement negativity equal (in magnitude) the sum of the negative eigenvalues?

The entanglement negativity, introduced in (Vidal and Werner 2002), is defined as $$\mathcal N(\rho) \equiv \frac{\|\rho^{T_B}\|_1-1}{2}.$$ It is mentioned there that this equals the sum of the ...
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What is the intuition behind the following entanglement distillation protocol for continuous variable systems?

The protocol is: We start with a supply of identically prepared bipartite non-Gaussian states. The overall protocol then amounts to an iteration of the following basic steps. The states will be mixed ...
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How can I print out a state vector of a specific wire?

Suppose we start from 2 wires (q0 and q1) and through some quantum gates, suppose we measure q1 wire only. As we measure the q1 wire, the state vector of this quantum state would be determined ...
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If two reduced density matrices are equal, does that mean that the two subsystems are the same?

Suppose we have a $3$-qubit system at time $t_0$ in the state $$\vert{\psi(t_0)}\rangle= \vert{q_0}\rangle \otimes \vert{q_1} \rangle \otimes \vert{q_2}\rangle. $$ We want to check if, for instance, ...

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