Quantum Computing Stack Exchange
Quantum Computing Stack Exchange

Questions tagged [density-matrix]

For questions about density matrices and related concepts and ideas, e.g. procedures for computing properties of quantum states from their density matrices.

A density matrix is a matrix that can be used to describe a quantum system in a mixed state, a statistical ensemble of several quantum states. This should be contrasted with a single state vector that describes a quantum system in a pure state.

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How do we derive the density operator of a subsystem?

The density operator can be used to represent uncertainty of quantum state from some perspective, aka a subsystem of the full quantum system. For example, given a Bell state: $|\psi\rangle = \frac{|00\rangle + |11\rangle}{\sqrt{2}}$ where Alice has…
ahelwer
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What's an easy way to determine a local density matrix?

In his lecture notes Scott Aaronson states: Now, consider the $2$-qubit pure state $\frac{|00\rangle + |01\rangle + |10\rangle}{\sqrt{3}}$. We'll give the first qubit to Alice and the second to Bob. How does Bob calculate his density matrix? By…
Sebastian Oberhoff
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Collapse of the density operator

I am a bit confused by the collapse of the density operator. Consider a system described by the density operator $$ \hat{\rho}=\sum_{m}P_{m}|\psi_{m}\rangle\langle\psi_{m}| $$ and a measurement of the…
Adrien Amour
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Modeling energy relaxation effects with density matrix formalism

I know there are measures that can be taken to mitigate the effects of dephasing (I'm referring here to Dynamic Decoupling and the other ideas it led to). I find it surprising that there is no equivalent procedure to mitigate the effects of energy…
psitae
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Can I obtain the pure state corresponding to a density matrix from its main diagonal?

Suppose we have a bipartite pure state as follows: $$|\psi\rangle=a_1|00\rangle+a_2|01\rangle+a_3|10\rangle+a_4|11\rangle\,.$$ Then, the density matrix is as follows: $$|\psi\rangle\langle\psi|=\left( \begin{array}{cccc} a_1^2 & a_1 a_2 & a_1 a_3 &…
reza
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On the probability of agreeing with different density matrices?

Let's say I have a density matrix and I (person $1$) suspect it to be of the form: $$ \rho_1 = p_1 |\psi \rangle \langle \psi | + p_2 |\phi \rangle \langle \phi |$$ $|\psi \rangle$ and $| \phi \rangle$ are orthogonal wavefunctions and $p_i$ are the…
More Anonymous
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What is an "x-type density matrix"?

i want to know what is a x-type density matrix structure? i want to know the general case of it. is this something like this? can one of matrix elements be 0? unfortunately there is no info about it in google. also i want know under what conditions…
reza
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What does it mean geometrically (in terms of vectors in the Bloch sphere) if the commutator of two density matrices $ρ_1$ and $ρ_2$ vanishes?

When the commutator of two operators vanishes then we can measure one without affecting the other. I'm not sure how this translates in the case of density matrices. If the density matrices are representing pure states then the density matrices would…
user12101
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Does partial tracing a system with three shared Bell states give the identity?

Suppose I share three Bell states among two participants Alice and Bob and Charlie in the following manner: $$ |\psi\rangle=\left(\dfrac{|0\rangle_1|0\rangle_2+ |1\rangle_1|1\rangle_2}{\sqrt{2}}\right)\left(\dfrac{|0\rangle_3|0\rangle_4+…
Upstart
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Purification applied to indistinguishability

In Zhandry's compressed oracle paper, one can read the following: Next, we note that the oracle $h$ being chosen at random is equivalent (from the adversary’s point of view) to $h$ being in uniform superposition $\sum_h|h\rangle$. Indeed, the…
Tristan Nemoz
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What is the largest absolute value attainable by an off-diagonal real or complex component of a $4 \times 4$ density matrix?

To repeat the titular question: "What is the largest absolute value attainable by an off-diagonal real or complex component of a $4 \times 4$ density matrix?"
Paul B. Slater
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Can we compute a full density operator $\rho_{AB}$ from its reduced density operators $\rho_A$ and $\rho_B$?

Given density operator of a composite system, say $\rho_{AB}$, we can always calculate reduced density operators of individual system i.e. $\rho_{A}=Tr_{B}(\rho_{AB})$ and $\rho_{B}=Tr_{A}(\rho_{AB})$. Can we calculate density matrix of a composite…
Omkar
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About production and disagreements between density matrices

So let's say there are $2$ experimentalists who have density matrix systems $A$ and $B$. They both agree that for the experiment they need identical density matrices $\rho_A = \rho_B$ which is a mixed state. My question is how do they agree upon…
More Anonymous
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Why can't the purity of a single qubit be less than $1/2$?

The density matrix of a single qubit system can be defined as, $$ \rho= \frac{1}{2}(\hat I+ \vec r.\hat{\vec \sigma}) $$ From here we can derive, $$ Tr(\rho^2)= \frac{1}{2}(1+r^2) $$ Since $ 0\leq r^2\leq1$, we have $$ \frac{1}{2}\leq…
Syed Emad Uddin
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How to combine/calculate for interference using density matrices?

Let's assume following two density matrices are corresponding to the A and B in the Stern-Gerlach apparatus bellow (I know Stern-Gerlach is a more of a physics experiment but I think it can equally be considered a quantum computing…
al pal
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